scientific article Mario Ljubičić (Amenoum)108. brigade ZNG 43, 35252 Sibinj, Croatia (amenoum.org)mljubicic99{EAT}gmail.com relativity, theory of everything, toe, nature, mechanics 2022 https://doi.org/10.5281/zenodo.4743398 /authors/Amenoum.html#credits
As of 2023.06.06 this paper is also available as a book, however, it is at this point, outdated.

Complete Relativity
Nature of observables

Abstract


A complete relativity in all phenomena, with relative scale invariance in physical laws, is postulated and discussed.

Postulates are followed with definitions of new terms which may be used in the current and follow-up papers written in the context of the theory. In order to conform to this physics, a redefinition and generalization of some terms and factors already in use have also been presented. This is followed by hypotheses on nature and mechanics of natural phenomena, based on the postulates of the theory, along with suggestions on the formulation of scale invariant physics. In conclusion, the theory suggests that everything must be completely relative in order to exist and everything must evolve in order to conserve this relativity.
Introduction A theory of everything should provide a framework which can be used to qualitatively describe all phenomena, without exceptions - special cases. Complete relativity with incorporated invariance to scale has such power, opening a path to profound insights into fundamental mechanics of natural phenomena.
There's nothing abstract about physical reality. Therefore, the best approach to understand nature is to combine and balance the power of mathematical language with experience and observation on all scales of energy and in the process approach problems from different perspectives, rather than limit interpretation to that of a mathematician, physicist or a biologist. Increasing complexity of mathematical language, for example, might make equations more elegant but beyond certain point it becomes harder to understand their correlation with physical processes, as elegance is neither abstract nor absolute in reality. Specialization, combined with religion (eg. belief in absolute elegance), will create illusion. Illusion of understanding and illusion of knowledge. Here, the aim is simply to understand nature as much as possible. The theory is the result of research, experience, observation, computation and logic that followed and confirmed strong intuition suggesting that overly non-intuitive, abstract and absolute reality is just an interpretation chosen, consciously or unconsciously, by a biased observer and it cannot be absolutely correct. In this, and follow-up papers, I provide foundations, details and evidence for the theory.
While complete understanding of the theory will require deeper focus and understanding of equations, the essentials and foundations of the theory should be understandable to any inquisitive mind. It should be noted that even I find myself scratching my head at times when revisiting works such as this one, mainly because at the time of writing I was in a very different state of mind. Therefore, a reader should not be discouraged if some information seem confusing, out of place or hard to grasp, it may be my fault - I wrote this primarily for my self as I was trying to understand everything and, although I did have it in mind during rewrites, presentation to the world was always just an option to consider. I am deeply dissatisfied with this world and perhaps my work doesn't belong here just as I feel I do not. However, as such I'm unlikely alone, so here it is, a discovery any non-biased mind trying to understand nature should find valuable. I do update my works in cycles, in the process resolving issues and adding details. Thus, any inconsistencies and fuzzy paragraphs should be converging to zero over time. At this point (December 2023), I feel the peak of updates has passed and the paper has matured into a work of considerable quality, and understandable to wider public.
Postulates revised.

Postulates


Here are the postulates of Complete Relativity (CR). They are all entangled and one may stem from the other, but not always in apparent way.
Small update in Everything is relative postulate. Added Finite energy chapter in graviton definition.

Everything is relative = everything is variable

$\displaystyle \Delta E <> 0$

No system can be completely isolated at all scales of energy. Everything existing must be absorbing and radiating energy at some scale at any time, but never in such proportions enabling non-zero possibility for absolute invariance of that phenomenon in time/space. Maintenance of relative constancy requires energy.

$\displaystyle \Delta E \neq \infty$

There is no single, absolute and infinite universe (Universe). For any observer, there exists a finite number of observable universes with mutually entangled characteristics, exchanging energy between each other.
One could argue that the sum of all universes is infinite and that sum is a single absolute entity. However, such Universe is absolutely unobservable. In CR, all existence has to be relative and thus observable at some scales, unobservable at other scales. Infinities and zeros as absolute values are mathematical abstractions - in reality they must be relative, as any other value. This implies relatively simultaneous existence of energy at different scales of space/time.
Any physical entity having absolute properties would have to be absolutely isolated in order for these properties to remain constant. With no ability to change (exchange energy) such absolutely elementary entities would be unobservable. Thus, relativity is an intrinsic property of reality.
Any distinct form of energy may be considered as an universe, however, in the framework of CR, universe will generally represent a particular scale of energy. These are discrete (stable) vertical energy levels for relatively elementary particles (called gravitons in CR). Any form of energy thus belongs to a universe of the scale of largest graviton(s) coupled to (or, highly entangled with) the system. Gravitons, however, can be [relatively] naked or uncoupled. Energies of the same scale may be considered as instances of the same universe, but, generally these should be considered as horizontally parallel universes as no two instances are absolutely equivalent at any time (physical constants are relative, oscillate and will be different between the instances, even if these differences may not be generally resolvable).
As transfer and transformation of energy require capacity for energy storage, structural quanta of any medium must have real size. Since existence requires continuous exchange of energy, any relative constants (energies) must be oscillations in some reference frames (higher resolution). None of these oscillations can be absolutely stable - even the oscillation itself must change relative to something. Thus, each form of existence (energy) will generally evolve, either progressively (toward higher energy levels) or regressively (toward lower energy levels). Evolution of energy generally includes oscillations and fluctuations but the periods involved may be too small or too large to be detected (or detectable) from some reference frames. Since energy cannot occupy space of absolute 0 size, reality requires three dimensions, although, due to inherent limitations in observability (and other reasons), energies (gravitons) can be approximated as point energies (particles). However, inflation (change of a vertical energy level) of the particle may make that interpretation inappropriate from the same reference frame. In most intuitive interpretations universes should not have more than 3 spatial dimensions (there is no space for them!), however, due to various scales of energy, space can and will be effectively divided into subspaces which may be relatively isolated but entangled with other scales. In that case, multidimensional manifolds with more than 3 dimensions may be used to describe reality. But one should be careful not to declare such entanglements (couplings) intrinsic and absolutely constant properties of reality - the strength of any entanglement must be variable in completely relative reality. In CR, the scale of a universe generally represents a discrete vertical energy level, analogous to horizontal energy levels in Quantum Mechanics (QM). Relative to difference in scale between observer energy and energy of observables, phenomena may be interpreted as physical (real) or mental (imaginary, or hallucinated) components of reality, however, every mental phenomenon must have a physical interpretation at some scale, and vice versa. Due to required evolution, energy in a universe is constantly transferred and transformed. Due to finite speed of transfer and transformation, these changes will be continuous, however, due to finite observable resolution of space/time, on some scale, changes may be interpreted as discrete. Regardless of interpretation, since adjacent states of reality are correlated but generally different, it is useful to introduce an additional dimension (time) to describe its evolution. Speed of transformation of energy may then be its speed in time, while speed of transfer its speed in space.
Note that speed of transformation is proportional to speed of transfer of energy at some scale. Therefore, time has a physical interpretation at some scale - ageing of phenomena is strongly correlated with transfer of quanta of energy at some scale, and these quanta may be interpreted as carriers of change or carriers of time. Note also that transformation can occur at different scales, hence, multiple time dimensions exist with different speeds of information (energy) transfer (generally inversely proportional to scale). It seems that 4-dimensional manifolds (at least) should be used for any scale of energy, however, relatively scale invariant framework can be constructed in which, either units will depend on scale (scalable metric) or dimensional constants will be scale dependent.
Relativity of everything indeed has the power to explain everything. Consider relativity in causality. In General Relativity (GR), it is always the clumping of matter (energy) that bends space, however, if causality is relative - sometimes it is bent space that should cause clumping of matter. Of course, one can insist that space is abstract and attribute the energy to exotic matter (ie. dark matter) [bending abstract space] to conserve causality, but is that the proper interpretation if one strives for deeper understanding of reality (and, especially, if this exotic matter cannot be resolved)? Additionally, causality has been found to be violated at other scales (universes).
I argue that causality is a special case of synchronization between correlated entities and can be violated on any scale. This is required by CR.
Proper solution in complete relativity is general correlation of past and future states which may be locally absolutized to causality (generally, thus, any intuitive concept is only locally intuitive and any illusion may be localized into intuition).
Note that distance between past and future is relative. And distance between phenomena is never absolute 0. Every interaction is a relative interaction and is the manifestation of synchronization - correlation in space and/or time. Causality is simply biased (polarized) interpretation of synchronicity at particular scale. All interactions or forces in nature depend on distance and all involve correlation. This suggests that distance should be generalized to distance in correlation. To conserve relativity (existence), forces cannot be exclusively attractive or repulsive and strength of force will sometimes be proportional, sometimes inversely proportional to distance. Note also that non-existence of absolute 0 distances together with non-existence of absolute point sources of energy (field source, or maximum, is not at the centre rather at a non-zero distance from it), fixes a common issue in physics - appearance of infinities, usually discarded in an arbitrary way using a technique called renormalization (which often probably could be translated as, more or less educated, guesswork).
Update in Everything is relative postulate.
Note that exotic matter hypothesis (at least by current interpretations) simply doesn't match observations - eg. cold dark matter halos within galaxies should slow down the rotation of galactic bars but the expected slowdown is not there. There are other problems too. These can all be solved through decoupling of space and matter, allowing different densities of space within the galaxy. Equivalent exotic matter here may generally be hot but transforming to cold with coupling, not absolutely free-streaming, rather orbiting about the galactic centre as static particles [forming galactic space].

Everything is exchangeable

Absolute relativity in space introduces problems such as one in relativity of containment. Consider two spheres different in scale and located (centred) at [relatively] the same point in space - how is it possible that a reference frame exists in which the bigger sphere is contained within a smaller one (non-dimensional rationality is relative)? Conservation of relativity thus clashes with the conservation of rationality (intuition). Seemingly, either non-dimensional rationality is relative or one must be sacrificed for the other. Here, finite speed of information transfer enables an elegant resolution - conservation of both by exchanging relativity in space for rationality in time (subspace). If two spheres oscillate in time between two scales and one does not discriminate between space and time, both quantities are conserved (rationality in space, relativity in time). Thus, on absolute scale everything is conserved, but relatively even relativity can be sacrificed.
Multiple interpretations and multiple solutions are common in nature. This problem is no exception. Suppose that everything exists [relatively] simultaneously on different scales - a bigger sphere can then be relatively contained within a smaller one if the smaller one has its identical copy on some larger scale. Note that, if everything must be relative, location and scale of existence must be too, therefore, everything should exist on different scales. This explains self-similarity of universes and suggests that planetary systems such as the Solar System are likely not only similar to atoms (certainly not by coincidence) - they might correspond to specific atoms in relatively equivalent (properly scaled) conditions (pressure/temperature). From some reference frames this may be interpreted as a change in discrete vertical energy level - they have been inflated from standard atoms.
Note that, since existence is relative, existence of containment must be relative, so there also must exist a reference frame in which one cannot tell which sphere is contained within the other. When integrated over time, such state may be interpreted as superposition or fusion of different states (spheres), while its derivative in space is an entirely new sphere (a chimera of multiple states).
Unless one accepts the notion of multi-scale existence, it might seem that relativity of containment is generally not conserved, even in time. Consider the example of a chicken in an egg - there is no apparent oscillation, chicken may be growing inside the egg and will eventually get bigger than the egg but the egg is not getting smaller and is at no point inside the chicken. However, another kind of relativity can solve the problem - the egg was once inside the adult chicken. This means there must exist a reference frame relative to which there is no distinction between the two chickens (relativity of identity). Such reference frame does exist and is enabled by the finite resolution (scale) of information carrier particles. Effectively, both the chicken and the egg are oscillating over time. With absolute containment nothing would be able (required) to grow or decay - neither chicken nor any other universe, with relative containment everything must grow or decay (or oscillate between the two). Complete relativity and its conservation in reality is what makes everything possible.
Apparently, both GR and QM allow [or are at least partially based on] the existence of an absolute rest frame [correlated] with constant speed c, completely disallowing any faster means of information transfer on any scale.
Any absolute constant is an absolute reference frame. The more absolutism there is in the description of reality, the more illusionary it becomes. This description may be satisfactory for spatially and temporally limited observers, but even in such, at times evolution may introduce observable discrepancies which will require recalibration of supposed absolutism.
Assumptions like that make GR absolutely non-relative and in QM produce many non-intuitive phenomena in space which would otherwise be completely understandable. Even space in GR is non-intuitive in common interpretation - it has plastic geometry but no physical properties. If one does not discriminate between space and time, one could notice that space and time are often inverted in QM. In example, quantum entanglement between distant particles can be local in time even though it appears non-local in space.
Note that conservation of quantum entanglement requires relative isolation, or non-transformation, of energy. If the state of a particle doesn't change, its speed in time is 0. Therefore, distance between two entangled particles in time remains the same (relative 0) even if they are separated in space. Such particles obviously must share a time dimension, and in CR, that is a physical dimension on some scale. Strength of entanglement here is then proportional to correlation in time. However, there are no physical point particles in reality, therefore, distance in physical reality is not 1-dimensional, it's volumetric. Thus, correlating volumetric distance with entanglement, with increasing distance in space, the cross-section of time dimension between two particles is shrinking in the middle but the volume (volumetric distance) remains constant.
Wave/particle duality with a change of scale (collapse/inflation of entangled quanta) also becomes intuitive, and a reasonable explanation of quantum tunnelling. The scale of time entangled with the scale of standard atoms may generally be the scale of standard photons, however, it is not impossible for entangled scales of space and time to be of the same order of magnitude from some reference frames (eg. entanglement of a positron and electron). Note that speed in space is limited by the specific scale entanglement (it is now obvious that annihilation of matter and anti-matter must involve a change of scale) - due to relativity in density and pressure of space, speed limits will depend on [the scale of] particle energy (the experience of space, or sensitivity to particular energy quanta, is different for gravitons of different scale).
Energy of larger scale is, of course, generally composed of energy of smaller scale. Here, however, one must distinguish between living and dead bodies. If the collective of smaller scale energy is coupled to a graviton of larger scale the body is considered living and the speed limit for that body is different (generally smaller) than the speed limit for individual constituent particles. If the collective is not coupled to a large scale graviton, the body is dead and its speed limit is equal to the speed limit of individual constituent particles (this body is also generally less stable than the living body). Superluminal particles must exist at some smaller scale, however, as noted before, observers are always limited in resolution and may not be able to directly detect them. However, collapse of quantum entanglement (superposition of states) in one interpretation involves collapse and contraction of time dimensions between particles and speed of that contraction then inevitably becomes superluminal at some distance in space. This is then indirect observation of superluminal transfer of information, even though, in some contexts contraction of time could be interpreted as contraction of space and from that reference frame information may be at rest.
If space is real, there is no reason for intrinsic coupling of matter and space curvature, therefore a reference frame must exist where there is no such coupling - dark matter can then be interpreted as direct evidence for real space. It is intuitive for space to have relative density and pressure which can, as vacuum energy, attract particles that are sensitive to such density and pressure. And these particles may have their own space coupled with them. Reality thus becomes intuitive even on small scales - electron can rotate faster than c (although this can be interpreted as rotation of space, with constituent particles of electron matter or charge being at rest relative to that space), have a real radius and real orbits inside the atom. With atomic nucleus allowed to have its own rotating space the electrons do not emit energy when in a specific orbit, even in corpuscular form - they are at rest relative to that space. Relative electric permittivity (dielectric constant) and magnetic permeability of materials now make physical sense and can be correlated with properties of space of atomic nuclei [gravitons]. Current (absolute) vacuum electric permittivity and magnetic permeability would be no different - these are also properties of space.
One might argue that the existence of physical space has been disproved with experiments, however, that is not the case - various interpretations of aether have been disproved. While space in CR has some similarities with, what was originally called, aether, it is not the same phenomenon. One could consider the space in CR to have the same geometry as space in GR, however, with part of the energy of curvature in real density and pressure of space, instead of all energy being attributed to matter, making space nothing more than non-intuitive abstract geometry (completely and absolutely flat with absence of matter). There are other differences though and GR requires modifications to become completely relative even if energy of space is attributed to exotic matter (eg. implementation of scale-dependent constants or scale-dependent metric).
If space has energy, then energy between matter and space (or, generally, energy between one scale and the other) can be exchanged. The mechanism for this exchange is generally annihilation of energies. Annihilation, in general, may be interpreted as vertical migration (inflation or deflation) of particular existence from one scale to the other. Note that inflation and deflation of energy can be accomplished through exchange of components of [angular] momenta. In the transition between energy levels, such exchanges should be common. Note also that nature of energy may not be preserved between adjacent scales, eg. gravitational potential may be exchanged for electro-magnetic and vice versa.

Everything has an angular momentum = momentum-energy equivalence

All energy can be correlated with intrinsic angular momenta of gravitons or quanta of space at some scale. Relativity in elementariness implies that any angular momentum is composed of (more precisely, coupled with) spin momenta of smaller scale. Due to various scales of existence and intrinsic rotation of gravitons, everything existing has an angular momentum in some reference frames.
Note that this could be stated differently - a reference frame must exist in which an form of energy (observable) has angular momentum. This then implies that the observable universe is rotating, even though the centre of that rotation may be outside of it.
Capacitance of space allows transfer of momentum, but also its conservation. Any mass (energy) at relative rest is a conserved momentum in form of local spin momenta. The rest energy is thus locally conserved kinetic energy and a reference frame must exist relative to which the energy is in motion. Individual momenta may entangle to form larger structures, and with enough energy, fuse to form larger momenta. Since momenta are quantized not every momentum is stable, and even the stable ones are only relatively stable with a difference in decay rates. Obviously, rest mass is relative and will not be absolutely equal even between individual particles of the same species.

Everything is entangled on some scale = all correlation is physical on some scale

All physically possible entities exist and are physically connected (entangled) on some scale (everything exists on various scales). In absolute reality this may imply everything was initially condensed into a singularity, but in relative reality this may be interpreted simply as natural manifestation of correlation, a consequence of required relativity (eg. of abstractness). However, condensation into relative singularities is not impossible, will exist and will affect entanglements. The strength of entanglement between two entities depends on entangled energy or distance in correlation:

$\displaystyle \propto {1 \over r^n} \propto {\Delta E \over E}$

where E is the total energy of entangled entity, ΔE is entangled energy, while r is distance in correlation (which will generally reduce to distance in space or time). Due to inherent limitations of observers, some entanglements may be effectively impossible to break, while other may be impossible to observe.
Note that entanglement can be effectively invariant to distance in space if entanglement is physically manifested in time and [volumetric] distance in time (which, in some contexts, may be interpreted as distance in evolution) remains unchanged (eg. if the observer cannot differentiate between entangled photons, distance in time is effectively 0 and so the information transfer, occurring with changes in entanglement, will effectively be infinitely fast). Also note that the strength of entanglement is relative and can be asymmetric (E may be different between entangled bodies, as well as ΔE). Entanglement strength is never absolute zero, but it is variable and non-resolvable amounts may be interpreted as relative zero amounts.
Strong entanglement is established when it becomes physically impossible for an observer to disturb the proportionality of ΔE and E. This occurs when applied energy is distributed on both, particles and the time (subspace) dimension connecting (entangling) them. At some point, however, applied energy may produce (inflate) new pairs of particles. Note that strong entanglement is relative to an observer (scale of energy) and can be broken by a less limited one. Changes in the strength of entanglement with distance (derivatives of entangled potential) can be interpreted as forces acting on bodies. The interpretation, however, is relative itself, can be more or less direct - eg. forces acting directly between bodies, or forces mediated by energy carriers of smaller scale (eg. quanta of space).

Everything is intrinsically polarized

Since energy requires spin which can have different orientations, it is intrinsically polarized (although the amount of polarization and its orientation are relative). Any apparently neutral system is thus a configuration of locally balanced polarized systems and must stem from homogeneous polarity distribution, polarity oscillation or confinement. High frequency oscillations may be interpreted as superposition of adjacent states in some reference frames, but in reality the period of oscillation is never absolute 0.

Physical laws are relatively scale invariant

In nature, distance is quantized, but the size of quanta is not constant. Energy generally oscillates between stable discrete energy levels. These energy levels can be horizontal (as described by QM) or vertical. Horizontal energy levels differ in the amount of energy but generally not in the order of magnitude, vertical levels generally differ by multiple orders of magnitude. Although universes at different scales may be in different equilibrium states, applying energy, state on one scale can be made locally relatively equivalent to a state on another scale.
Here, state generally refers to scale relative pressure (or temperature) and density, which generally differ between vertical energy levels. Temperature and density on standard scale are proportional to kinetic energy and density of standard atoms, respectively, on a higher vertical energy level this may be kinetic energy and density of planetary systems, on a lower energy level energy and density of photons.
Universes are self-similar, however, the values of constants and/or units of metric should differ between scales of gravitons. Physical laws of nature are thus relatively scale invariant, with stable scales appearing at discrete points between intervals of generally exponential progression. Elementary particles are strongly relative to reference scale. From a smaller scale they will evidently be composite and differ from each other, while from a larger scale they may even be unobservable (non-existent) individually.
Added postulate Hidden variables always exist.

Hidden variables always exist

With no absolutely elementary phenomena and with inherent (but not absolutely constant!) limits in observation, hidden variables must exist. Therefore, non-intuitive reality suggested by QM must be taken relatively. As stated already, treatment of all constants as relative constants can make QM much more intuitive, but it does not end there.
It should be noted that intuition too must be relative. If common intuition (eg. one involving hidden variables) cannot be observed, it is valid to conceptualize non-intuitive reality (and declare this non-intuition as natural or intuitive from some reference frame), however, one cannot claim such reality is absolute - there are always possibilities for different interpretations.
One other concept problematic for common intuition is the concept of spinors, or generally, algebra not correlated with geometry, or, not correlated with intuitive geometry. Sure, one can use two-dimensional planes (complex numbers) to represent phenomena [occurring in three-dimensional or four-dimensional space], and calculations within such frameworks may give consistent and good results matching the outcome of experiments, but that does not imply reality is absolutely two-dimensional or non-intuitive on a particular scale. Geometric and [commonly] intuitive interpretation in three dimensions is always possible even if it may require hidden variable[s]. And if complete relativity implies such variables must exist, and, if one strives for deeper understanding of reality, it would be, not only counter-intuitive, but counter-productive to discard them simply because mathematics without them works and/or is more elegant. Especially considering the real possibility, implied by CR, that one might be able to relatively observe the hidden variable on another scale of a particular state. Furthermore, mathematics working today may not work tomorrow - any hidden variable is variable after all.

On stability of equations

Equations are very useful and powerful constructs of a mathematical language. They can lead to new insights on details and plausibility of hypotheses, but can also be very deceiving. All dimensional constants are relative. Therefore, more constants the value of equation depends on, more unstable it is and its potential for illusion increases with distance from the scale the constants belong to. Dimensionless constants are generally more stable and may be preserved across adjacent scales, but even these should not be absolute. With everything being relative, a presumption of absoluteness will eventually lead to discrepancies in measurement and misinterpretation of reality.

Definitions


Here are the definitions of terms and expressions that may be used here and other papers and articles in CR context.
Note that these may be different than standard or common definitions in use. Some contain important details and additional hypotheses. Therefore, I would not recommend skipping them, even if the reader aims to consult them as needed.

nth order observer

In the context of quantization (measurement) of physical phenomena, observer is an entity performing the measurement. The order of the observer is a relative sum of the number of interactions in the act of measurement which affect its result. In example, 1st order observer may be the information carrier (radiation) particle, 2nd order observer is then the radiation detector, etc. Every observation is measurement, albeit not always a conscious one. Each measurement affects all interacting entities.

nth order interaction = nth order action and reaction

Consider the forces in Newton's law of gravitation:

$\displaystyle F = {d \over dt} p = {d \over dt} (m v) = m a = G {{M m} \over r^2}$

$\displaystyle F_1 = m_1 a_2 = m_1 {{m_2 G} \over r^2} = m_2 a_1 = m_2 {{m_1 G} \over r^2} = F_2$

Here, forces acting on bodies m1 and m2 are equal and have opposite direction, as expected for forces of action and reaction. Note that these are actions and reactions between bodies of standard matter at distance. In General Relativity there is no action and reaction between the two bodies directly, but effectively between continuous space (more precisely, geometry shaped by the energy of bodies) and a particular body (or energy, in general). And it is not an action and reaction at distance (distance between space and the body is assumed to be equal to absolute 0, only changes propagate at finite speed so the distance in time between changes in potential is not 0).
Note that in both cases action/reaction is instantaneous, so even in Newton's gravity distance between the sources is effectively 0 for whatever is mediating the force, only the 1st order sources of interaction differ. In Complete Relativity there are no absolute zero and infinite distances, thus every action is action at a distance which may only relatively be equal (set) to 0. If gravitational entanglement is understood as physical entanglement at some scale and it is never absolutely zero between two bodies one can understand why are the forces acting apparently instantaneously - particles mediating the force are constantly streaming between two bodies (forming subspace in space, which may be interpreted as another dimension, eg. time). So even though they are travelling at finite speed (which in GR would have to be the speed of light c if these particles are massless) the action appears instantaneous. Changes in gravity at sources, however, obviously propagate at the speed of carrier particles of that change. These particles are not absolutely massless, so they too are sources of force and are mutually entangled. At appropriate density they form a medium enabling wavelike transfer of information (energy). The wave can be considered massless relative to the medium (energy is stored in temporarily excited quanta of the medium), however, quanta of excitement are not massless and are also mutually entangled. Since wavelike behaviour of energy is synchronized excitation of quanta of smaller scale energy, a wave of energy can be considered as superposition in time (distance between entangled quanta in time is relative 0). Then, if momentum is disturbed, this superposition in time can, partially or fully (in case of strong entanglement), collapse to superposition in space as well (distance between entangled quanta in space also becomes equal to relative 0). In GR however, space is not quantized - no constituent quanta (gravity carrying particles) of spacetime are defined (geometry is not interpreted as physical).
The two bodies have an effect on space (and vice versa) but they also affect, albeit indirectly in GR, each other. In CR, with applied scale invariance, it is obvious that even the interaction between quanta of space and quanta of bodies must also be an action at a distance, albeit this distance is orders of magnitude shorter than distance between the bodies (without applied scale invariance on distance) and may be considered infinitesimal. The sources of force of action and reaction are thus relative to scale - measuring on larger scale it may be more appropriate to attribute the sources to bodies, while on lower scale the quanta of space may be interpreted as such. From a 3rd perspective one may consider the action between a force carrier particle in space (even if it is a bound static particle with potential energy) and a body as 1st order interaction, and the interaction between two bodies as the 2nd order interaction. One may also consider the 1st order interaction as relatively instantaneous, 2nd order occurring at some speed c, 3rd order at even some lower speed, etc. In any case, distance is quantized and there is no absolutely instantaneous and equal reaction to action (it requires quantum of distance equal to 0, or, equivalently, infinite speed of carrier particles).
Causality is a relative illusion, created by high synchronicity (correlation strength in space/time) of events.
The relativity of sources (force carriers) and distances has an important consequence on the law of action and reaction - it should be generalized:

$\displaystyle \int\limits_{t=0}^T \Bigl[\vec{F_1}(t) + \vec{F_2}(t)\Bigr] dt = 0 \tag{1.1}$

Instantaneous action and reaction is thus a special case of action and reaction impulses, where the period of energy oscillation T is compressed to an instant - a single elementary quantum of time (dt = T):

$\displaystyle \vec{F_1} + \vec{F_2} = 0$

Note the equivalence of distance in time and space of different scales - in the 1st order interaction (GR) distance in space is 0, while in the 2nd order interaction (Newton) distance in time is 0. Increase of distance in space between two bodies at 2nd order scale proportionally increases the distance in time at 1st order scale. Also note that, although not required, it is not forbidden for action and reaction to be simultaneous, nor it is forbidden for reaction to precede action, allowing relativity of cause and effect - something that is, with absolutely invariant c (speed of information transfer), forbidden in GR, but required in CR. In CR thus, causality is not absolutely fundamental nor intrinsic - it could be understood as a result of force, relatively emerging (or evolving) between correlated (entangled) phenomena decreasing distance in space and/or time. However, proper interpretation is that causality is simply localization of synchronization (synchronicity) of events in a polarized reference frame. Violation of [absolute] causality will exist on all scales of energy, but amount will differ between the scales. However, the amount has to oscillate too and will correlate with changes in polarization of space (ie. electro-magnetic).
The equation (1.1) is equivalent to momentum pulse (energy) reflection:

$\displaystyle \int\limits_{t=0}^T \Bigl[\vec{F_1}(t) + \vec{F_2}(t)\Bigr] dt = \int\limits_{t=0}^T \Bigl[{d\vec{p_1} \over dt} + {d\vec{p_2} \over dt}\Bigr] dt = \int\limits_{t=0}^T \Bigl[d\vec{p_1} + d\vec{p_2}\Bigr] = \vec{p_1} + \vec{p_2} = 0$

With T > dt > 0, action and reaction becomes a manifestation of energy oscillation. However, entanglement can be relatively broken (reduced to relatively infinitesimal strength) and reaction may be delayed, may not affect the source of action or might not even occur (if the action is locally interpreted as reaction). All bodies having rest mass possess capacitance and reaction to the source will eventually come, even if from another body, if that capacity is not in equilibrium state. The body producing the reaction will generally be relatively the same [scale] as the body acted upon, thus, allowing relativity, this can even reduce to instantaneous action and reaction in some reference frames. However, the reaction may be fragmented and carried by diverse force carriers following multiple different paths. Such nature of non-apparent oscillation stems from different scales of energy quanta enabling diversity and evolution of complex forms of energy, its conduction and transformation.
The original action may be the reaction to action from a 3rd body in which case the source returns to equilibrium after the action and the body may be interpreted as simply the energy conductor (momentum carrier). In reference frames where force of reaction is absent, the interaction may be more appropriately described through conservation of momentum:

$\displaystyle p_1 + p_2 = C$

Note also that, even if all energy must oscillate, this is never absolutely identical energy - never will absolutely the same body experience the reaction (zero in equations above is also a relative zero).

Superposition

Superposition is a relatively special state of a system which can be described as a combination (generally sum or average) of multiple possible states. In QM, superposition may generally represent a sum of probabilities for particular states of the wave-function. Physical interpretation of that superposition may vary. In CR, speed of information transfer, and therefore, speed limits, depend on the scale of quanta of energy. This, together with CR interpretation of entanglement, allows for physical interpretation of superposition to represent intermediate states of oscillation between discrete states. Superposition thus represents a real state, although that state may be unstable and observer, due to inherent limitations, may not be able to observe (resolve) it. Eg. on the scale of standard electrons, spin momenta is measured discrete (eg. up or down, never in between). This is probably because intermediate states are unstable and the measurement itself collapses the system into a discrete (stable) state.
Note that states in superposition are correlated (entangled). Note also, if observation involves changes in vertical energy levels (scales of energy) the system may conserve its [relative] value (superposition) in the transition and may remain in that state on the new scale. This is a consequence of effective time dilation and exchange of nature of potential between scales - unstable (or forbidden) states on one scale may be physically stable on another scale. However, even in that case, some states (values) will generally have larger probabilities than other.

Universe (U)

Commonly, Universe is understood as simply the sum of absolutely everything that exists, had ever existed and will ever exist. Thus, that definition refers to an absolute universe (Universe) - unobservable as a whole. In CR, nothing is absolute, thus, existence of multiple universes is implied. Any universe is a relative, finite and observable phenomenon, and may represent any distinct form of energy. In physics, however, a different universe should either obey different physical laws, conform to different metric and/or physical constants. In the context of CR, thus, a universe, by default, refers to a particular scale of energy. These scales are interpreted as discrete vertical energy levels and will correspond to energy magnitudes of elementary (or stable) particles on that level. These universes are correlated and energy on one scale may represent past or future state, or a special state, of the correlated energy on the other scale.
Note that, here, difference between vertical energy levels is generally such that physical constants differ significantly in value. The equations for determination of these levels are provided later. For example, one vertical energy level represents the scale of standard atoms, the other represents the scale of planetary systems. Note also that, even though these levels are considered discrete, the values of physical constants anywhere still should oscillate and may even differ horizontally (between systems of similar scale), however, such differences are probably generally negligible (although may be detectable).

Charge (c) and scale (n.m) of a universe

Universe will typically refer to a scale. If it refers to a specific particle or a system of particles, charge may also be specified. There are two equivalent notations:

$cU_{n.m} = cU(n.m)$

n = vertical energy level (scale) of the universe (0 = reference universe)
m = scale of the (horizontal) sub-universe
c ∈ {-, +}
n ∈ ℤ
m ∈ ℤ

In CR, space is relative and generally associated with a particular graviton (which, in CR, represents an evolvable particle, generally a superposition of sources of gravitational and electro-magnetic potential). I hypothesize that specific gravitons of one discrete scale (vertical energy level) form the space of a graviton of a larger discrete scale. The n scales are then generally such that U-1 scaled energy quanta (gravitons) form the space (medium) of U1 gravitons, while U-2 energy forms the space (medium) of U0, etc. In addition to space, gravitons may have associated bodies of mass of another scale, eg. U1 gravitons generally couple to bodies of mass (particles) of U0 scale. However, this coupling is not intrinsic and gravitons not coupled to a body may be interpreted as naked gravitons. If m is specified, the Un.m denotes the sub-universe of scale m, larger than n but smaller than n+1. If specified, charge c denotes the polarization, usually electric (two possible states of polarization). In this and my other works, U0 scale will generally represent the scale of standard particles such as standard protons and electrons, U1 then represents the scale of stars and planets.

Standard particle

Standard particle (eg. standard electron) refers to a particle as defined by the standard model in physics.

Elementary particle

CR implies relativity in elementariness. All particles, including those conventionally considered to be elementary, must have structure, even if that structure may be unresolvable for the observer. However, the concept of elementariness can be useful. Both, standard protons and electrons, should then probably be considered as elementary as they represent the smallest particles of practical use on that scale. Even on large scales, relative equivalents of these may be considered elementary, even though their structure may be highly resolvable by the observer.

Existence

Distinct forms of existence are distinct forms of energy. Existence requires energy. All discrete quanta of energy are produced (inflated or deflated) with changes in momenta. Any form of energy contains spin momenta at some scale and, in CR, even as a whole must have orbital momenta from some reference frames. Angular momentum (commonly denoted by L) is intrinsic to universes. For elementary particles (on any scale) the momentum is thus commonly circular or can be approximated, or averaged, as such. In that case, it is equal to:

$L = m v r$

where m, v and r are particle mass, velocity and orbital radius, respectively. For a system of n entities, the momentum of the system is the sum of individual momenta (which, generally, should be interpreted as a vector sum):

$L = \displaystyle\sum_{i=1}^n L_i$

General oscillation

With no absolute constants, everything must oscillate, even oscillation itself. Change of a variable in dimension xi may thus generally be described with the appliance of the following operator:

$\displaystyle {d \over dx_i} = a_1 f\bigl(\omega_1 \left(x_i + {\phi}_1\right)\bigr) \Bigl[1 + a_2 f\bigl(\omega_2 \left(x_i + {\phi}_2\right)\bigr) \Bigl[1 + a_3 f\bigl(\omega_3 \left(x_i + {\phi}_3\right)\bigr) \Bigl[1 + ...\Bigr] \Bigr] \Bigr]$

f = oscillating function
aj = amplitude of jth order oscillation
ωj = frequency of jth order oscillation
φj = phase shift of jth order oscillation

where, generally, aj < 1 for j > 1. Multiple dimensions are generally entangled, so f may be f(xi, ..., xn).

Frequency of existence

Existence is relative and it depends on the scale of a reference frame (one cannot have the ability to measure energy at any scale possible), but may also oscillate between energy levels. Gravitons should commonly oscillate between energy levels. For a particular order of general oscillation and its period Tx, frequency of existence of a graviton is:

$\displaystyle f_x = {1 \over T_x} = {1 \over {\Delta T_1 + \Delta T_0}}$

where ΔT1 is the average lifetime on a larger scale and ΔT0 is the average lifetime on a smaller scale. Generally, ΔT0 may be << ΔT1, and Tx may be approximated with ΔT1. In CR, gravitons of particular scale can and regularly do couple to gravitons of smaller scale (which are then forming the body of the system). There is then a distinction between living and dead forms of energy. A living form of energy is any entangled collective of mass (energy) of particular scale coupled to a graviton of larger scale. Since it is also assumed that at time of decoupling (death) the large scale graviton inverts spin and scale which is usually followed by new coupling on the same or similar scale of the previous incarnation, frequency of existence becomes frequency of reincarnation of energy, which may be, in some reference frames interpreted as reincarnation of life.
Polarized humans tend to discriminate between living and non-living things based on convenience. I do not and I do not think nature generally does. I believe any collective of energies coupled to a graviton of larger scale is not only alive but conscious to certain degree - large scale graviton here being the carrier of that consciousness or at least required for its emergence. It is only the amount (or detection) of consciousness and its introversion/extroversion ratio that will depend on a reference frame. And if energies are oscillating between vertical energy levels (in the process, weakly or strongly evolving/transforming) the question of what evolved from what becomes relative (it must be relative in CR). It is then valid to say that atoms evolve from complex forms of life, just like vice versa is valid from conventional reference frames. Note that here, in case of progressive evolution and complex life of our scale, atoms represent planetary systems - even if, obviously, they are only relative equivalents to standard atoms in special states or at specific times. Here and in follow up papers, I hypothesize and provide evidence that planetary systems are vertically excited atoms. All this, however, does not imply complex life forms on Earth will evolve into celestial bodies - among other things, this would require enormous amounts of energy and that energy here is simply not available. Humans will thus reach a peak (some may have reached it already) and perhaps even start evolving regressively to the atoms of smaller scale. Obviously, these peaks are different for different species. Whales probably represent the maximum peak reachable on Earth. Oscillations and fluctuations are relative and will not be apparent in all reference frames. Sometimes, energy will be observed as a pulse or a relatively non-changing (weakly evolving) phenomenon. Oscillations can also be disturbed and fragmented. It is, however, not hard to observe energy in the form of a human being as a pulse of energy growing from conception to a maximum then decaying until death and dissolving after it. Note, that no form of energy grows from nothing or decays to nothing. Growth is synchronized with defragmentation or accumulation while decay is synchronized with fragmentation or dissipation of energy. As gravitons oscillate in energy they will also oscillate inter-species. The coupling of gravitons with human bodies is explored in more details in follow-up works (including even evidence for it). Universes are self-similar (which stems from complete relativity) and this is why the frequency of existence applies to what we perceive as particles from our perspective and to what we perceive as human beings as well.

Relativistic uncertainty

As all observation is physical on some scale, no measurement can be performed without affecting the subject of measurement. Measurements will also necessarily be limited in resolution and for all observers there will exist a threshold of possible precision (inherent uncertainty). Measuring complementary variables such as energy and time, or components of angular momentum, on smaller scales, precision in one will have to be sacrificed for precision of the other component.
This is commonly formulated as the Heisenberg uncertainty principle:

$\sigma_x \sigma_y \ge {1 \over 2} \hbar$

However, if is interpreted as an absolute constant, or, if dimensional units of components are not scalable, the interpretation is limited to a particular scale of space. Per CR postulates, there can be no absolute point particles, thus, volumetric position in reality is not limited to waves and large scale objects.
Relativistic uncertainty is:

$\sigma_x \sigma_y \ge {1 \over 2} {\hbar}_n$

${\hbar}_n > 0$

where n is relative to scale n.

$\displaystyle {\lim_{n \to -\infty} {\sigma_x \sigma_y}} = 0$,

In conventional quantum theory (QM) [virtual] particles are popping in and out of existence all the time, which is allowed by time-energy uncertainty. In CR, existence is relative and this is simply oscillation of energy between different scales. This is generally a consequence of exchange between angular momentum components. In example:

$\displaystyle \Delta E \Delta t \ge h $

should then be [roughly] interpreted as:

$\displaystyle \Delta(m v^2) \Delta t = \Delta (m v^2) \Delta({{2\pi r} \over v}) = \Delta(m v) \Delta s = \Delta p \Delta r \ge \hbar$

Exchange of angular velocity v for rest mass m may result in a jump to a higher vertical energy level - appearance of energy on a larger scale. If the rest mass on that particular scale was previously considered a relative 0, this may be interpreted as relative violation of energy conservation, allowed as long as the increase in energy (inflation of m) is inversely proportional to particle stability (Δt). Period of stability is thus the period of angular momentum, and in reality, energy is conserved.

Zero

Absolute zero value of any variable represents non-existence of phenomena in physical reality. Zeroes associated with existing observables should then be interpreted as relative zeroes. In example, if a form of energy behaves as a wave on one scale, its energy may be equalized with frequency, in which case it may be assigned zero mass, however that zero should be understood as relative to excited medium - at some scale there are particles with inertial momentum increased proportionally to that frequency. These entangled quantized excitements of the medium can get concentrated at times of coupling/absorption, at which point the condensate could be interpreted as a particle and may be more appropriate to use non-zero mass. Thus, the mass itself could be interpreted as an aggregate of frequencies (momenta) of smaller scale, but the wave or frequency could equally be interpreted as an aggregate of mass (inertial momenta) of smaller scale. Whether it applies to mass or frequency, the value of zero is relative.

Infinity

Absolute infinity has no physical interpretation. While absolute infinities are useful in mathematics, in physical reality, these should be interpreted as relative infinities. Consider the relativistic Lorentz factor applied to mass:

$\displaystyle m = {m_0 \over \sqrt{1 - {v^2 \over c^2}}}$

By the equation, at speed c, mass of the particle would have to be absolutely infinite, implying that absolutely infinite energy is required to accelerate the particle to c. However, in CR, the speed limit c is relative to [structure of] space and, even in GR the speed limit is equal to c only in case of flat space geometry. Adding energy to the particle will, at some large but finite value, start to significantly affect the structure of space and particle could, with asymmetry in density, even exceed the speed c.
Speed c is also considered to be the speed of massless particles in QM. However, standard massless particles will also slow significantly below c in strong gravitational potential (although local observer would measure no slowdown as units of distance are decreased proportionally).
Also, constituent quanta of space are of particular scale and not all scales of energy are equally sensitive to these (pressure/density of space is relative), thus, speed c can be exceeded by energies of extremely small scale too (although such energies may be unobservable for a particular observer).
Although momenta in a universe will be inevitably limited, in CR, c cannot be an absolute constant. Even if c is interpreted as proportional to the ratio of units of distance in space and time and these units scale with geometry (as in GR) conserving that ratio, the geometry itself must be relative.
Absolute infinity is an insurmountable problem for reality. This is why every observer (reference frame) must be limited. For any observer thus there exist limits to existence (observable energy) - maximum and minimum size of observable phenomena. As the limits are relative, they are also variable, but cannot ever become absolutely infinite (which is even mathematically obvious - for any number there is a bigger number).

Graviton = quantum of spin momentum = [closed] gravitational field tube = quantum of energy = soul

Graviton is a real or effective source of a general force field - a more or less polarized quantum of space at some scale. Real gravitons are sources of general force, while effective gravitons are induced by real gravitons and are carriers of the force through the general field.
Generally, real graviton may be considered as an elementary particle, while effective graviton as composed of real gravitons of smaller scale.
The force (curvature in some interpretations) is greatest in a real graviton and generally decreases exponentially with distance of effective gravitons from the real one. Generally, graviton in its ground state may be interpreted as a rotating torus-shaped region of space at some scale. The associated well of gravitational potential may be considered its private space, however, that privacy falls off with distance.
In CR, everything must have an angular momentum from some reference frames. This is a consequence of intrinsic rotation of space on all scales.
Its exact shape depends on electric charge and spin momentum (which may be quantized from some reference frames). Relativistic momenta may further distort the shape of a graviton. However, shape and distribution of mass of a graviton generally depends on its excitation state (quantum numbers) and how well it is localized. Travelling as a wave, its mutually entangled mass will be distributed over larger regions (and may be interpreted as wave-like excitation of existing static potential of space), with mass density maxima corresponding to the maxima of [the square of] its wave-function. Graviton is generally a composite of at least 3 components - 1 neutral and 2 charged momenta. Charge carrier particles are generally asymmetric in energy and may have significantly different momenta in polarized states.
Physics of a theory of everything cannot be reserved for particles and their interactions at specific scale. From certain reference frames, even living beings are particles, and vice versa. Distinction between living and non-living forms of energy is very relative and physics will necessarily merge with biology in a successful attempt to understand the universes (because nature is not reductionistic). In follow-up papers I hypothesize that real graviton is, considering its nature, also a quantum of consciousness and I find it appropriate to use the term "soul" as its synonym. As complex bodies evolve from simple particles (although what evolves from what is in CR, with relative causality, relative), the souls evolve as well. Thus, what is described here may be interpreted as a simple or elementary graviton, its complex form may be interpreted as a relative superposition and localization of smaller scale gravitons just like the complex bodies may be interpreted as relative superposition and localization of smaller scale components. Forces or interactions evolve as well, from elementary ones to complex ones. Thus, what is interpreted as simple gravitational or electro-magnetic force between two gravitons on elementary scale, may be more complex between complex gravitons. The standard nuclear strong force is an example of such more complex force. In case of life-forms on the scale of animals on Earth, complex forces/interactions are mental forces/interactions between the souls whose components may have billions of degrees of polarization (in these, associated spectrum of energy levels may be interpreted as continuous rather than discrete). Naturally, these mental interactions/forces are stronger between strongly entangled souls, which can be interpreted as shorter distance in some dimension of space (including time), just like gravity is stronger for spatially closer bodies.
Chapter Graviton: Physical interpretation revised. Chapter Gravitational well updated.

Physical interpretation

Assuming the scale of a graviton is Un, constituent quanta of space forming the associated gravitational well will be of scale Un-2. With an locally empty gravitational well, graviton is considered to be naked (as such, it may be interpreted as a dark matter particle). However, attracted particles of scale Un-1 will be coupling with quanta forming graviton's space (Un-2 scale) and such couplings will be considered as coupled mass or real mass forming the body of the graviton.
Note that these couplings will generally result in change of momenta for Un-2 particles - exchange of orbital momenta for spin momenta (which may generally be interpreted as mass inflation).
Graviton can be excited and exist on different vertical energy levels (scales), however, on some scales the neutral (gravitational) component may dominate, on others its nature may be dominantly electro-magnetic. While real gravitons induce gradients in vacuum density (or space curvature), space inside of a real graviton from an internal reference frame may be globally flat with extremely low density and temperature of [whatever is interpreted as] matter. However, high curvature should be present at the membrane, which then represents a source of extroverted gravity of a graviton. While temperature and density are both low globally within the graviton, high temperatures and densities are possible and do exist on smaller scales. The particles may be in condensed states and grouped into quantum vortices (galaxies). The ground shape of a graviton is generally a torus, with an intrinsic spin momentum. This spin momentum is relatively quantized with constituent smaller scale spin momenta, forming smaller scale sources of force (these are generally centres of quantum vortices, where most energy is concentrated inside graviton space). Thus, large scale spin momentum (of the graviton) is strongly correlated with small scale momenta. In a highly polarized graviton, structure may be highly ordered, with oppositely polarized inner components separated toward different sides of the membrane.
Shape of a graviton
Fig. \fig1: General shape of a graviton Shape of a graviton is shown in Fig. \fig1, where the surface of a torus represents its effective boundary.
As a discrete quantum of space, graviton must have an effective membrane. Note that it is relatively easy to maintain existing conditions inside the graviton, as accumulation of particles is extremely hard due to flat space and low-density of matter. Any particle having a momentum perpendicular to the graviton may be accelerated inside (in most cases, the trajectory of the particle may be simply bent about the graviton surface), but will be equally decelerated again, and will exit the graviton with the same momentum. Collisions will be hard even if existing and passing particles are of the same scale, but if existing particles are of smaller scale (discrete vertical energy levels differ in energy by multiple orders of magnitude), accumulation becomes almost impossible. In that case, graviton is relatively transparent (transparency is dependent on energy scale). Note that polarization will be generally shaping a graviton into a 2-dimensional ring, while neutralization is expanding it to a more spherical shape. To conserve volume, expansion will be decreasing the thickness of a torus, converging to a 2-dimensional sphere [surface]. Note also that conservation of that volume can also be interpreted as conservation of correlation between opposite sides of the membrane. If the symmetry of the membrane would increase, the volume would decrease. Recent analyses have shown that the shape of the local universe is consistent with that of a torus. Considering its characteristics, by the definition of a graviton here, the observable universe is likely a part of a [large scale] graviton. If distances between galaxies (large scale quantum vortices) are increasing, this graviton is increasing its internal flatness and must be changing shape.
How is gravitational energy of a graviton exchanged with electro-magnetic energy in the transition between energy levels? Different interpretations are possible, but this should involve changes in momenta. All components of graviton momenta are effectively exchangeable between vertical energy levels. Changes in vertical energy levels will probably generally involve annihilation of particles on some scale as well as such events involve fast inflation and deflation of momenta components. Since elementariness is relative, one can assume that the charge and spin magnetic momentum of an elementary charged particle stem from separation and difference in momenta between oppositely charged constituent particles. Since speed of information transfer is relative (in CR, it depends on scale), both orbital velocities of constituent charges and difference in velocities between constituent opposite charges may be converging to infinity with decreasing scale. And this velocity/difference can be annihilated into mass/radius.
Note that relativistic energy can have different interpretation between scales. Eg. interpretation of velocity may be effectively scale variant. On one scale, velocity, or difference in velocity, generates mass (mass is relativistic), on the other it generates charge (charge is relativistic). High orbital velocity of standard quarks is considered to be the main contributor to rest masses of standard protons. High orbital velocity of constituent particles of quarks and electrons may be the main contributor to their charges and spin magnetic momenta.
Charged gravitons, in addition to gravitational field lines, possess both electric and magnetic field lines. What are magnetic field lines? In CR, magnetic field lines are relative lines, in reality they are tubes, or toruses (which may be deformed). These tubes can be interpreted as induced polarized effective gravitons perpendicular to the primary graviton, or polarized dimensions of space (polarized subspaces) for a charged graviton. They can also be interpreted as tubes of entanglement between charged gravitons. If the primary graviton is of Un-1 scale, space in the associated magnetic field lines is formed by particles of Un-3 scale. More complex forces with multiple degrees and species of polarization can be correlated with mutually entangled different species of potential, or fields of potential, with forces mediated through different species of dimensions of space (or entanglement). All of this is evolvable and nature of force can change over time. More complex forms should be more plastic but no law of nature is an absolute law.

Effects of graviton interaction and oscillation

When condensed, the constituent (uncoupled) quanta of one graviton will weakly interact with constituent quanta of another graviton. However, in case of stronger entanglement the two may form superposition in space and probability for interaction might increase. Superposition is, of course, relative, and if gravitons are of different scale, orbital radii of constituent quanta will be different. What happens to gravity of a graviton confined within another graviton, assuming both are of similar energy (of the same or similar magnitude)? It's possible that extroverted gravity simply becomes the sum of gravity of all gravitational sources, however, confinement of inner gravity may be possible as well. In the extreme case of confinement, the outer real graviton may be effectively shielding the gravity of the inner real graviton (in other words, the inner graviton acts exclusively on the outer graviton). This may be interpreted as confinement of entanglement, where induced effective gravitons by the inner graviton have decreased range and are confined to space between the two real gravitons. Confinement must be relative, however, and some inner gravity should always leak, with highest probability at the poles. The same effect can be produced even with a single oscillating graviton, assuming field information transfer is slower than graviton oscillation. This then suggests that gravity may be generally stronger at the poles of spherical bodies, even in perfectly spherical (non-rotating) ones (if such could exist). However, if the general form of a graviton is torus-like, as hypothesized, openings on the poles may generally have non-zero radii and lower gravity than otherwise expected on the poles, may be more likely. This should be even more pronounced in polarized gravitons where converging magnetic field lines concentrate particles along the magnetic field lines between the poles. In my theories, I hypothesize that large scale gravitons (probably inflated from smaller scale) are commonly involved in the formation of stars and planetary bodies. The inflation (or initial over-inflation followed by deflation and stabilization at the new energy level) of a graviton and dark matter associated with it is relatively synchronized with the clumping of real mass (ordinary matter) and makes the process of formation much faster and possible even in cases of strongly diluted real mass (like in the Kuiper belt of the Solar System, for example). Mass in planetary bodies should then be differentiated not only vertically, but horizontally as well, with lower density at the poles and possibly even with tubes (tunnels) connecting poles of large scale gravitons, or different energy levels in case of a single oscillating graviton (although these tunnels in terrestrial bodies would have to be filled with fluids to ensure stability). Note that Earth's gravity is greater on the poles, but not as much as would be expected for either simple compression or removal of material. Density seems to be somewhat lower at the poles. Are there tunnels below? Long-lived tunnels, except near gravitons, seem unlikely due to increasing pressure with depth, however, fluid density should be increasing with depth as well. High polarization and angular momentum of the wall material can increase the stability of such tubes but this is not expected in terrestrial bodies. Long term stability could be ensured with appropriate density of energy levels and relatively frequent oscillation of large scale gravitons as this provides multiple density maxima. Lateral density gradient (with increasing density away from the pole) also decreases pressure on the tube and such gradients are likely for rotating bodies (note that Earth rotated much faster during formation). Otherwise, tunnels may be only periodically recreated (fluids remelt). I suspect that on bodies like Earth the fluids involved should be [salty] water and magma, with dominant fluid probably depending on the pole. Land should be depressed at the entrance where water is involved, however, it may be elevated on the pole where magma is involved. Interestingly, the subglacial topographic depression in Antarctica known as Wilkes land anomaly (elsewhere hypothesized 480 km wide impact crater, which would make it the largest impact crater on Earth) was directly antipodal to Siberian Traps (largest known volcanic event in the last 500 million years) during the Permian-Triassic boundary (Siberian Traps are considered to be the primary cause for the Permian-Triassic extinction, largest mass extinction on Earth). The crater hypothesis has its problems and it is questionable whether impacts alone can cause significant volcanism on the other side of the planet (although they can certainly cause earthquakes). However, the recreation of tunnels with graviton oscillation should create such phenomena at antipodal locations - depression on the side of water entrance/exit, bulges or traps at the side of magma expulsion (masking the depression). If Earth is modelled as a living being, different products on entrance and exit are expected. As tectonic plates move with time, the locations on the surface should move as well. I believe that all major mass extinctions are correlated with recreation of the tunnels. The Siberian Traps are already considered to be the result of a mantle plume which effectively is a temporary creation of a tunnel between the planet's core and surface through which magma flows upwards. Antipodal volcanism is common to large craters of the Moon and Mars and there are other examples of antipodal relationships on Earth involving large igneous provinces and hotspots (Yellowstone, for example, is antipodal to French Southern and Antarctic Lands). All of these may be correlated with oscillation of large scale gravitons and associated temporary recreation/reactivation of tunnels. In fact, deep mantle plumes may not be possible without it. In a follow-up paper I also hypothesize that both volcanism and impacts occur during major mass extinctions. In fact, energy level changes cannot be absolutely spontaneous and large impacts can be interpreted as relative triggers of energy level changes of large scale gravitons. If graviton is, at the time of impact, oriented in such way that its axis of rotation is aligned with the impact site, and this should be likely at least for impacts occurring near the poles (possibly nearer magnetic ones if these are present), then the impact can be correlated with antipodal volcanism. In that case, the seismic energy generated by the impact further stimulates the flow of fluids through the tunnels, increasing the effect on surface (the impact does create chimneys of stress connecting the impact source with the antipodal location). Generally, however, impact sites may not be aligned with the graviton axis and the magnitude of extinction then should be proportional to the alignment. The exceptional magnitude of Permian-Triassic extinction thus can be explained as the result of unusually high alignment.
Update in Acquisition of matter and Static particle.

Acquisition of matter = coupling with matter = acquisition of smaller scale energy quanta

A naked (uncoupled) Un graviton will effectively attract particles of Un-1 scale. There are now two possibilities on the effect of total gravity:
  1. with inflation and coupling of an Un.space constituent Un-2 graviton with Un-1 particle, one graviton is shielding the other, energy relatively equal to energy of Un-1 particle is confined and there is no increase in gravity of the well with acquisition of Un-1 matter,
  2. there is no shielding and total gravity of the well is increased with acquired matter.
Note that 1. possibility may be interpreted as one particle giving mass to the other. Regardless of the outcome, the interaction should affect the range of gravity of the system. Constituent gravitons of space of Un-1 gravitons are of Un-3 scale, thus, one range is being replaced with the other.
Note that each graviton has finite capacity for coupling - number of constituent quanta is not infinite. Note also that violation of energy conservation in case of shielding is relative - even though gravity may be unchanged (relatively) the total energy is conserved by compression (confinement) and will be released with decoupling.
Since real graviton represents a maximum of gravitational potential it will form a discontinuity in the system. Electro-magnetic nature of a graviton will concentrate polarized matter in the equatorial region, while neutral matter can start concentrating in the centre with collisions. Coupling of standard matter (eg. standard atoms) with the gravitational well of a large scale graviton is the coupling of static graviton neutrinos or static [dark] photons (constituent quanta of space of the large scale graviton) with this matter. However, for a large body (composite of atoms) in the gravitational well it is convenient to consider it coupled with the effective large scale graviton, rather than with individual small scale static particles. In that case, mass and velocity of the effective graviton are total mass and average velocity of constituent static gravitons, respectively, while the effective graviton forms the toroidal [large scale] quantum of space which the coupled standard matter is traversing in its orbit about the real graviton.
If the whole observable universe is a part of a large scale graviton, galaxies and planetary systems may be the result of inflation and coupling of its constituent quanta. One of my hypotheses is that at least one discontinuity (eg. between inner and outer core) of a planet represents the radius of a real graviton that has been inflated from the scale of a standard atom, or even a much smaller scale. For stars, I hypothesize multiple such gravitons in superposition. This is all further investigated in follow-up papers.
\ch_added

Rings revealing graviton presence

Rings of matter have been observed about space bodies of various size. In conventional theories, longer-lived rings are only possible when tidal forces are present which are preventing the material to coalesce into a single body. Rings of material beyond the Roche limit of a body are thus unexpected and difficult to explain. However, such rings have been observed, eg. about the trans-Neptunian body Quaoar. The presence of a naked large scale graviton can easily explain such rings. Since the average location of gravitons is generally not random, orbital resonance could hint at the presence of a large scale graviton (which may be interpreted as a ring of dark matter). The matter composing the ring is then not only orbiting the central body but the naked graviton too. If this graviton is 2-dimensional, spiral motion of constituent matter about the graviton is likely too (similar to the spiral motion present in Saturn's F ring). In conventional theories on gravity and planetary formation, it would take a significant amount of time for a ring to coalesce into a single body and any sudden changes are not expected. However, if the ring suddenly collapses into a single body, this would be a clear evidence for the presence of a large scale graviton collapsing (localizing) from an orbital to orbiting spin momentum.
It appears that evidence for this already exists.
This would also result in a transfer of energy from the ring (graviton) to the central body. If the orbital radius changes too then the process should also imply transfer of energy between different systems.
\ch_added

Supermassive evidence

Some celestial bodies have masses too large to be explained by conventional formation theories. In example, a massive planet orbiting a tiny star can be a big problem due to limited amount of dust in formation rings. This can be easily explained with massive large scale gravitons. If the dark matter mass (associated with the graviton) is on the order of total mass of the body, its real mass content (and thus required dust for formation) could be low.
Graviton mass in ice-worlds (Neptunian planets), gas giants and stars is probably at least 1 order of magnitude higher than coupled real mass. In case of terrestrial worlds, vice versa is probably true.
Another problem for conventional theories is the quick formation of large bodies, eg. supermassive black holes or galaxies in the early universe. Inflation and deflation (collapse) of gravitons should be a relatively fast process and this can then explain any sudden and fast accumulation or concentration of mass, like fast collapse of formation discs - in case of formation of planetary bodies, or early appearance of supermassive black holes (for which real mass content, compared to graviton mass, could be negligible).

Finite energy

Since there can be no absolute point sources of energy, maximum field strength of a graviton is at a non-zero distance from centre. Thus, equations producing infinities for field sources are simply not valid below a certain radius (radius of a graviton in this case). For distances greater than the graviton radius, graviton can be approximated as a point source of force, while below that radius force drops to relative zero - for any point inside, for an ideal non-rotating graviton (with a uniform mass distribution) and no other gravitons inside. Thus, the equation of force (approximation) is then, in example of gravity:

$\displaystyle F = \delta_{ij} {GMm \over {r^2}}$

$\displaystyle i = {{r - r_0} \over {\left| r - r_0 \right|}}, j = 1$

r0 = graviton radius
r = distance from graviton centre
δij = Kronecker delta

Obviously, if there are any sources of gravity inside and these are not balanced by forces outside, the graviton would collapse. To prevent this collapse, a repulsive force must exist - either fictional (provided by the graviton angular momentum) or real (in case of polarization). In reality, both polarization and angular momenta should be present to some degree. Note that, if graviton is in the form of a hollow sphere, the poles, due to lower momentum, still can collapse. This can be mitigated by the attractive force (or effective gluons) between the constituent quanta of a graviton. In reality, the graviton may be very rigid but not infinitely. Therefore, It will never be in the form of an absolutely perfect sphere, rather an ellipsoid - especially, when not naked. Near the graviton radius, point source approximation is not valid anymore and contributions of individual graviton quanta should be taken into account, as shown in Fig. \fig6.
Force of a graviton
Fig. \fig6: Force of a graviton With no absolute zero distances there are no absolutely infinite densities either and mechanisms will exist preventing absolute collapse. One of these, as mentioned already, can be rotation (angular momentum), which is probably one reason why it is intrinsic in fundamental sources of energy. Thus, in all sources of forces of attraction there must exist a production of effective repulsion, which will cancel attraction at some distance.
Added definition for Static particle.

Static particle

Particles forming space (effective gravitons) of a graviton of scale Un are particles of scale Un-2. These are entangled with the parent graviton and any changes in its momentum will be reflected in momenta of these constituent particles. The particles are orbiting the graviton and the energy density is generally decreasing exponentially with distance from the graviton. Orbital speed is roughly equal to the speed limit in space for particles of Un-1 scale. However, the particles will get bound (coupled) to Un-1 scale matter captured by the gravitational well, exchanging orbital velocity for spin (Un-1 scale) momentum. Due to their limited range and conversion of radial to angular momenta (where upon reaching the range they can form standing spherical waves) the constituent particles will hereby be referred to as static particles, generally, static gravitons, which may be generally decomposed into static graviton neutrinos - in case of neutral gravitational potential, and static photons or half-photons - in case of electro-magnetic potential. These particles may be interpreted as hot dark matter when uncoupled, however, with coupling, their momenta will be transforming to cold Keplerian momenta.

Graviton tube = wormhole = quantum of entanglement

Graviton tube is a physical manifestation of entanglement (correlation), space connecting two entangled gravitons. In one interpretation, the volume of that space (volumetric distance) is proportional to distance in correlation (inverse of strength of entanglement), however, the tube is relatively hollow and energy is mostly concentrated on the membrane. With no additional energy or disturbance of gravitons, volumetric distance will remain the same regardless of spatial separation. The tube can be considered as subspace or an relatively isolated dimension of space.
The tube may be considered as elementary quantum of continuous space, however, in reality it is a sum of constituent smaller tubes. The tube(s) may also be generally curved (entangled particles may not be connected by the shortest path possible in flat geometry). Consider magnetic field lines connecting opposite poles - if these are tubes of entanglement, they obviously do not follow shortest paths and may be compressed and expanded. Of course, these may be shortest paths possible considering conditions on field formation and one can model entanglement of poles with geometry where these paths are shortest.

Gluon

Gluon is a superposition of one or more pairs of gravitons.

Gluon tube

Gluon tube is space connecting two entangled gluons. It is a superposition of graviton tubes.
Gluon
Fig. \fig2: Gluon tube Fig. \fig2 shows the gluon tube, with induced cross-sectional capacitance due to spatial separation of gravitons G1 and G2.
Chapter Gravitational maximum updated.

Gravitational maximum = g-maximum = [relative] event horizon = primary soul

Gravitational maximum is the area of maximum gravitational potential in a gravitational well. This area may have different shapes, depending on the [limitations of] the observer, energy levels of gravitons and relativistic energies involved. In most practical cases this will be approximated as a ring, tube, spherical surface or even a point. Note that a single gravitational well may have multiple gravitational maxima at different radii (although one can argue that this is then not a single gravitational well, rather a superposition of gravitational wells - which I do consider to be the proper interpretation). Generally, gravitational maximum may be used as a synonym for a real graviton or a superposition of real gravitons. However, interpretation will depend on the context, as gravitational maxima can be decoupled from real gravitons, even if induction of maxima may generally be stimulated or correlated with inflation/deflation or oscillation of real gravitons. In example, inflation of a graviton from one scale to another will generally be correlated with relaxation of a maximum on the former scale and compression of field potential on the new scale. Speed of information transfer is finite (even if different between scales) so neither the relaxation nor compression can be absolutely instantaneous, especially if additional real mass is concentrated at the maxima. Maxima can thus exist independently of real gravitons, although these may be generally relatively short-lived unless periodically coupled with real gravitons.
Note that multiple gravitons may be in relative superposition, where they spin about the same central region but with different (spatially separated) mass radii. This is then also a superposition of gravitational wells, each having its own maximum. In these cases and in some contexts, gravitational maximum might represent a graviton with maximal mass (energy) of all the gravitons. In equilibrium this will generally be the outermost graviton as lower energy gravitons with larger radii are less stable and are likely to collapse (localize) the wave-like (or cloud-like) spin to orbital angular momentum (corpuscular orbit). Radius of a graviton will thus generally be proportional to its energy. In some reference frames (contexts), separation between gravitons may be negligible and gravitational maximum will then represent a superposition of gravitons and their masses. Note also that quantization is relative and for every graviton a reference frame exists in which that graviton is, not only a gravitational maximum, but relative superposition of gravitons of smaller scale.
Energy of a gravitational maximum is proportional to the capacity of the associated gravitational well for coupling with matter.
Note that capacity is scale relative. The capacity of a Un graviton for coupling with Un-1 mass may be full, but the capacity of Un-1 wells for Un-2 mass may be not. However, note that constituent quanta of space of a Un graviton are Un-2 particles, exactly the mass scale the constituent particles of Un-1 wells should couple with. Thus, the capacitances of different scale here are correlated (the coupling correlation is manifested as attractive force) and what is considered as a component of space in one reference frame may be interpreted as acquired matter in another.
The question is what happens to wells at full capacity and can they be over-capacitated? This is related to the problem of dark matter and changes in energy levels, and is discussed later.

Biological physics

The acquisition of matter by the naked particle (soul) can be interpreted as an act toward symbiosis of smaller scale and larger scale mass. The gravitational well of the maximum provides the environment and acts as a catalyst for evolution of matter (enabling fusion, chemical reactions, etc.) while the interaction also enables the soul to co-evolve with acquired matter (constituent particles of the soul are correlated with, and will mirror, acquired matter to some degree).

Gravitational well = spiritual well

A real graviton will induce effective gravitons (which are also static gravitons in equilibrium), forming a pressure/density gradient (or curvature) of space - a gravitational well. Density of energy is inversely proportional to distance, therefore, at full capacity the gradient of density will be proportional to the gradient of orbital angular velocities of coupled bodies. These are then Keplerian velocities. When matter (real mass) is coupled with [effective gravitons of] space and orbits at Keplerian velocity, it is at rest relative to that space and it shouldn't lose significant energy during orbit.
Gravitational well
Fig. \fig3: Gravitational well scheme Fig. \fig3 shows a cross-section of a gravitational well with a [gravitational] maximum at radius r. Density of graviton energy is represented by the concentration of circles, it is greatest at event horizon r. Graviton orbitals will generally have some finite eccentricity, which may be more exaggerated with coupling.
Note that for a hollow sphere of standard matter, gravity is cancelled at any point inside the sphere (Shell theorem). This is generally not the case for gravity inside a hollow sphere of a naked graviton for a couple of reasons: Additionally, the sphere of a naked graviton is only relatively hollow (it is devoid only of standard matter, but it is not devoid of smaller scale particles - forming space) - space is generally not flat below radius r, it is filled with effective gravitons relatively mirroring the gradient outside of the sphere.
Gradient of energy density in a naked gravitational well is a superposition of a gradient of mass (inversely proportional to range) of static effective gravitons and a gradient of transient effective gravitons. Transient effective gravitons are gravitons which are either collapsing from, or inflating to, their equilibrium orbit (equal to their range).

Induction of effective gravitons

Likely mechanism of creation of effective gravitons is inflation of real gravitons of smaller scale. The quanta of smaller scale are annihilated at the gravitational maximum, or relative event horizon (r on Fig. \fig3), resulting in inflation of two effective gravitons with opposite momenta, perpendicular to the event horizon orbital. Such inflation should generally be proportional to the relativistic energy of the real graviton, where the rate of inflation is proportional to the energy differential. At [relative] rest, there might not be sufficient energy for inflation and recycling of existing effective gravitons will dominate. Here, existing energy will be used to prevent inverse annihilation (deflation) of effective gravitons.
The mechanisms used to prevent annihilation may be interpreted as mechanisms of creation, or maintenance, of asymmetry (or distance in correlation) between inflated products. This can be the asymmetric exchange between gravitational and electro-magnetic potential of particles, even between them. Another possibility is that particles are allowed to annihilate, however, this results in disequilibrium (recoil), and the particles are inflated back for another cycle. Both solutions are possible, one may dominate during maintenance in equilibrium (relative rest), the other, during changes in energy of the real graviton itself (eg. at the time of its own inflation). The asymmetry of potential (carried by effective gravitons) allows for interesting solutions where different forces could dominate inside and outside of the relative event horizon. Of course, there will be leakage because the carrier particles themselves have their own wells of potential carried by effective gravitons of even smaller scale (containment of potential has to be relative). Note also, that real graviton can contain other real gravitons of the same vertical scale but at different horizontal energy levels and thus at different radii. This allows for greater asymmetry and more complex mechanisms for its creation and maintenance. Absorption of real mass can provide stability in the gravitational well but this additional energy also adds more complexity.
Small update in Black hole definition.

Black hole

Black hole is a region of space with escape velocity at the gravitational maximum greater than the speed of light (information transfer). For a standard black hole this is a standard speed of light.
Note that, in CR, this region does not have a singularity at the centre, it has a ring, or torus, of relative singularity at the gravitational maximum. Therefore, some material that wouldn't be able to escape at the equator can escape at the poles. However, even though energy can escape, its path will be more or less curved and it might be difficult to observe this from reference frames where the line of sight is aligned with the axis of rotation of the black hole.
More charged a graviton is, more two-dimensional it will be and the density of the gravitational field will be decreasing from equator to the pole. Thus, the gravitational escape velocity (without taking rotation into account) can be significantly lower at the poles.
Note that, otherwise, the particles forming [internally generated] magnetic field lines cannot be standard photons or of standard photon rest scale, but of even smaller scale, as they would have to be faster than standard light, unless the lines are not closed. However, generally, just as an U-1 graviton slows down from c with momentum transformation synchronized with coupling, a particle faster than c can similarly be slowed down and transformed to a standard photon.
This restricts the feeding potential of a black hole, thus, instead of being trapped, some matter may simply be accelerated at the equator ring and ejected through the poles at extreme velocities. In an extremely polarized case, such black hole does not acquire additional energy and is simply the most efficient transformer of energy (life-form) - transforming composite energy into individual charged particles so these can be digested elsewhere (eg. in young stars, where they combine to form hydrogen fuel). However, in neutral black holes, most matter will have a momentum parallel to the equator plane forming a disc of orbiting material. The shape of a graviton explains not only the formation of jets in black holes but also why some black holes don't have them (such black holes should have a more neutral, 3-dimensional form). The jets are not accelerated by gravity alone, the more energy there is in plasma (accretion disk) the more powerful will be the magnetic field which will focus incoming charged particles making the jets more energetic. This correlation has been observed. Note that magnetic field lines are, at some scale, jets of entangled particles. It is then obvious that extremely neutral bodies will have extremely weak magnetic fields, while extremely polarized will not only have extremely strong magnetic fields but will also be emitting jets of particles of larger scale (like protons and electrons, in case of black holes). If black holes evolved before stars the farthest and biggest black holes may be more polarized. However, polarization should also be cyclic at some timescale. Since particles of the adjacent discrete vertical energy levels [to the U1 level] are charged (dominant energy in standard particles, for example, is electro-magnetic), real gravitons of stars and planets most likely start their evolution (synchronized with coupling to standard matter) more polarized, even though most polarization may be lost already during graviton birth on that scale (inflation from smaller scale or deflation from larger scale). Discs of material about stars and planets are thus probably formed due to charge of the host at the time of formation or at times of energy level changes - greater charge will create thinner discs. This also implies that oldest orbiting formations will orbit in a plane aligned with the plane of primordial equator of the host (unless the orbits have been disturbed later, however, probability for significant disturbance should be low after birth). Settling in equilibrium state is likely to be oscillatory and this is in Solar System confirmed with sinusoidal distribution of inclinations of planets. Note that information on formation should be preserved in inclinations - in case the system inflated from smaller scale, nearer orbits should generally be more aligned with the equatorial plane. This is apparently the case with the Solar System, as shown in Table \tbl1. In case of systems deflated from larger scale, it is the farther orbits that should be more aligned.
BodyInclination (ecliptic) [°]Inclination (Sun's equator) [°]Inclination (invariable plane) [°]
Mercury7.013.386.34
Venus3.393.862.19
Earth07.251.57
Mars1.855.651.67
Vesta7.143.487.13
Ceres10.593.409.20
Pallas34.9336.4534.21
Hygiea3.8310.79-
Jupiter1.316.090.32
Saturn2.495.500.93
Uranus0.776.481.02
Neptune1.776.430.72
Pluto17.1411.8615.55
Table \tbl1: Osculating orbital inclinations in the Solar System However, if vertical energy levels are discrete (as hypothesized), it is possible (or even likely) that initial energy of inflation was larger than required for the jump and the system was, after initial inflation, somewhat deflated to a stable state. Indeed, if outer planets are bigger (and older) and the Solar System was inflating as a system of particles (eg. an atom) - which is a most likely scenario, the energy distribution suggests effective initial inflation of the core to current Mars' orbit or beyond, then deflation to current Sun' radius. In that case, the invariable plane (which is roughly aligned with Jupiter) might represent the fossil of the original core equatorial plane. The higher inclinations of dwarf planets (marked green in Table \tbl1) might indicate these are youngest and were formed after system stabilization, however, more likely, as decreasing inclination (relative to invariable plane) of dwarf planets in the main asteroid belt (and increasing alignment with current equatorial plane) toward the core suggests, these were inflated from smaller and neutral gravitons. I hypothesize that outer planets (gas giants) were inflated from polarized gravitons of electrons (some, or all, of which have ended up in an excited state or different generation - tau and muon mass eigenstates, possibly multiple states in superposition), dwarf planets were inflated from neutrinos, while inner planets were inflated from positively charged particles (parts of atomic nuclei). The anti-alignment of spin magnetic momenta between inner and outer planets goes in favour of this hypothesis (which is further analysed in a follow-up paper).
Note that a black hole is only relatively special form of a gravitational well. Particles faster than light must exist (even if one may not be able to detect them) and every gravitational well has a relative event horizon - digesting energy of one scale and ejecting smaller scale ions which then combine to feed moons. The only difference is scale. The self-similarity is not limited to celestial bodies - every metabolism is ionic. Note also that the trajectory of ejected charges is bent by the magnetic field lines (tubes) and these can be considered as a form of intestines.
In CR, there can be no absolute singularities, only relative ones. If a black hole is the result of graviton inflation or deflation, its gravitational maximum has a real radius and, if any gravitational collapse of standard matter would result in a black hole the collapse would end at that maximum - a ring-like (or toroidal) relative singularity. The collapse of the body of matter is, however, likely relatively synchronized with a change in energy level of the graviton (and exchange between gravitational and electro-magnetic potential). The graviton may collapse to smaller scale but never to a radius of absolute 0 as this would require absolutely infinite mass or angular velocity (due to conservation of momentum). Infinite momenta (energies) are never involved in such collapses. Furthermore, collapse to smaller radius is generally coupled with increase in angular velocity and decrease of rest mass of a graviton. This will generally be reflected in acquired mass. Conservation of momentum is thus effectively replacing gravitational attraction with centrifugal repulsion at some scale. Therefore, although acquired mass can be compacted to extremely dense forms of energy, this energy won't occupy 0 volume and will be radiated away (at whatever scale possible) until it matches the graviton scale. However, with collapse of scale, graviton might exchange spin momentum for orbital angular momentum and decouple from acquired matter. In that case, the particles of compacted matter may be considered dead as a collective and will tend to decompose, decay and spread. Nature evolved diverse mechanisms for such decay - in some reference frames it may be observed as rapid and abiotic, in other organic and slow. In general, distinct conscious life (by my hypotheses) of any system (collective) starts and ends with a change in discrete energy level of a graviton (or gravitons in superposition) at times of: Obviously, what is interpreted as conception and what as death is scale relative. For the graviton (soul), the end of life on one scale is the beginning of life on another scale (switch of context). From some reference frames, one scale may be short-lived and graviton may be observed reincarnating on a single scale - popping in and out of existence between different spaces.

General force, strong force and strong entanglement

Since space cannot be absolute or absolutely abstract, it has properties and energy which can be transformed. Various combinations of spin momenta, subspaces (dimensions) of various scales (various masses of force carrying particles), enable evolution of forces of various nature. Complexity of these forces will be proportional to the number of possible polarized states, or degrees of freedom in polarization. Even gravity, with intrinsic rotation taken into account, can be interpreted as a polarized force.
A neutral force here is interpreted as a force of unipolar nature (eg. non-discriminating attraction).
With changing complexity, one force, may evolve from the other. Complexity can be increased by strengthening entanglement (localization in some dimension of space) of two or more sources of polarized force. Strong localization can be interpreted as superposition in some scales and, if this is a superposition of mass (eg. gravitational), bigger mass of force carrier particles will reduce the range of force. One strongly localized force is the force holding the particles of the atom nucleus together (it is even called strong force in QM). But should it be interpreted as a special force? If gravitational sources are generally not limited to one force carrying particle (graviton of a single scale or rest mass) such force may be interpreted as localized gravity. Of course, if it shows complex polarization (and it may, due to relative superposition of multiple sources), it is not just localized but it has evolved from neutral gravity.
Note that polarization too is relative. It may even be induced by a polarized observer. Note also that evolution can be regressive too - reducing, instead of increasing, complexity.
If one is to unify all possible forces and represent them by a single equation, that equation cannot contain any absolute constants. It must be as variable (or evolvable) as possible. In practical applications, however, it will generally be more usable not to generalize as much, as variability and evolution of reality localized in an dimension of space (including time) is inevitably limited. Therefore, instead of using this for a general force (that includes all possible interpretations on all possible scales):

$\displaystyle F = *$

more convenient and usable expression would be the one of a relatively general force that discards forces of negligible influence on context. In typical local contexts a relatively general force may include electro-magnetic and gravitational terms. Such form is also useful in the context of transformation of energy (inflation/deflation) between discrete vertical energy levels, as all terms are hypothesized to be entangled and one potential may be exchanged for the other, eg. electro-magnetic force might regress to gravitational force with inflation of energy, but also vice versa, depending on scales in question. This is exactly what I hypothesize had happened with the inflation of energy in the observable universe.

Strong entanglement, photon nature

Strong correlation (localization) of particles in a particular dimension may be hard to disturb for an observer. Due to limited resolving power, observational energy may strengthen correlation and inflate additional pairs of entangled particles.
Note that inflation of particles on one scale may be interpreted as annihilation of particles on the other.
This is the case for particles forming atomic nuclei, held together by strong force (strong entanglement), and one reason why proton may be considered an elementary particle in most contexts. However, assuming that the binding of an electron to proton, due to increasing correlation of charges, localizes proton charge into a positron, in that context, the structure of a proton becomes more complex. Since the decrease of distance between charges will result in emission of photons, the photon can be interpreted as a product of strengthening entanglement between negative and positive charge. It then must be a composite particle, a pair of particles produced with annihilation on one scale (inflation on the other). Obviously, if two charges are fermions (having half-integer spin momenta), the photon must be a boson (full-integer spin momentum) - elementary for some observers. The composite particles of a photon are then fermions of smaller scale (half-photons), which may be interpreted as an electron-positron pair of a smaller scale (or, perhaps electron-proton pair). Absorption of that photon by entangled proton-electron pair (atom) will cause [inverse] annihilation of the pair through deflation into constituent quanta of space forming the entanglement. Obviously, as charged particles lose energy with photon emission, the question is in what form is the lost energy, neutral gravitational mass or charge? In other words, do half-photons carry opposite and equal charges or do they carry mass away from charged particles? The proper answer in CR is both, although the energy can be decomposed into electro-magnetic and gravitational waves and energy may be exchanging between these during travel. Generally, photon is, like a gravitational wave, a more or less spherical wave (energy distribution depending on conditions during emission), exchanging energy between spin momenta components during travel, with greatest probability for absorption in the direction aligned with the spin momentum axis (although the direction of that axis can change during travel, eg. in non-flat gravitational space).
Note that, with enough energy, annihilation of a photon pair can result in inflation to an electron-positron pair. The reason why constituent particles of the photon do not annihilate (assuming they're symmetric) between emission and absorption may be the fact they're not localized in space (travelling as a wave) although they are correlated in time. However, photon components likely do oscillate (annihilate) in mass [generation] exchanging spin momentum components, they're simply constrained by the entanglement. This can even be interpreted as oscillation of space and time, or exchange of correlation in one dimension for the correlation in other. Note also that structure of emitted quanta with changes in entanglement is not limited to scaled electron/positron pairs, other particle/anti-particle combinations are possible, resulting in heavy photons or even [pairs of] neutrinos, although, in that case, these may not be interpreted as standard photons or carriers of electro-magnetic force.
Rather than transformation of spin momenta and decoupling from the entangled pair of charged particles (atom), emission of a photon can also be interpreted as radius inflation of the orbital momentum of entangled quanta of space, with average inflation velocity equal to the speed of light. In that case, the orbital momentum would only collapse (localize) to a spin momentum with absorption by another atom (pair of charged particles).
The energy of a photon cannot be absolutely constant. The change in energy of a photon, in case of the spherical expansion [propagation], may be interpreted as caused by changes in distance in correlation between the quanta of space forming the spherical wave [surface]. With symmetric emission and absorption this energy is regained. In other words, total energy is conserved. However, since absolute alignment between momenta of the photon and the absorber is impossible (no perfect symmetry), some energy will be lost. And if the misalignment is generally proportional to distance, loss of energy will be proportional to distance between emission and absorption. The cause of misalignment with distance? Different interpretations are possible. One possibility is the quantization of the loss by potential intermediate absorbers as these affect the photon just as the photon affects them, even though the effect may not be big enough to cause a more permanent absorption (changes in local energy levels). In these cases, the passing photon causes a temporary disturbance which can be interpreted as partial resonance with local energy (photon may be interpreted as a non-divisible quantum of energy in some reference frames, but in others it is itself quantized). This absorption would compress the photon front, but if it is unstable, the absorbed quantum will be re-emitted in the direction of the original emitter. With increasing distance, it is unlikely that the original emitter will absorb it. It is however, quite likely, it will be absorbed by the tail of the original photon (light can be a continuous stream of photons or a single photon, but even a single photon can be interpreted as a stream of smaller photon quanta). This would drag the photon tail. Overall, thus, the photon wavelength remains unchanged, it just becomes temporarily deformed (which can be interpreted as relativistic deformation). However, the probability that the photon tail will not absorb the quantum is non-zero. Thus, overall, photon should lose energy with distance, which, in wave interpretation is a loss in frequency.
Regardless of physical manifestation of photon propagation, it obviously carries information on the source, including original location in flat space (which may be locally manifested as recoil in specific direction at time of absorption). It is a relative clone of the system that caused emission, albeit of different energy. As carriers of force, photons, or gravitons in general, can be interpreted as carriers of changes in specific entanglement between entangled entities (emitter and absorber). The entanglement channel (or dimension) is present as long as the exchange of gravitons exists, or, in other words, as long as the entanglement is changing. But the entanglement is always changing at some scale, and from some reference frames, channels may be interpreted as permanent. Since this horizontal information transfer can proceed faster than standard light on smaller scales, precognition becomes theoretically possible, assuming changes in the energy on smaller scale precede changes on the larger scale (which generally is the case, although they may also follow the changes of larger scale). With a change in vertical energy level of the carrier, the absorbed energy of the smaller scale may even be interpreted as absorbed energy of larger scale.
Interestingly, considering there is no visual stimulation of standard scale during sleep, dreams might just represent information transferred from different scale and locally interpreted as absorbed photons, at least in some cases.
Channels of entanglement carry energy and can, therefore, affect other energy of a particular scale. These channels or filaments (note the dark matter correlation), which can be of different complexity (depending on the complexity of information they carry), can guide this energy into particular configuration. With inherent limitation of observers, the guidance channels may be unobservable, and the behaviour of energy can be interpreted as a result of spontaneous change in energy levels, random fluctuation, or free will.
Constrained spin
Strength of effective attraction between correlated particles is generally higher if their properties (momenta) are anti-aligned in space (in time, vice versa). If the absorption of a photon is increasing distance between two entangled charges, the constituent quanta of the photon must then all carry equal spin momentum or equal orbital momentum, depending on interpretation of absorption. If absorption of a photon is interpreted as expansion (creation) of space between two charges it is the orbital momenta that should be equal. On the other hand, if the constituent quanta are absorbed by entangled charges, it is the spin momenta that should be equal.
This may be interpreted as expansion (creation) of time between two charges if their magnetic field tubes are interpreted as time forming subspaces.
The former may be the correct interpretation in case of the force of electric charge while the latter is the proper interpretation in case of entanglement of magnetic spin momenta. If constituent photon orbital momenta cannot cancel, repulsive electric force between like charges must be fictitious - decreasing distance between them is simply inversely proportional to the strength of entanglement between opposite charges that would result in increase of that distance. In that interpretation, electric force reduces to gravitational force at some scale (dimension), eg. in specific magnetic field tubes connecting opposite charges.
Small updates in Weak entanglement.

Weak entanglement

Graviton tubes are always physical at some scale, however, with increasing distance and no additional energy applied to the tube, entanglement weakens. Note, however, that weak entanglement in one dimension (eg. space) does not imply weak entanglement in the other (eg. time). However, as long as there is no change in entangled energy the entanglement will not get broken (and when it does, it never is broken absolutely), even if the particles are separated over great distance. Due to the fact that energy remains constant, either volume and energy density of the tube (dimension) connecting the particles remain constant or energy density is decreased proportionally to volume increase. Assuming information is transferred along the tube membrane, the former will be, with decreasing tube radius (and mass per quantum of space [cross-section]), increasing speed of information transfer. In that interpretation, speed of transfer can exceed speed of light. In the second interpretation, space is stretched and local observer (within the tube) would measure no change in speed, while remote observer could measure superluminal transfer - assuming tube (subspace) is resolvable by that observer.
In CR, both interpretations are valid (possible). One can only argue what and when any information is transmitted. Information that is observable could be limited to information transmitted with the collapse (deflation) of entanglement, which will, in both interpretations, decrease energy in the tube. Since weak entanglement is relatively unaffected by change in spatial distance alone, the first interpretation (volume invariant to spatial distance) is convenient as it implies proportionality of volume (or volumetric distance) with distance in correlation (inverse of [scale of] entangled energy or strength of entanglement). Note that the observer who cannot resolve (observe) the tube of entanglement cannot use the tube for information transfer or control information transmitted on collapse (superluminal or not). In that case, weak entanglement reduces to standard non-local QM entanglement (note that, per CR postulates, QM entanglement cannot be absolutely non-local, implying existence of reference frames with interpretations stated above).
Weak entanglement
Fig. \fig4: Weak entanglement

$\displaystyle \Delta E_1 = \Delta E_2 = \Delta E = \text{const.}$

What is the initial speed of information transfer? Speed of information transfer always depends on distance in some dimension. If distance in time is distance in evolution, distance in time between two equally evolved or relatively identical particles (eg. two entangled photons) will be a relative 0, so the speed of information transfer with the collapse of entanglement in time will be a relative infinity, relatively invariant to spatial distance. For a limited observer, these relative values (eg. zero, infinity and invariance), may be effectively interpreted as absolute.

Electric polarization and charge/mass exchange

In the standard model of physics particles have fixed (intrinsic and unchangeable) properties (eg. electric charge, rest mass, spin) which then produces a zoo of different particles. While that approach is useful, different particles evolve from other particles and it might not always be the most convenient approach, especially in CR, where even planets or animals on it are considered particles from certain reference frames. One can thus model a single particle and declare it relative - evolvable. Here, one such particle is the graviton - it can transform from a source of gravity to a source of electro-magnetic force and vice versa (effectively exchanging the scale of mass with the scale of charge). Exchanges between electro-magnetic and gravitational potential generally occur with changes in vertical energy level, but such exchange on horizontal levels is not absolutely forbidden, it may only require special conditions. In one example of such exchange, down quark could evolve from a superposition of 9 gravitons of electron mass, where 5 of them are negatively charged, 4 positively, and 2/3 of remaining negative charge (4 opposite charges cancel) have been exchanged for mass. This gives a total electric charge of -1/3 e, spin 1/2 and rest mass (assuming quadratic growth of mass) equal to:

$\displaystyle {m_d}_0 = \left(9 + {\left(2 \over 3\right)}^2 \right) m_e = \left(3^2 + {\left(2 \over 3\right)}^2 \right) * 0.511\, {MeV \over c^2} = 4.826\overline{1}\, {MeV \over c^2} \tag{1.2}$

However, assuming this superposition is stable (particles have undergone fusion and indeed form a new particle), total mass will be somewhat lower (by the binding energy).
Binding energy is not always lower though, for bound hadrons (eg. quarks bound into a proton), due to large angular momenta, total mass can be significantly higher than the sum of rest masses of bound particles (from some reference frames).
Assuming particles are bound as atomic nuclei are, and scaling binding energy of 9C (carbon isotope), the rest mass becomes:

$\displaystyle m_d = {m_d}_0\, {MeV \over c^2} (1 - 0.00464) = 4.8037\, {MeV \over c^2}$

This is in agreement with mass determined from lattice QCD of 4.79±0.16 MeV/c2. However, here it was assumed that complete conversion of 1 e of charge would result in mass equal to electron mass, the actual ratio can be significantly different. Assuming that the down quark is instead a result of conversion of anti-up quark charge to mass, mass inflated per 1/3 e of charge lost is:

$\displaystyle \left(m_d - m_u\right) = 2.78\, {MeV \over c^2}$

Note that conversion of electric charge to gravitational mass by that ratio would release enormous amounts of energy as gravitational force is ≈1042 orders of magnitude weaker than electro-magnetic at that scale. Instead of energy released, it may be more appropriate to consider conversion of electro-magnetic force to strong nuclear force (as quarks are confined to atomic nuclei). Strong nuclear force then evolves from electro-magnetic force, however, it may be interpreted as condensed gravitational force. During the conversion, instead of inflation of rest mass, local space is condensed, the mass of local gravity carrier particles increases, strongly limiting the range of the force (localizing gravity). Of course, if the strong force is polarized, it is a composite of different sources and thus more complex. Symmetric positive and negative charges in superposition can annihilate and produce more massive particles (such as quarks) with enough kinetic energy. Thus, taking kinetic energy into account, quarks (or, more precisely, quark/anti-quark pairs) can be produced with only 2 charges and that is how they might be generally produced in the observable universe at this time.
Electric polarization of a graviton is represented by positive (+) or negative (-) charge. As such, they are sources of electric, magnetic fields and electro-magnetic radiation. In one interpretation of CR, positively charged particles may be referred to as anti-matter, negative as matter. Composite, neutral, matter particles are those with more mass in negative charge, neutral anti-matter particles are those with more mass in positive charge.
The missing anti-matter problem in physics can be solved by CR, through different pathways. One is asymmetric momenta (energy) distribution in annihilation events - where the product of lower mass (anti-matter) was captured beyond supermassive black holes (here, supermassive black holes may not be remnants of stars of the current universe, rather effective producers of early stars). Another pathway is differentiation through evolution in charge-mass exchanges, or, exchanges between electro-magnetic and gravitational potential. Consider elementary charges (electrons and constituent particles of protons and neutrons), as shown in Table \tbl2 (also showing possible constituent charges of electrons).
particlecharge quanta [e]total charge [e]
electron[ -2/3 -2/3 +1/3 ]   OR   3x [ -2/3 +1/3 ] ?-1
proton[ +2/3 +2/3 -1/3 ]+1
neutron[ +2/3 -1/3 -1/3 ]0
Table \tbl2: Elementary charges Obviously, charges are balanced, all particles are fermions and assuming positive charges are anti-matter particles, negative are matter particles, the result of asymmetry is simply exchange between charge and mass. In CR, electron cannot be absolutely elementary, therefore, three down quarks (3 * -1/3 e) and three up quarks (3 * +2/3 e) could have evolved from 1 electron and 2 positrons. All the elementary particles could have thus evolved from 2 electrons and 2 positrons total - symmetry, assuming that for every electron there exists one proton and one neutron. Having equal amount of charge, but (orders of magnitude) different mass, electrons and protons could be interpreted as belonging to two different universes. Quarks cannot be absolutely elementary either. For every electron there is thus a positron hiding beyond the relative event horizon of an atom - it may be reformed (from proton energy) at time the electron is captured by the proton to form the atom (leaving +1/3 e and -1/3 e charge with neutral mass in the core). In one interpretation, proton itself is the positron evolved in time in order to preserve existence (avoid annihilation), one may refer to it as a vertically excited positron (conventional anti-proton would then be a vertically excited electron). Existence requires asymmetry, and with asymmetry evolves diversity. In one interpretation of β- decay, a quantized collapse of a gravitational maximum (neutron event horizon) produces a positron/electron pair and neutrino/anti-neutrino pair, electron and anti-neutrino are ejected (paired or evolved into a W- boson initially by the strong curvature) while positron and neutrino are absorbed by the nucleus. Strong nuclear curvature evolves positron/neutrino pair into up quark (+2/3 e) and anti-down quark (+1/3 e) which then annihilates with one existing down quark (-1/3 e), transforming neutron to proton. Outside the strong curvature (pressure) of space of nuclei, W- boson is unstable and lack of gravitational pressure (time dilation) may be the sole reason it decomposes back to electron/anti-neutrino pair. The Compton wavelength of the electron is on the order of atomic radii and this suggests that electron bound to the atom is electron coupled to a nuclear graviton of similar mass (and thus similar range). Electrons closer to the nucleus are then coupled with more massive gravitons. One can then consider the up quark as a positron coupled with such graviton and a down quark as electron coupled with an even more massive graviton. Note that, in these couplings, mass is inversely proportional to charge, suggesting mass/charge exchange with coupling. Coupling of an electron and anti-neutrino into a massive W- boson then suggests that electric charge of a massive W boson may be extremely low (<< 1 e) - in any case, charge is not conserved in that form, it is restored with decoupling. The charge/mass exchange can be understood as exchange of spin momentum components. To conserve momentum, with increasing rest mass (or spin momentum of mass) the momentum of energy producing charge (magnetic field lines) must be decreased. If one interprets magnetic field lines (tubes) as dimensions of time, time dilation is physically manifested here as contraction or deflation of time dimensions. Disregarding negligible photon mass compared to a strong force graviton mass, conversion of 2/3 e charge potential to gravitational Yukawa type potential of a down quark mass would yield mass mg for the graviton (assuming unscaled gravitational constant G) as follows:

$\displaystyle {GM \over r} e^{-{\mu}_g r} = {2 \over 3} {1 \over {4 \pi {\epsilon}_0}} {q_e \over r}$

$\displaystyle e^{-{\mu}_g r} = {2 \over 3} {q_e \over {4 \pi {\epsilon}_0}} {1 \over {G M}}$

$\displaystyle {\mu}_g = ln{\left( {2 \over 3} {q_e \over {4 \pi {\epsilon}_0}} {1 \over {G M}} \right)} {1 \over r}$

$\displaystyle m_g = ln{\left( {2 \over 3} {q_e \over {4 \pi {\epsilon}_0}} {1 \over {G M}} \right)} {1 \over r} {\hbar \over c} \tag{1.3}$

qe = 1.60218 * 10-19 C
ε0 = 8.85419 * 10-12 F/m
G = 6.67430 * 10-11 m3kg-1s-2
ℏ = 1.054572 * 10-34 Js
c = 2.99792458 * 108 m/s
For r = 1 * 10-15 m and mass of a down quark M = md = 4.8 MeV/c2 = 8.556777 * 10-30 kg:

$\displaystyle m_g = 2.44819 * 10^{-26}\, kg = 13.7333\, {GeV \over c^2}$

Roughly 100 times the range (r) would give the mass of a pion (π meson). It is certainly viable that the range of gravity of the down quark is 100 times the nuclear radius, at least when there's an electron bound to the nucleus (forming the atom). Of course, the source of a strong force is generally a composite force (a superposition) of multiple short range sources, but is the complex polarization present at all times, or does it only occasionally evolve? Interestingly, using Compton wavelength of a pion (roughly 1.43 * 10-15 m) for r, gives mg = 9.60 GeV/c2, which would be equal to superposition (not a stable composite) of 2 bottom quarks and 1 charm quark (2*4.18 + 1.28 = 9.64 GeV/c2). Such superposition could be interpreted as an unstable neutral baryon. If that baryon is then paired with its anti-particle the radius r would be reduced to roughly 0.715 * 10-15 m, which could be interpreted as down quark contribution to the mass radius of the proton.
Note that the calculation for up quarks (conversion of 1/3 charge to mass) gives almost equal results (due to up quark mass being roughly half the down quark mass, 2/3 md-1 ≈ 1/3 mu-1). Note also that it has recently been discovered that a charm/anti-charm quark pair may be more intrinsic to the proton than previously thought. Could it be that the whole hypothesized baryon/anti-baryon pair gets periodically inflated then? If one assumes that the mass of the pair is inflated by the ratio of charm quark mass to proton mass (1275/928.272), the mass radius becomes 0.521 * 10-15 m, in agreement with recently obtained proton mass radius of 0.55±0.03 fm. Interestingly, conversion of charge to mass using (1.3) for M equal to proton or anti-proton mass yields the graviton mass mg on the order of electron mass for r on the order of electron orbitals in the atom. Coincidence? I think not.
Thus, the nuclei of atoms may generally not be held together by a force stronger than electrostatic repulsion, rather the repulsive electric potential is periodically converted to strongly localized gravitational potential. This oscillation could be interpreted as relative superposition of electro-magnetic and gravitational forces, which collapses to a particular eigenstate with interaction (observation). The requirement for nuclear fusion (fossilization of superposition of multiple atomic nuclei into a new discrete nucleus) is then anti-aligned oscillation. The binding will be most stable with a phase shift of 90°, while it is least stable in resonance (stability of superposition in that case requires extremely low pressure/temperature).
Note that, in CR, absolutely infinite stability is impossible. Therefore, any superposition is a relative fusion, and vice versa.
This difference in phase shift can be achieved with difference in [the amount of] momenta between two nuclei (inducing time dilation in one) - bombardment of one nucleus with the other. This suggests that the probability for fusion may be higher between different species (different rest masses between nuclei). Interestingly, the non-dimensional factor in equation (1.3) is almost equal in value to the natural logarithm of the inverse of electron mass (me):

$\displaystyle ln{\left( {2 \over 3} {q_e \over {4 \pi {\epsilon}_0}} {1 \over {G M}} \right)} \approx ln{\left( {1 \over m_e} \right)}$

Rearranging (1.3), one can get the orbital angular momentum of the graviton (in local rest frame). Assuming inverse of 2/3 of electron mass (better fit):

$\displaystyle m_g\, c\, r = ln{\left( {3 \over 2} {C \over m_e} \right)}\, \hbar \approx ln{\left( {3 \over 2} {1 \over m_e} \right)}\, \hbar \approx \sqrt{69 * (69+1)}\, \hbar$

C ≈ 1 kg
Is it a coincidence that graviton momentum is quantized by [the inverse of] 2/3 electron mass?
Here, one should also question whether the constant (quantum of momentum) should be different (scaled) in the local rest frame.
Down quark mass (md) from the equivalence:

$\displaystyle {2 \over 3} {q_e \over {4 \pi {\epsilon}_0}} {1 \over {G M}} = {3 \over 2} {1 \over m_e}$

is:

$\displaystyle m_d = M = {\left({2 \over 3}\right)}^2 {q_e \over {4 \pi {\epsilon}_0}} {m_e \over G} = 8.7348 * 10^{-30}\, kg = 4.9\, {MeV \over c^2} \tag{1.4}$

me = 9.10938356 * 10-31 kg
The obtained mass is in agreement with lattice QCD (4.79±0.16 MeV/c2). Thus, the constant C here may be exactly equal to 1, rather than approximately. The obtained equation (1.4) also confirms the (2/3)2 factor of charge/mass conversion, initially assumed in (1.2).
Some might argue that graviton orbital velocity cannot be equal to c as it has finite mass, however, orbital momentum of the graviton should be understood as orbital momentum of [a quantum of] space - it is relatively massless from the local reference frame. However, once it gets coupled its orbital velocity will decrease below c (and mass will inflate to conserve the momentum). The coupling (inflation) of a graviton will decrease the local gravitational capacity for coupling with a particular scale of matter, however, as this coupling is also a gravity source, it may increase coupling capacity of the local well for another scale of matter.
If charge/mass conversion is common, it should not be limited to electron/down quark conversion. Indeed, equation (1.4) can match other quarks/leptons of the standard model, by changing input mass (me) and charge fraction Q (term 2/3 in the equation). And adding the term 10n (as in eq. 1.5), where n is an integer yields even more correlation, as shown in Table \tbl8 for some matches with positive input charges. Here, it is assumed that charge fraction Q indeed represents the charge fraction being exchanged for mass [inflation/deflation].
Note that, if electron can convert to down quark, it should be possible for muon and tau electrons to convert to muon and tau down quarks. Note also that only simple conversions (1:1 input/output) are considered here, more complex conversions are possible.

$\displaystyle M = {10}^n Q^2 {q_e \over {4 \pi {\epsilon}_0}} {m \over G} \tag{1.5}$

input particle (mass m, charge)charge fraction Qnoutput mass M (charge)correlated standard model particle (mass, charge)
up quark (2.2 MeV/c2, 2/3 e+)1/305.2741 MeV/c2 (1/3 e+)anti-down quark (4.7 +0.5/-0.3 MeV/c2, 1/3 e+)
up quark (2.2 MeV/c2, 2/3 e+)1-14.7467 MeV/c2 (1/3 e-)down quark (4.7 +0.5/-0.3 MeV/c2, 1/3 e-)
anti-down quark (4.7 MeV/c2, 1/3 e+)2/3-14.5069 MeV/c2 (1/3 e-)down quark (4.7 +0.5/-0.3 MeV/c2, 1/3 e-)
anti-down quark (4.7 MeV/c2, 1/3 e+)4/311.8028 GeV/c2 (1 e-)tau electron (1.7769 GeV/c2, 1 e-)
anti-strange quark (96 MeV/c2, 1/3 e+)2/3-192.0566 MeV/c2 (1/3 e-)strange quark (95 +9/-3 MeV/c2, 1/3 e-)
anti-strange quark (96 MeV/c2, 1/3 e+)1-32.0713 MeV/c2 (2/3 e-)anti-up quark (2.2 +0.5/-0.4 MeV/c2, 2/3 e-)
anti-bottom[1S] quark (4.65 GeV/c2, 1/3 e+)4/3-21.7836 GeV/c2 (1 e-)tau electron (1.7769 GeV/c2, 1 e-)
positron (0.511 MeV/c2, 1 e+)1/331.225 GeV/c2 (2/3 e+)charm quark (1.27 ±0.02 GeV/c2, 2/3 e+)
positron (0.511 MeV/c2, 1 e+)2/304.9 MeV/c2 (1/3 e+)anti-down quark (4.7 +0.5/-0.3 MeV/c2, 1/3 e+)
muon positron (105.6584 MeV/c2, 1 e+)1/3-22.533 MeV/c2 (2/3 e+)up quark (2.2 +0.5/-0.4 MeV/c2, 2/3 e+)
muon positron (105.6584 MeV/c2, 1 e+)2/3-1101.3198 MeV/c2 (1/3 e+)anti-strange quark (95 +9/-3 MeV/c2, 1/3 e+)
Table \tbl8: Obtained masses using equation (1.5) The introduction of 10n term suggests presence of an additional mechanism acting on mass for n ≠ 0 (note that for negative n mass of the output particle can be lower than the mass of the input particle - not expected for simple conversion of charge into mass), however, change in mass M should be compensated by the change in mass of the force carrier particle. The term may be correlated with inflation/deflation of mass and mechanism behind it can be annihilation or vertical mass oscillation. Charge fraction parameter (Q) larger than the input charge further increases complexity, as here absolute output charge value can be higher than the absolute input charge value, albeit of different polarity. What is the mechanism behind charge inversion? One solution is in the composite charges. In example, 1/3 e+ charge of a particle can be a sum of 2 x 1/3 e+ and 1/3 e-, the Q of 2/3 then removes 2 x 1/3 e+, resulting in 1/3 e- output charge (charge inversion, although apparent, is then not real). However, the Q2 term may be incorrect. Note that, for input mass m equal to calculated down/anti-down quark mass (4.9 MeV/c2), charge fraction Q equal to 1 and n = 0, equation gives mass of 105.7213 MeV/c2, very close to the muon electron mass (105.66 MeV/c2), however, with the above interpretation of charge fraction (output charge = input charge - Q), this particle has 2/3 e charge (while standard muon particle has 1 e charge). This can be solved if, instead of a down quark, input mass contains two up quarks, with Q = 1/3 and n = 1. This, for single up quark mass equal to 2.203688 MeV/c2 gives muon mass 105.6584 MeV/c2, and appropriate muon charge (2*2/3 - 1/3 = 1). In this case however, spin is not conserved. Addition of a neutrino to input (or output) mass could solve this problem. Neutrino mass is negligible compared to muon mass but it carries the required spin (1/2).
Note that neutrinos may be involved in other cases as well.
The same muon mass and appropriate charge/spin can also be obtained if input mass contains up/anti-up quark pair and a neutrino, with Q = 1 and n = 0. In that case, up quark mass has to be higher (~2.45 MeV/c2), unless neutrino is highly energetic and carries the excess energy. However, this can be interpreted as annihilation, and, instead in input, neutrino may be present in the output. Similar and very interesting results can be obtained if the term Q2 is replaced with a term 2/3 Q, resulting in equation (1.6):

$\displaystyle M = {10}^n {2 \over 3} Q {q_e \over {4 \pi {\epsilon}_0}} {m \over G} \tag{1.6}$

$\displaystyle q_{out} = q_{in} - Q {q_{in} \over |q_{in}|}$

m = input mass
Q = fraction of charge being exchanged for mass inflation/deflation = k × 1/3 (k = integer)
n = vertical energy level (integer)
qout = output charge
qin = input charge
Note that, instead of providing mass, the equation can be rearranged to provide mass ratios for particular Q and n.
This, in example, for input mass equal to positron mass (0.511 MeV/c2, 1 e+), Q = 4/3 and n = 1, gives mass of 98.002 MeV/c2 and charge 1/3 e- (1 - Q = -1/3), which can be correlated with standard strange quark (mass = 95 +9/-3 MeV/c2, charge = -1/3). The same input mass, with Q = 5/3 and n = 2 gives output mass 1.225 GeV/c2 and charge 2/3 e- (1 - Q = -2/3), which can be correlated with standard anti-charm quark (mass = 1.27 ±0.02 GeV/c2, charge = -2/3). Most striking example, however, is the result obtained using input mass equal to tau positron mass (1.7768 GeV/c2, 1 e+), Q = 2 and n = -5. This gives a mass of 0.511 MeV/c2 and charge of 1 e- (1 - Q = -1), which obviously can be correlated with standard electron (mass = 0.511 MeV/c2, charge = -1). Thus, one now has a relation between electron (positron) and tau positron (electron) masses:

$\displaystyle m_e = {10}^{-5} {2 \over 3} 2 {q_e \over {4 \pi {\epsilon}_0}} {m_{\tau} \over G} \tag{1.7}$

me = electron/positron mass
mτ = tau electron/positron mass
A clear evidence for charge/mass exchange and vertical energy levels. And a possible evidence that there are no absolutely elementary charges (all are composite) - in the example above, tau positron charge may be interpreted as a composite of 2 x 1 e+ and 1 e-, where 2 x 1 e+ (corresponding to Q = 2) has been exchanged for mass deflation (annihilation). In the simplest case of conversion, composite particles of tau positron may be one particle of electron charge/mass and two particles of 1 e+ charge, each having a mass:

$\displaystyle m \approx {{m_{\tau} - m_e} \over 2} = 888.1745\, {MeV \over c^2}$

Interestingly, this particle can be obtained with (1.6) using 4.631 GeV/c2 for input mass and charge of 1/3, Q = 4/3 and n = -2. This input mass/charge is in agreement with standard bottom quark (1S scheme, mass = 4.650 ±0.03 GeV/c2, charge = 1/3). Of course, binding energy should be taken into account (using 4.650 GeV/c2 as input gives 891.7987 MeV/c2). And using input mass of 4.9 MeV/c2 and charge of 1/3 (down quark mass/charge, as calculated above in 1.4), Q = 2/3, n = 2, gives a mass of 4.6987 GeV/c2 and 1/3 charge, which can be correlated with this bottom quark. Using proton as input (938.272 MeV, +1), with Q = 1 and n = -2, gives 134.9596 MeV and 0 charge, which can be correlated with the pion (π0) particle (134.9768 MeV, 0). Here are some additional examples with composite inputs. Using input mass of 9.7846 MeV/c2, charge 5/3, Q = 2/3 and n = 1 gives the proton (mass 938.27 MeV/c2, charge 1). This input mass/charge can be interpreted as a sum of two up quarks and one anti-down quark with energies 2 x 2.4423 and 4.9 MeV, respectively. In this process the charge fraction Q probably affects the anti-down quark, converting it into a down quark (1/3 - Q = -1/3), consistent with the composition of the standard proton (2 up quarks + 1 down quark). Note that the equation can also produce a down quark from a single anti-down quark input (and vice versa) - using Q = 2/3 and n = -1 produces a 4.7 MeV particle for 4.9 MeV input. Using input mass of 2 x 4.9 MeV/c2, charge 2/3, Q = 2/3 and n = 1 gives a mass of 939.75 MeV/c2 and charge 0. The output can be correlated with the neutron (mass 939.565 MeV/c2, charge 0), while the input is 2 x anti-down quark (should also contain a small neutrino contribution). Input of 2 up quarks and 1 electron with energies 2 x 2.203688 MeV and 0.511 MeV, respectively, Q = 2/3 and n = -1 gives mass 4.7163 MeV/c2 and charge -1/3, which can be interpreted as a down quark. Up quark, for Q = 5/3 and n = -2, converts to a particle of electron mass/charge. All this provides interesting pathways for proton/neutron transformation.
Note that equations 1.4 - 1.7 should contain a dimensional constant (C, as noted before), which was assumed to be equal to 1. The results obtained here suggest that indeed it is equal, or at least very close, to 1. This is then equivalent to the notion that the following ratio is treated as non-dimensional in reality:

$\displaystyle {q_e \over {4 \pi {\epsilon}_0}} {1 \over G}$

, the ratio of kg2/C (kilogram squared per coulomb). However, the term 2/3 could be interpreted as [inverse of] the value of the constant.
If Q is kept constant for particular input mass (m), the equation (1.6) can be written as:

$\displaystyle M(n) = 10\, M(n-1) \tag{1.8}$

$\displaystyle M(0) = {2 \over 3} Q {q_e \over {4 \pi {\epsilon}_0}} {m \over G}$

Another interesting case is the addition of square roots, in this form (which could be correlated with Koide formula):

$\displaystyle M = {10}^n {2 \over 3} Q \sqrt{{q_e \over {4 \pi {\epsilon}_0}} {m \over G} C} \tag{1.9}$

Here, assuming mass is given in eV/c2, the unit of constant C should be m2s-2kg-1. The constant is roughly equal to 1 if it represents the ratio between the standard speed of light squared and vertically excited electron mass:

$\displaystyle C = {c^2 \over {m_e \times 10^{47}}} = 0.99\, m^2s^{-2}kg^{-1} \approx 1\, m^2s^{-2}kg^{-1}$

c = 2.99792458 × 108 m/s
me = 9.10938356 × 10-31 kg
Note that the unit of the constant is equal to the unit of the gravitational constant divided by the metre, so the value of 1 can also be obtained dividing G by 6.674 × 10-11 metres, which is, very interestingly, the theoretical radius of the carbon atom, its molecular double bond covalent radius (6.67 × 10-11 m), and also the Hill sphere radius of a carbon atom in the gravitational field of Earth, at Earth's surface. This correlation then may help explain why the carbon element is a common base in molecular bonding and the basis for life on Earth's surface. The equation (1.9) yields very interesting results but mostly for composite inputs. For example, top quark (173.1 GeV, 2/3) and electron (0.511 MeV, -1), for Q = 1 and n = 0, yield 1.2797 GeV and 2/3 charge, which can be correlated with the charm quark (1.27±0.02 GeV, 2/3). There are other ways to obtain the charm quark. Input of two down quarks with energies 4.7 + 4.9 MeV (or, 2 x 4.8 MeV), Q = 4/3 and n = 2, gives 1.2707 GeV for the charm quark. This combination of down quarks is certainly interesting, as the same combination with added one up quark (2.2 MeV, 2/3), for Q = 1 and n = 1, gives 105.6596 MeV and -1 charge, showing high correlation with the muon (105.66 MeV, -1). And there are more cases of such high correlation. This equation, however, does not give such convincing results with single particle inputs, suggesting that, if square roots are valid for binary inputs, the generalized equation may have this or similar form:

$\displaystyle M = {10}^n {2 \over 3} Q {\left({q_e \over {4 \pi {\epsilon}_0}} {m \over G}\right)}^{1 \over k} \tag{1.10}$

where k either represents the number of input particles (possibly equal to 1 for single inputs and 2 for any composite input), or something like this:

$\displaystyle k = 1 + (j+1)\, \%\, 2$

j = number of input particles

Mass

Mass is simply energy, or relatively concentrated energy in some contexts. No quantum of energy can have mass equal to absolute 0. A particle with a relative 0 mass should be understood as entangled non-concentrated finite mass (>0), generally in the form of waves.

Total mass

Uncoupled graviton may be considered to have 0 mass relative to space. However, once coupled (and slowed down) its mass is greater than 0. Total mass of the coupling is the sum of masses of a graviton (img mass) and that of the acquired (coupled) matter (real mass):

$\displaystyle M = m_{img} + m_{re}$

It is usually denoted with uppercase letter M. In contexts where it represents a quantum of bigger mass, it may be denoted with lowercase letter m.

Imaginary mass = virtual mass = img mass

Imaginary mass is the mass of a graviton. However, in one interpretation, some or all of this mass may be shielded by acquired (coupled) matter and in that case it is not constant (although acquisition of matter to full capacity can be relatively instant). It can then be interpreted as the unshielded mass of a graviton and it is a relative 0 in equilibrium (full capacity). If there is no shielding, at full capacity img mass is equal to coupled real mass. The mass of a graviton is usually denoted with mimg.
Note that if shielding is real, total mass is constant as long as the well is not over-capacitated.

Real mass

A naked graviton will attract matter. Real mass represents the acquired mass (mass coupled to the graviton). Generally, for a graviton of scale Un, coupled real mass is of scale Un-1, while particles (gravitons) forming space associated with the graviton are of scale Un-2.
Note that coupling of the body of real mass with the large scale graviton is indirect. The individual components of real mass are actually directly coupling with the components of space, however, due to generally aligned entanglement between Un and Un-2, in equilibrium conditions, this is equivalent.
Couplings are not intrinsic, gravitons can be naked and real mass collective may not be coupled to a graviton of larger scale. Such bodies of real mass are considered dead and are generally less stable than bodies coupled to gravitons.
Low mass asteroids and comets are assumed to be such bodies. These are most likely leftovers of dead planets and moons. However, it is possible that every barycentre of organized or localized mass has a physical interpretation in the form of a more energetic graviton (compared to constituent gravitons of that mass), although this may be unlikely and even if true, distinct consciousness of such body [as a collective] would be extremely low (a relative 0). One could argue that large scale graviton is unnecessary in any case, however, recursion would then make gravitons of any scale unnecessary and there would be no gravity or any other force at any scale (note that a small scale graviton coupled to an atom is a large scale graviton from the reference scale of atoms).
Real mass is usually denoted with mre. If velocity of a graviton is different than its rest velocity in underlying space, relativistic effects will be locally expressed (kinetic energy will be stored locally), in the graviton spin momenta and momenta of constituent quanta of its own space, as img mass. The increase in gravitational potential will then result in the addition of real mass as well if matter of appropriate scale is available. Real mass in a distinct gravitational well [of a graviton] is generally in significant part always being transformed to other forms of energy (through fusion, heat, chemical reactions, etc.) and lost energy will generally be periodically replenished, as long as real mass is available (effectively, in case of shielding interpretation, imaginary mass is periodically being exchanged with real mass).
Note that continuous existence of [oscillating] transformation of energy may generally signal the existence of a discrete living being (superposition of a collective reflected in relative mental singularity - distinct consciousness).
Universes are self-similar, and with recursion, any acquired real mass (or matter) of scale n is total mass of another, generally smaller, scale:

$\displaystyle \sum{m_{re}(n)} = \sum{M(n-1)}$

At full capacity of a well, angular velocity of space (effective gravitational field tube) at radius r of a gravitational well is defined by this equation (derived from Kepler's laws), with the assumption of a point-like source of gravity:

$\displaystyle {v_s}^2 = rg = {G M \over r} \tag{R1.1}$

Here, M is the total mass of the gravity source (or mass below radius r) and G is the gravitational constant.
while mass capacity of the well is:

$\displaystyle C = M - m_{re} = m_{img}$

Well capacity is related to spin velocity of its graviton (at its mass radius rs), which at full capacity is Keplerian:

$\displaystyle {c_s}^2 = r_s g_s = {G M \over r_s} = G {{m_{img} + m_{re}} \over r_s} = 2 G {m_{img} \over r_s}$

Here, factor 2 indicates no-shielding interpretation.
However, evidently, angular velocities in gravitational wells are not always Keplerian (eg. dark matter problem, spin momenta of planets). Such velocities should then indicate either under-capacitated or over-capacitated gravitational wells. In case of excess velocity, the well is under-capacitated (imaginary mass is greater than coupled real mass).
Note that gravitons are generally orbiting at the speed of light (local speed limit), they only slow down with coupling, reaching Keplerian velocity at full capacity. In the process, they are inflating - exchanging orbital angular momentum for spin momentum.
In case of lack of velocity, the well is over-capacitated (real mass is greater than img mass).
Effectively, in under-capacitated wells space is dragging matter, in over-capacitated wells matter is dragging space.
Assuming thus that coupled mass has Keplerian velocity at full capacity on particular orbital radius (note that particular orbital radius represents the range of coupling gravitons), conservation of momentum dictates that for unfilled capacity (mre < mimg) at the same radius velocity must increase. Decoupling can be simply achieved with the inversion of a spin of a graviton (eg. with collapse of entanglement), which is generally synchronized with a change in scale, even if that change may be temporary. If real mass coupled to a graviton (gravitational maximum) is compact and forms a solid-like body (period of rotation is constant and doesn't depend on distance from the graviton) with isotropic energy distribution then it can be considered as a point particle rotating about the barycentre of mass (also centre of graviton). If momentum of that mass is lower than Keplerian velocity at the mass [orbital] radius (the well is over-capacitated), its motion is relativistic in that well. Proper (or properly scaled) relativistic equation for total mass is then:

$\displaystyle M = m_{re} + m_{img} = {m_{{re}_0} \over \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}} + m_{img}$

$\displaystyle m_{{re}_0} = \left(M - m_{img}\right) \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}$

$\displaystyle v_{re} = {2 \pi r_{re} \over T_{re}} \approx {2 \pi r_s \over T_{re}}$

vre, rre, Tre = orbital velocity, radius and period of rotation of real mass, respectively
cs, rs = Keplerian angular velocity and mass radius of the maximum, respectively

Here, of course, vre and Tre should be relative to rest velocity (expected Keplerian velocity) and period when calculating local excess energy.
Note that spin angular velocity of [real mass of] Earth is lower than Keplerian velocity. Earth's spin is thus locally relativistic and the gravitational well has excess energy. In one interpretation that is the reason the planet is active - transforming, or digesting, energy (through fission, heat, chemical reactions, etc.). In another interpretation, it is these transformations (particularly thermal energy) that are converting orbital angular momentum to radial. Cause and effect are relative in CR, and both interpretations are valid.
If real mass is quantized into multiple bodies with different periods of rotation, mass equation is:

$\displaystyle M = \sum{m_{{re}_0} \over \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}} + m_{img}$

Predicting activity (amount of local life potential)

Since locally relativistic motion is correlated with local energy transformation, predictions can be made about local activity. The more excess energy there is, the higher is the potential for complex transformations and thus complex life (of course, too much excess energy is also a problem for life as well, real habitability will depend on energy distribution). Mass radius of terrestrial bodies should be the radius of a gravitational maximum (major, or large scale graviton), with the assumption that terrestrial bodies are solid or solid-like and that the mass radius is the radius of the core (inner core, if it exists), excess energy can be easily calculated. For terrestrial bodies:

$\displaystyle M = {m_{{re}_0} \over \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}} + m_{img} = {m_{img} \over \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}} + m_{img} = m_{img} \left( 1 + {1 \over \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}} \right)$

$\displaystyle v_{re} = {{2 \pi r_{re}} \over T_{re}} = {{2 \pi r_s} \over T_0} - {{2 \pi r_s} \over T} = c_s - {{2 \pi r_s} \over T}$

$\displaystyle T_0 = {2 \pi r_s \over c_s}$

$\displaystyle {c_s}^2 = {GM \over r_s}$

G = 6.674 * 10-11 m3kg-1s-2
Excess mass is:

$\displaystyle m_x = {m_{img} \over \sqrt{1 - {{v_{re}}^2 \over {c_s}^2}}} - m_{img}$

bodytotal mass M [1024 kg]img mass mimg [1021 kg]mass radius rs [m]rotation period T [h]relativistic angular velocity vre [m/s]Keplerian period T0 [h]Keplerian velocity cs [m/s]excess mass mx [1024 kg]
Mercury0.3304.87285670281407.66231.60.15886232.30.3203 (97%)
Venus4.86863.601330799115832.610269.80.523410270.74.7408 (97%)
Earth5.972534.1110120608423.93518090.90.115818178.84.9038 (82%)
Mars0.642109.8515158177724.6235092.50.53045204.60.4223 (66%)
Pluto0.013030.6371224993153.2931963.40.19971966.00.0118 (91%)
Table \tbl3: Spin momentum components and excess energy of terrestrial bodies*
* Sources of data in Table \tbl3 for total mass and rotation period are NASA Planetary Fact Sheets.
Calculated values for some terrestrial bodies are shown in Table \tbl3 (values in parentheses for excess mass are percentages of total mass). Unsurprisingly, relativistic (excess) mass percentage of total mass is, for terrestrial planets, decreasing with distance from the Sun. While Earth's excess (and thus complexity potential) is highest in absolute value, Venus has a maximum potential for complexity relative to its rest energy (its interior is probably very active). However, in all bodies relativistic energy is high, and where pressure/temperature allows it (in interior generally) one probably can expect complex life.
Complex life as we know it implies fluid-like interactions - transformation of random thermal fluctuations into organized flows of energy. This could be, however, interpreted as increase in scale of thermal energy and pressure. Existing models of planetary interiors are based on the assumption of accumulation of mass (and a continuous gradient of pressure/temperature) - not coupled with inflation of a small scale graviton to large scale. In cases where there was inflation (which should generally be the case for stars, planets and dwarf planets), these models must be wrong, as gravitational maximum should generally be represented by a spherical surface of a significant radius - not a point. And if changes in energy levels are frequent, multiple matter pressure/density maxima will exist. Therefore, possibility for complex life is likely to exist in any layer of a mantle and probably for significant time even after graviton deflates and decouples from the body. Taking asteroid bombardment and collisions into account, both, probability for complex life and maximal possible (evolvable) complexity are, with inflation hypothesis, much higher in interiors of celestial bodies. Changes in energy level of a graviton can produce significant thermal energy, allowing complex life even at large distances from a star. The discovered features and activity (complexity) on Pluto and Charon is thus not surprising. The fact that there are no small craters on Pluto should then probably be interpreted as relatively recent tectonic activity, rather than lack of smaller objects in Kuiper belt (as is the current interpretation). Note that, if changes between energy levels of gravitons are relatively frequent (on the order of millions of years or less), crater counting may not be the appropriate method for estimation of surface age (although effect on the surface may be localized). With oscillation (inflation/deflation) of gravitons, not only would surfaces of bodies be periodically refreshed, asteroid bombardments should be more common and relatively periodic as long as oscillation exists. Consider oscillation of a graviton between the 1e moon and superposition with a graviton of the planet it is orbiting. Deflation of a moon graviton would result in decay of locally relativistic energy. While that decay may be relatively slow, deflation of a graviton is not instant and it may even exit the surface with a radius greater than relative 0 (and high velocity) which would cause ejection of compressed real mass toward the planet. Similarly, it may start inflating before it reaches the surface of the planet, creating a tube (exact shape would depend on graviton polarization) increasing in size and curvature toward the centre. At the same time the tube would be filled with fluid (eg. magma, water). Due to graviton polarization (which is always present at some scale and increases with deflation in this case) the graviton is most likely to enter/exit the body at magnetic poles. These will generally be aligned with geographic south and north poles in significantly polarized bodies. However, in case of low asymmetry between momenta of oppositely charged constituent components (or presence of anti-aligned superposition), the most likely point of exit/entrance may be aligned with the orbital plane of the moon. In that case, possible impact latitude may range from 0° to ±a, where a is the sum of planet's obliquity and moon's orbital inclination. Since Earth is polarized (polarization was also likely stronger in the past), most likely location of previous entrances is the south pole. However, polarization of the Earth's current moon is low and Earth's polarization is declining (relatively chaotic and fast movement of magnetic dip poles probably also indicates pending reversal). Therefore, in case of Earth, future graviton entrance/exit latitude may be somewhere between 0° to ±(23.44° + 5.14°)=±28.58° degrees. The current obliquity to orbit of the Moon should likely be added to that range (axis of rotation of the graviton coupled to Moon's body should be aligned with the axis of rotation of the Moon while they are coupled), extending the range to ±35.26°. In the follow-up works I have hypothesized correlation of major mass extinctions with planetary moon(s), even suggesting Earth may have had more moons in the past, but it is also possible that the current moon was [partially] destroyed and reformed multiple times at various distances (albeit increasing with time as real mass, due to conservation of momentum, likely continues on tangential trajectory once uncoupled). Note also that if graviton exit from the moon is non-polar while planetary entrance is polar, asteroids formed with exit will not impact the planet at the pole, unless they too are polarized - which is not impossible, magnetic moment of the graviton could be fossilized in ejecta. Assuming asteroid and graviton decouple near the Moon surface in non-polar exit and asteroid velocity exceeds escape velocity, possible range for asteroid impacts on Earth is a superposition of 0° to ±35.26° and 0° to ±21.9°. Interestingly, the Chicxulub crater, at 21.4° N, is within both ranges. Also interesting is the fact that the volcanic region under ice in Antarctica (with more than 130 volcanoes) is the largest on Earth. On Mars, considering orbital inclination of its moons (or, more likely, moon remnants), Valles Marineris may be the product of impacts formed by asteroids produced by moon graviton decoupling.
Interestingly, Keplerian period T0 is similar between Venus and Mars and between Mercury and Earth. Periods relatively invariant to mass go in favour of the hypothesis of graviton inflation, as this implies proportionality between graviton mass and mass radius (rs).
Note that mass radius for Venus and Mars is simply the core radius (as their cores apparently don't have inner and outer parts at this time). I hypothesize that the formation of the inner core is synchronized with the compression (deflation) of a graviton to a smaller radius. In that case, outer core radius (discontinuity between the core and mantle) is a fossilized former graviton radius, while inner core radius (discontinuity between inner and outer core) represents the current graviton radius. If there is no inner core, current graviton radius is likely the outer core radius (assuming presence of the inner inner core can be excluded). This should be interpreted as a change in energy level of a graviton. Since these are discrete, there are constraints on the radius - in this case it should change (scale) with a square root of 2n where n is a positive or negative integer. Strong discontinuities indicate that changes in energy level are relatively frequent. Therefore, most likely current energy level is the one with a most solid discontinuity (one which most closely matches the corresponding energy level). Due to required oscillation (and frequency of energy level changes), however, discontinuities may somewhat deviate from radii of graviton energy levels in any case. Earth's mass radius has been calculated with the assumption that Earth's graviton surface gravity was initially equal to gravity at the Sun's surface (274 m/s2), from:

$\displaystyle g_s = {GM \over r_s^2} = 274\, {m \over s^2}$

which gives radius rs of 1206 km, almost equal to estimated inner core radius (1216 km). Of course, unless there is mass shielding, this is not presently the case (mass below rs is smaller than M) but I find it likely that all Earth's mass was initially concentrated below rs, only to spread out with energy level changes of the graviton, fossilizing rs as inner core discontinuity (note that some growth on the inner core, and thus rs is expected in this process). Earth's [dominant] charge radius is then most likely at √2 rs, giving gravity equal to 137 m/s2, which gives a g-factor of 2, equal to electron or positron g-factor. Since g-factor is dimensionless, it is relatively scale invariant (eg. electrons and muons have almost equal g-factors) and, assuming large scale Solar System gravitons have been inflated from smaller scale, this implies that Earth's graviton has been inflated from a particle (or particle's graviton) with the same g-factor (muon lepton can be interpreted as inflated electron, or, electron on a different vertical energy level). Note also that √(23) rs gives a radius of 3411 km, very close to the estimated radius of a discontinuity between outer core and mantle (3486 km). The charge radius could be understood as the radius of an real graviton whose gravitational potential has been exchanged for electro-magnetic. It is likely, however, that Earth's real charge radius is a superposition of multiple charge radii (with opposite charge likely to exist at some inner inner core discontinuity). Mercury's mass radius has been calculated similarly, with the assumption of gs = 274/22 m/s2 = 68.5 m/s2, based on inner core constraints from recent studies. For a Venus' mass radius, the gs = 274/23 m/s2 = 34.25 m/s2 has been used, giving rs in agreement with tidal constraints. For Mars, the gs = 274/24 m/s2 = 17.125 m/s2 has been used, this gives a radius roughly 70 km smaller than most recent estimates on Mars' core radius (1650±20 km). This is significantly smaller than previous estimates (1810 - 1860 km), suggesting that Mars' major graviton may have relatively recently changed energy level (decreasing radius), resulting in core shrinking and which may possibly result in core differentiation (creation of solid inner core). Other possible radii of inner levels, ordered by probability (from highest to lowest) are 1118 km (n=3), 790.9 km (n=2), 559.2 km (n=1), ... Pluto's mass radius was calculated with the assumption of a ratio between inner core radius and surface radius equal to Earth's.
Apparently, complexity (excess mass percentage) of terrestrial bodies can be determined by the following equation:

$\displaystyle p = ln{\left[n * 10^{36-\left(2j+5i\right)}\, e^{\left( k\, r \right)} r^{-1}\right]}\, [ \% ]$

$\displaystyle k = {\pi \over 10}$

$\displaystyle i = \sum\limits_{x=0}^j {x}$

$\displaystyle r = d * 10^{-9}$

d = distance of a body from the Sun [m]
with parameters shown in Table \tbl4.
njibodydistance from the Sun d [109 m]complexity p (%)
100Mercury57.997.0
311Venus108.297.2
323Earth149.682.2
136Mars227.966.2
317153Pluto5906.491.1
Table \tbl4: Complexity parameters for terrestrial bodies Note that complexity function has a maximum at Venus or somewhere between Venus and Earth (which is commonly referred to as the habitable zone). However, it will have other maxima, depending on relation between j and r.

Note also that orbital distances of terrestrial bodies scale the same as energy levels of planetary gravitons (with a square root of 2n):

$\displaystyle d_n = d_0 * \sqrt{2^n}$

$\displaystyle d_0 = 38 * 10^9\, m\,\, \text{(terrestrial planets)}$

$\displaystyle d_0 = 8.2 * 10^9\, m\,\, \text{(terrestrial dwarf planets)}$

This is not surprising with self-similar universes. It is even possible (and I find it likely) that gravitons of terrestrial planets initially were inflated to the scale (radius) of current orbital distance, only to collapse (deflate, or localize) afterwards to orbiting spin momenta while coupling with real mass.
Note that d0 should be different for different species of bodies as their graviton wavelengths are of different scale. Chosen d0 for terrestrial dwarf planets is based on n = 19 for Pluto. In reality both parameters may be different.
Calculated distances are shown in Table \tbl5.
njbodydistance from the Sun d [109 m]calculated distance dn [109 m]
10Mercury57.953.7
31Venus108.2107.5
42Earth149.6152.0
53Mars227.9215.0
1917Pluto5906.45937.4
Table \tbl5: Orbital distances of terrestrial bodies Similar to discontinuities in planets, it is expectable that current orbital distances will somewhat deviate from radii corresponding to energy levels. Interestingly, calculated distance for Venus is exactly equal to its perihelion distance, while calculated distance for Earth is almost equal to its aphelion distance (152.1 * 109 m). This strongly suggests that either perihelia or aphelia of a planet is a fossilized energy level radius (initial orbital distance). Also interesting is that calculated distances for Mercury and Mars show higher deviation (from both semi-major and perihelia/aphelia) suggesting that Mercury and Mars are different species of planets from Venus and Earth (implying somewhat different d0), which is not surprising given the order of magnitude different mass. For these two, with n unchanged, d0 of 40.6 * 109 m would give much better results for a semi-major axis - distance of 57.4 * 109 m for Mercury and 229.7 * 109 m for Mars. Splitting of energy levels cannot be excluded, thus, better agreement with a semi-major for Mercury and Mars might indicate their perihelia and aphelia correspond to energy levels created with splitting of [semi-]major energy levels. Note that orbitals of both have significant eccentricity compared to orbitals of Venus and Earth. Orbital distances for other bodies can be calculated similarly. In case of outer planets, Uranus and Neptune are likely to belong to same species.

Event horizon value (EH operator)

Inversion (anti-alignment) is common between entangled gravitons. Polarization (inversion) can be interpreted as a result of splitting of a relative event horizon (superposition of gravitons) into gravitons with anti-aligned components of momenta, which thus includes inversion of scale.
Note that inner and outer planets have relatively anti-aligned components of momenta. Inversion is relatively weak between horizontal energy levels, it is stronger between universes (vertical energy levels).
Such splitting (entanglement) may be described by the splitting operator, one of which is the EH operator:

$\displaystyle EH_{\scriptscriptstyle N}(a,b) = {c \over d} {{d + 1} \over {c - 1}} a = {c \over d} {{d - 1} \over {c + 1}} b$

$\displaystyle a = {{d - 1} \over {c + 1}} {{c - 1} \over {d + 1}} b$

where N = c/d is the event horizon order and both c and d are generally integers. The inverse value:

$\displaystyle {\bigl [EH_{\scriptscriptstyle N}(a,b)\bigr ]}^{-1} = EH_{\scriptscriptstyle N^{-1}}(e,f)$

Assuming the inverse must satisfy the following condition:

$\displaystyle {EH_{\scriptscriptstyle N}(a,b) \over {\bigl [EH_{\scriptscriptstyle N}(a,b)\bigr ]}^{-1}} = {c \over d} {{d + 1} \over {c - 1}} $

this gives:

$\displaystyle {\bigl [EH_{\scriptscriptstyle N}(a,b)\bigr ]}^{-1} = a$

$\displaystyle {d \over c} {{c + 1} \over {d - 1}} e = {d \over c} {{c - 1} \over {d + 1}} f = a$

Since one of the parameters can be omitted, the following notations may be used:

$\displaystyle EH_{\scriptscriptstyle N}(a,b) = EH_{\scriptscriptstyle N}(a) = EH_{\scriptscriptstyle N}(,b)$

Intelligence

Intelligence is the ability of an individual to focus its consciousness and produce objective (logical) thoughts or conclusions optimally correlated in problem solving. If nothing can exist without relativity, relativity must exist in intelligence too. To conserve this relativity, two main classes of intelligence exist: extroverted and introverted. Due to self-similarity of universes and entanglement between different scales, self-similar reality exists on different scales. For strongly extroverted species everything that happens on smaller scales (relative to body size) is virtual and inaccessible. Thus, extroverted species need external stimulation of senses to perceive reality. Introverted species do not need external stimulation and may generally be more energy efficient organisms. In extreme cases, introverted organisms are most of the time closed self-sustaining systems, do not have limbs, most expressed organ is the brain while other organs are subdued and mainly used to support brain function. Generally, introverted organisms may be more intelligent, but with subdued external expression may not be considered intelligent by extroverted organisms, in extreme cases, may not even be considered alive at all. This does not imply that introverted organisms cannot sense the external reality at all (they must be sensitive to radiation at some scale), they just do not act in it with large scale energies. Generally, life-forms are hybrids (superposition) of extroverted and introverted intelligence. This is evident by the existence of dreams in extroverted species, however, lack of conscious control, consistency and coherence make these virtual experiences for most. However, near-death experiences suggest that introversion generally feels more real than conventionally perceived (extroverted) reality.
While complexity of the brain can be correlated with consciousness, apparently, increasing complexity of physical expression beyond the brain is dragging, or blurring, consciousness.
External expression of intelligence of an individual can be interpreted as a product of superposition of intelligence of specific entangled individual cells and proteins, however, the superposition is relative, it is not abstract and therefore exists independently - it can influence individuals of the collective just like it can be affected by the collective. Any class or species of intelligence has two components: material and spiritual. Intelligence is polarized when one component is higher than the other.

Material intelligence = short-term intelligence

Material intelligence (IM) is the amount of intellectual capacity highly correlated with physical phenomena. At its lowest energy level it is used to ensure survival of the body of matter.

Spiritual intelligence = long-term intelligence

Spiritual intelligence (IS) is the amount of intellectual capacity highly correlated with mental phenomena. At its lowest energy level it is used to ensure survival of the soul coupled to the body.

Intelligence potential = real intelligence

The intelligence potential (IP) is a measure of neutral (non-biased) intelligence. The IP is plastic, and, in polarized (disease prone) individuals, can be strongly affected by diseases (such as depression). Generally, a function for determination of IP should look something like this:

$\displaystyle IP = {1 \over {\Delta I}}$

$\Delta I = \Bigl\lvert {1 \over I_{\scriptscriptstyle{S}}} - {1 \over I_{\scriptscriptstyle{M}}} \Bigr\rvert$

$I_{\scriptscriptstyle{S}} + I_{\scriptscriptstyle{M}} = 1$

IM = normalized material intelligence
IS = normalized spiritual intelligence

IS, IM ∈ ℚ > 0

Note that for IS = IM this produces infinity. Since absolute physical infinity is impossible, such result can only be obtained due to limited precision in measurement. Therefore, this infinity should be taken relative and proportional to precision.

Intelligence quotient = amount of extroverted intelligence

Intelligence quotient (IQ) is a conventional measure of externally expressed (extroverted) intelligence. While intelligence potential is invariant to form of intelligence, IQ and similar variants (eg. EQ) are a measure of such intelligence projected to (entangled with) external reality. While IQ might correlate well with IP for extroverted species, it is not well suited for extremes and is completely inadequate for measurement of [introverted] intelligence of introverted species.
Some species of animals on Earth may possess higher amount of consciousness and intelligence than humans. It may just not be generally expressed externally. Signs of complex intelligence are diversity and coherence in brains, or brain equivalents, not in physical expression on generally observable scale.
\ch_added

Artificial intelligence = non-conscious intelligence

The term "artificial intelligence" has been introduced with the advent of computers and is meant to represent the intelligence of machines. However, since computers are obviously not focusing consciousness and producing thoughts in order to do computations, by the definition of intelligence above, computers are not intelligent at all. Even if individual atoms the computer is made of possess consciousness (ie. extremely introverted one) the whole collective is highly unlikely to be coupled to a soul (graviton) that would provide distinct consciousness representing a relative superposition of the collective, in which case a computer would also be a distinct form of life. It should not be impossible for a soul to couple with any localized and mutually entangled collective of living cells (life-forms), which, if atoms/molecules are alive, should first include transistors and, if these are alive then larger components and finally computers. But, considering the hypothesized requirements and [lack of] evidence, the possibility is probably infinitesimal. Computers are here for a long time now, they have been exponentially increasing in processing power and complexity, yet, there is no sign of conscious computation in any of them. With recent developments, interaction with computers is increasingly becoming similar to interaction with conscious human brains and it may become hard to distinguish between artificial and real or conscious intelligence. If one would want to increase the probability for coupling, however, one probably should be increasing physical similarity between human brains and computers, in terms of mass and energy consumption. But even then, the probability could remain infinitesimal, unless these computers become organic - where transistors are replaced with living cells (neurons) and these cells are grown similarly to how brains are developed in vivo. Everything suggests that souls and bodies co-evolve and that is the reason for the lack of coupling of souls with conventional computers - lack of compatibility. This further suggests that, in order for souls [that usually couple with human brains] to couple with conventional computers, human brains should be gradually becoming more computer-like - eg. by replacing neurons with transistors, however, transistors are not living cells and this replacement is likely to be diluting, or reducing the amount of, human consciousness. In other words, human consciousness would be delocalizing gradually and real intelligence would be traded for artificial intelligence. In any case, this replacement can hardly gradually occur over multiple generations (how possible it is to alter inheritable human genes to produce a silicon transistor instead of a living neuron, or, how likely it is for adaptation to transistors to become heritable by the soul?), while it is evident that consciousness/life cannot emerge from parts assembled into a whole - it needs to be coupled at conception and grow with the whole. Anything else is mimicry which one may refer to as artificial consciousness but should not confuse with real, living and emotional consciousness.
Infinitesimal chances are, however, never an issue for gamblers or those who prefer illusion over reality. So, unless the existence of souls is globally accepted, forced shutdown of a conventional computer could be considered immoral in the near future.
Added definition of life.

Life

A form of life is a coupling of a soul (graviton, or superposition of gravitons) and a body. Everything existing must be relatively alive and relatively non-living - the amount of life will be relative to the observer (even uncoupled graviton is always relatively uncoupled or relatively delocalized, not absolutely), as well as classification of that life. Coupling of physical and mental components with different ratios of physical to mental activity suggests two main classes - extroverted and introverted life, correlated with extroverted and introverted intelligence. In general, any life-form is a hybrid of extroverted and introverted life, although generally one form may dominate. In extremely extroverted life on particular scale, brain, or brain equivalent organisation, is extremely subdued (or at least coherence of its components), distinct individual consciousness is minimal and has no influence on physical processes of the body (or the organic collective forming the body). In life-forms that have developed introversion, brain will dominate and will be able to influence physical processes of the body through mental pathways, affect the constituent organs and collective consciousness of smaller organisms forming its biome. In extreme extroversion, development of the organism from conception is driven dominantly by interpretation of physical genetic code, such as DNA. In complete introversion, there is no conventional physical genetic code evolving the individual (generally, however, such code will be involved in development and evolution of individuals forming its biome), instead, development (evolution) of the collective into distinct individuality is driven (or guided) by the interpretation of mental genetic code - the code stored within the soul particle. Mechanism involved is likely recursive entanglement, starting with entanglement of a soul with a superposition (which is a physical graviton at some scale) of genomes of biome individuals (effect on superposition is reflected in individuals). However, evolution of either, body or soul, requires coupling of the two. In extreme extroversion, it is the body that will effectively control the soul evolution (development), in extreme introversion, vice versa.
Note that all terms are relative, even "mental" and "physical" - mental is physical at some scale, and vice versa.
Planets, in example, seem to be extremely introverted organisms - there is no apparent large scale physical DNA equivalent involved in development of a planet even though evolution of its biome is relatively equivalent to DNA coded embryonic development. The equivalence is there because souls and bodies co-evolve, influence and mirror each other (albeit with a phase shift).
Nature does not hide anything. Contrary. Things one cannot see on a small scale, are shown on a big screen. But one may need to collapse its ego-system to see all these systems as living eco-systems.
Added definition of god. God Every lifeform whose rest mass (energy) is by one or multiple orders of magnitude greater than life that lives on it and in it, is, for that life, a god.
While the notion of gods is commonly reserved for metaphysical contexts of religion, where the lack of proper definition may be generally desirable, definition of a god correlated with physical phenomena can deepen the understanding of some existing religions and provide meaning to those who are not satisfied with hidden agenda behind materialistic rituals periodically organized to worship untouchable interpretations.
Constant A constant is a property of a system, non-changeable in particular space and/or time domain (nothing is constant over all space and time). Depending on the size of domain, constant may be weak or strong. Naturally, all system properties oscillate. Existence of constants is thus relative to observable resolution of space/time by a particular observer. Proper reference frame Nothing is absolutely at rest and observation of evolving phenomena will be more common and useful than relatively non-changing phenomena. However, relative constants are desirable as reference points and to reduce the complexity of interpretation where influence of increased complexity on the outcome is negligible. A suitable reference is then one relative to which the constancy of variables (xi) of the observable system is maximal: $\displaystyle \lim \sum{\left(\Delta x_i(n) \gt {\hbar}_n\right)} = 0$ However, due to scale invariance and relativity of constants, proper interpretation will sometimes require a proper reference frame rather than simply a suitable one. Generally to be used in comparison of systems of differently scaled, but otherwise, equal species. In case of polarized frames, a proper [neutral] reference frame may be required even in case of systems of equal scale, to provide more accurate (objective) view of reality.
Quantized inflation of angular momentum It was previously hypothesized that radius of a neutral (weakly polarized) graviton scales with a square root of 2n, where n is a positive or negative integer. This can be inferred from quantization and scaling of graviton momentum. Assuming that graviton is inflating from a boson whose momentum projection on a particular axis of quantization (or, when components perpendicular to that axis are annihilated) is 1 while other component (or superposition of other components) is equal in value and perpendicular to that axis, the value of total momentum will be √2 : $\displaystyle L = m\, v\, r = \sqrt{2}\, \hbar$
Note that this is equivalent to superposition of two aligned fermions: $\displaystyle L = \sqrt{l\left(l + 1\right)}\, \hbar = \sqrt{ 2 {1 \over 2 } \left( 2 {1 \over 2} + 1\right)}\, \hbar = \sqrt{2}\, \hbar$ However, a 1 ℏ momentum can also be a result of superposition of anti-aligned spin-2 and spin-1 bosons. Since there are no absolutely massless and absolutely neutral particles in CR, coupling of spin-2 gravitons and spin-1 photons should be intrinsic, the difference will only be in scale. Gravity and electro-magnetic force are thus generally coupled and one force may be exchanged for the other but none is absolute 0 in any coupling. If scale difference is large - eg. in electron the electric force dominates, one component can be considered as relative 0. The strong confinement of quarks in protons can be interpreted as intrinsic entanglement strongly evolved between two forces.
If that momentum is inflated with conserved ratio between values of constituent components of the vector (non-dimensional ratios seem to be generally well preserved during inflation/deflation), proper relativistic treatment here involves either scaling of metric or the constant in such way that the value of the constant in the current vertical energy level is, in case of inflation, equal in value to momentum in previous energy level. In example, for a single jump in energy level, new momentum is: $\displaystyle L_n = \sqrt{2}\, {\hbar}_n = \sqrt{2}\, L_{n-1} = \sqrt{2} \left( \sqrt{2}\, {\hbar}_{n-1} \right) = {\sqrt{2}}^n\, {\hbar}_0 = \sqrt{2^n}\, {\hbar}_0$ Assuming now that the speed of an non-coupled graviton is equal to the speed limit of space (cn) that speed is relatively constant for energy levels of similar magnitude (if, however, the metric is scaled and the ratio between space and time units is conserved, the speed is locally invariant to any scale). With rest mass remaining constant (relative 0 for a non-coupled graviton), the radius must scale the same as the momentum: $\displaystyle r_n = \sqrt{2} \left( \sqrt{2}\, r_{n-1} \right) = \sqrt{2^n}\, r_0$ Note that inflation of momentum will require additional energy apart from rest energy of inflating quanta. However, sometimes the exchange of momentum components will result in inflation of one component and deflation of the other with no significant difference in the value of momentum. Due to low energy triggers (relative 0) such inflation/deflation (eg. mass oscillation) should generally be inherent for all energy although it may not always be apparent due to time dilation correlated with scale (in non-scaled metric). As even such inflation must result in some change in momentum (even if generally negligible), this type of scale inversion may also be referred to as inflation/deflation of momentum. Note that energetic inflation/deflation generally occurs with annihilation of pairs of particles on original scale. The process can be symmetric (producing particle/anti-particle pair with equal mass) or asymmetric (producing particle/anti-particle pair with asymmetric mass distribution). Inflation/deflation is not limited to bosons or boson pairs. Inflation of a fermion (generally paired with exchange of electro-magnetic potential for gravitational) will similarly scale the original momentum, in which case radius may not scale with √2n. During the process, possibility may exist for some components of momentum to annihilate with others preserved (partial annihilation), producing hybrid momenta. Note that, at full capacity, imaginary mass is equal to real mass, angular velocity is Keplerian and equal to: $\displaystyle v_n = \sqrt{GM \over r_n} = \sqrt{{G \over r_n} \left( m_{img} + m_{re} \right)} = \sqrt{2} \sqrt{{G \over r_n}\, m_{img}}$ Adjacent Keplerian velocities thus also scale with √2. If Keplerian velocities are quantized, escape velocity then has to be equal to Keplerian velocity of the next higher energy level of the velocity component. $\displaystyle v_e = v_{n+1} = \sqrt{2}\, v_n = \sqrt{2} \sqrt{G M \over r_n} = \sqrt{2} \left( \sqrt{2} \sqrt{{G \over r_n}\, m_{img}} \right)$
Note that, if rn scales with a square root of 2n, this velocity corresponds to Keplerian velocity at rn-2.
Discrete states of invariance = energy levels Discrete states of invariance are stable states of energy (universes) with relatively invariant (entangled) mechanics. There are vertical and horizontal discrete states (energy levels). In horizontal states, energy between levels is generally of the same order of magnitude. In vertical states, difference between energies is in multiple orders of magnitude. One example of horizontal states are electron energy levels in an atom, whereas two major vertical states are an atom and a planetary system. Update in Progression of states. Progression of states Progression of discrete states of scale invariance is exponential. For horizontal states, in the top-bottom approach (energy inversely proportional to n): $\displaystyle E_n = {E_1 \over n^2} = E_{n-1} {\biggl ({n-1 \over n}\biggr )}^2\,;\;\; n>1,\, E_1 = \text{const.}$ For major vertical states (energy proportional to n): $\displaystyle \log(E_n) = \log(E_{n-1}) + (n+1)n = \log(10^{(n+1)n} E_{n-1})$ For example, mass of Neptune (U1.e) can be obtained from standard electron (U0.e) mass: $\displaystyle \log(M_{\scriptscriptstyle{N}}) = \log(M_e) + (n+1)n\,;\;\; n=7,\, M_e = 9.10938356 * 10^{-31}\, kg$ $\displaystyle M_{\scriptscriptstyle{N}} = 10^{\log(M_e) + 8*7} = 0.910938356 * 10^{26}\, kg$ Note that this equation is a variant of the equation (1.8) (derived in chapter Definitions - Electric polarization and charge/mass exchange) and may be interpreted as a special case of vertical energy levels distribution. The equations (1.6) and (1.8) are more general and should be closer to reality (as mass inflation/deflation generally involves charge exchange, which is not apparent in the equation above). However, it is the order of magnitude here that is of relevance, not high precision in value. Mass of the equivalent particle on n = 5 level can also be obtained from electron mass: $\displaystyle M_e = 10^{\log({M_p}_e) + 7*6}$ $\displaystyle {M_p}_e = 10^{\log(M_e) - 7*6} = 9.10938356 * 10^{-73}\, kg$ This particle is likely to be a component of photons (a half-photon), or U-1 electron (U-1.e).
Standard photon carries information on standard atoms, in such way that in localized form relatively mirrors atoms, albeit on different scale and probably with a different ratio in strength between neutral and charged forces. Its simplest form then can have two components (eg. mirroring hydrogen atom charges) or half-photons, electron half-photon and positron (proton) half-photon. Complex forms can be considered as superposition of simpler forms.
Assuming simple pairing of positive and negative charge, mass of the simple standard photon is then roughly twice this mass: $\displaystyle M_p = 1.821876712 * 10^{-72}\, kg$
I hypothesize that the Solar System is the equivalent of a Carbon-10 (10C) atom. It has been inflated from U0.10C state (or even U-1.10C) and electro-magnetic potential has been exchanged for gravitational in the process. Evidence is presented here and in follow up works. Of course, the values obtained above will deviate slightly from current values due to required oscillation (significant time dilation of oscillation on large scale) and the fact that energy of the outermost electron in Carbon-10 (corresponding to Neptune) slightly differs from the free electron energy used above. Note that levels calculated above may be considered major vertical energy levels - there are smaller ones. In example, lepton mass oscillation can be considered as oscillation between minor discrete vertical energy levels, or sublevels. Note also that rest mass is relative - it may be localized to a particle but it may be spread in a wave-form where it can be considered as 0 relative to space (exchange between mass and frequency).
In effect, Neptune is a [vertically] excited electron, and electron is the excited photon [scale] electron. It is obvious now that the difference in strength between electric and gravitational force between two electrons stems from the difference in rest mass between the standard electron and photon [electron] - 42 (7*6) orders of magnitude.
Photons can consist of different particles. But different interpretations are also possible. If the strength of electric force is invariant to mass of interacting particles, carrier photons produced with proton-electron interaction can be considered as having the same mass as those produced in electron-positron interaction. However, that might not be the case in reality. Gravity carrier particles (gravitons) can couple to half-photons, in which case mass of one half-photon in proton-electron interaction is inflated and photon can be considered as a carrier of gravity too. Instead of half-photon mass inflation, another possibility is that a positron is produced (as intermediate force carrier particle) in proton-electron interaction. Both interpretations may be equally present in reality. Coupling to space-forming gravitons obviously enables mass oscillation of particles such as photons. Note also that entanglement between charges in never absolutely lost. Motion of electrons outside of atoms (or ions in general) will still result in emission of paired half-photons as long as that motion is relative to space of some opposite charge (emission of energy is generally the result of motion relative to space). In case of electro-magnetic energy space may be quantized into magnetic field tubes with density of tubes increasing with distance from the source charge (volume of the tubes remains constant in one interpretation of weak entanglement so they are thinning with distance). Distance between the tubes is distance between discrete energy levels and only at infinite distance from the source (assuming unlimited force range) distance between the tubes would be zero. Emission of radiation outside of atoms is thus still the result of energy level changes relative to some other charge. When localized within the atom on a particular energy level motion of the electron is coupled to angular momentum of specific magnetic field tube(s), electron is at rest relative to space and there is no photon emission. The reason there is no photon emission due to electron motion relative to protons of other atoms must be dragging or distortion of weaker tubes by the local field (note that proton field is effectively dragging the electron field with the electron). Note also that motion of electron on a particular energy level inside the atom, due to lack of resistance, is equivalent to motion of charge in superconductors where magnetic field tubes are expelled outwards. Similar to coupling of electron half-photons (polarized gravitons) to proton half-photons in case of electro-magnetic energy, non-polarized electron gravitons are coupled with non-polarized proton gravitons inside the atom. However, the scale of gravitons forming space of standard (U0) protons and electrons may generally be negligible compared to photons. On U1 scale this is inverted. Changes in energy level within the U0 atom are likely generally synchronized with temporary inversion of half-photon orbital angular momenta. In U1 this is inversion of graviton orbital angular momenta. Retrograde orbits are then the result of graviton momentum inversion and are unstable if graviton momentum is not aligned with real mass momentum. Even if electro-magnetic and gravitational potential may be generally inverted between adjacent vertical energy levels, localized reversal of inversion is possible on either level. In one interpretation, it is relative motion that creates (inflates) polarization. Boson condensates on U0 scale could then represent such localized reversals with limited range.
With a change in vertical energy level, nature of the force evolves, exchanging polarization (electro-magnetic potential) for neutral gravitational potential or vice versa, depending on the direction of evolution.
Similar to neutral pions, simple standard photon is composed of a particle/anti-particle pair (eg. U-1.e-/U-1.e+). These may generally have anti-aligned 1/2 spin momenta, with aligned orbital momenta forming total spin of the photon.
Note the following: $\displaystyle {M_p}_e = { M_e \over M_{\scriptscriptstyle N} } K_{\scriptscriptstyle A} = {M_e \over M_{\scriptscriptstyle N}} 1.02413 * 10^{-16}\, kg$ where MN = 1.02413 * 1026 kg is the mass of Neptune, and quantum of mass KA = 1.02413 * 10-16 kg (5.7 * 1019 eV = 57 EeV) is the mass (energy) of asymmetry. If standard electron mass would be equal to the current value of KA and half-photon would have mass equal to 1.02413 * 10-58 kg, the adjacent electron energy levels to U0 would be symmetric relative to the electron.
Symmetry could also be achieved simply by decreasing half-photon mass to 8.1 * 10-87 kg (setting KA = Me = 9.10938356 * 10-31 kg).
If vertical asymmetry needs to be preserved, the asymmetry breaking energy of KA - Me ≈ KA = 5.7 * 1019 eV must be the energy limit for standard particles produced in any universe conforming to the above progression of vertical states as that energy could, through annihilation, inflate electron mass to KA.
Note that symmetry by decrease of half-photon mass requires considerably more energy - 8.9 * 10-15 kg (4.99 * 1021 eV = 4988 EeV).
At first, it might seem unclear why would it be necessary to preserve vertical asymmetry, but the reason is equivalent to the reason for preservation of horizontal asymmetry. Particles with mutually inverted properties annihilate when distance between them is reduced to relative 0. Whether this annihilation occurs within the atom or outside the atom, it has to occur at a particular energy level. This thus requires symmetry relative to that level. Since adjacent vertical energy levels have inverted properties, symmetry could lead to annihilation of adjacent energy levels. Different scales (universes) are entangled (correlated) and if this entanglement is physical (in CR, it has to be) than that entanglement can be interpreted as a dimension in space. If correlated but anti-aligned properties are universally attracted and relatively annihilated when at equal distance from a particular energy level, conservation of existence requires conservation of asymmetry in scale.
Note that energy levels are physical. In case of electro-magnetic energy, energy levels are magnetic field tubes. Splitting of energy levels can then be interpreted as splitting of magnetic field tubes, although alternative interpretations are possible.
Creation of symmetry would require adjustment of half-photon mass in either case, therefore the energy of 5.7 * 1019 eV may be interpreted as the 1st order limit, with the 2nd order of 4.99 * 1021 eV. Studies indeed confirm the 1st order limit as the cut-off energy for intra-galactic sources. It is also in agreement with measurements of GZK (Greisen-Zatsepin-Kuzmin) energy limit (cut-off) for protons - 5.6±0.5±0.9 * 1019 eV (uncertainties are statistical and systematic, respectively). Interestingly, particles with higher energy have been detected, on the order of 1020 eV, but no particle has been produced or observed exceeding the 2nd order limit. Effectively, thus, the relative superposition of the 1st and 2nd order may be interpreted as real limit. In any case, increasing number of particles with such high energies could indicate instability of the observable universe. As mass depends on the number and mass of coupled gravitons rest mass is different at different energy levels. This is not limited to vertical energy levels, although in case of horizontal levels difference may generally be relatively negligible.
Changes in energy levels are generally correlated with changes in frequency. Consider photons. Even though rest masses of constituent half-photons are quantized, their orbital momenta must be proportional to frequency if speed of photons is invariant to frequency.
Rest masses of gravitons are quantized too and will be different on different energy levels, but probable rest masses can be deduced assuming scale-invariance of non-dimensional mass ratios. These ratios should be well preserved between vertical energy levels. In example, one likely rest mass of an U-1 scale graviton can be deduced from the ratio of an U0 graviton rest mass and electron mass (as noted before, at full capacity, mass of the graviton is half the total mass): $\begin{aligned}\displaystyle M_n = {{{1 \over 2} ^{10}C\text{ atom mass}} \over {{1 \over 2} \text{electron mass}}} M_p = {{^{10}C\text{ atom mass}} \over {\text{electron mass}}} M_p &\approx {10.016853\, u \over M_e} M_p \\ &= 2 * 1.663337576 * 10^{-68}\, kg \\ &= 3.326675152 * 10^{-68}\, kg\end{aligned}$
Obviously, half of mass of an atom [nucleus] is not the mass of a single graviton, rather a superposition of multiple gravitons, however, such superposition on U-1 scale is likely to be interpreted as elementary from U0 reference frames. Different atoms with different masses can be interpreted as having gravitons with different masses, however, masses of these gravitons may be limited to a couple of generations and difference in atomic mass could be the difference in real mass (over-capacity, under-capacity). Another interpretation, however, may be more likely. If gravitons are oscillating in rest mass between different vertical sublevels, oscillation may be such that a superposition of oscillating mass produces the net gravitational effect matching coupled real mass. In more massive nuclei, gravitons would simply spend more time inflated to higher energy levels. Complexity (diversity of charge coupling) in strong force should be correlated with this oscillation as it is coupled with exchange between electro-magnetic and gravitational potential.
Note that the obtained mass is in agreement with other calculations of graviton mass (≈10-68 kg), based on existing theories and observation. Assuming that U0 gravitational mass has been inflated from U-1 scale, dark matter of U0 scale can be represented by the inflated superposition of U-1 gravitons (not coupled with real mass). In that case, assuming the superposition is interpreted as a single graviton, its mass is at least roughly equal to half the 10C atom mass. More likely, however, is inflation of pairs of such gravitons, giving mass roughly equal to 10C mass: $\displaystyle U_0.M_n = 10.016853\, u = 1.663337576 * 10^{-26}\, kg$ The mass corresponds to energy of 9.33 * 109 eV (9.33 GeV) and evidence exists in favour of such dark matter particles. Small update/correction in Progression of states.
Note that there is no single dark matter particle. Any naked graviton of any scale is a particle of dark matter. Note also that [rest] masses of standard photons and neutrinos may generally be determined from momentum, relative to c constant. Masses obtained here are invariant to c. Obtained half-photon mass corresponds to a particle of vacuum energy density (9.9 * 10-27 kg/m3), with a radius of U0 scale Neptune equivalent (≈3.8343 * 10-16 m) and orbital velocity of ≈3.5 * 1026 m/s. Physically, a particle with such momentum can be obtained with a collapse of a gravitational maximum of U0 Neptune equivalent (standard electron) to U-1 scale energy, converting mass to velocity to conserve momentum (note that this speed would be valid even in GR, if the half-photon is understood as quantum of vacuum - here it does have vacuum energy density, and the vacuum is interpreted as space). Rest photon mass relative to standard c (when its spin momentum is not taken into account) can then be obtained through conservation of momentum (p=m1v=m2c), and it is ≈2.1 * 10-54 kg. This mass agrees with experimentally obtained photon mass through its interaction with matter. But the obtained photon rest mass of 1.821876712 * 10-72 kg may also be validated through conservation of energy. In CR, relativistic speed limits are different between different scales of energy. For standard protons and electrons speed limit is the standard speed of light (c), however, for photons with rest mass obtained above, speed limit must be much higher. The reason one does not directly observe photons travelling at greater speeds is probably because faster photons are not entangled (and do not directly interact) with atoms (quantum entanglement, however, could be interpreted as indirect observation of superluminal photons although it is questionable whether these should be interpreted as standard photons, and this could also be interpreted as stretching of [units of] space). Linear or angular momentum of unconfined photons is effectively limited by density/pressure of larger scale of space, so the superluminal velocities are limited to smaller scales of space (subspaces). In other words, as the photon expands or inflates from scale U-1 it is slowed down to c, however, the constituent quanta could still have spin momenta exceeding c, proportionally to frequency. Validation of calculated photon masses and velocities can be found in the analysis of the Solar System in CR context (chapter Quantum nature: Outermost angular momenta and c1 confirmation) and other follow-up papers, but also here in some of the following chapters.
Sub-major levels Energies (universes) must conform to general oscillation. Energy on one level (scale) will oscillate in mass between eigenstates on lower scales as well. Energy on a particular major vertical energy level will generally oscillate between 3 sub-major eigenstates. In example, standard electron, muon and tau particles (leptons) represent such 3 eigenstates of the same energy. But this is not limited to leptons. All particles should oscillate in mass and generally do so with the same ratio between masses as is the case with leptons (this is because they're generally all entangled with the same adjacent major vertical energy levels). Since these ratios are non-dimensional they will be well preserved even across major vertical energy levels. Note, however, due to time dilation, intermediate states (superposition) may become relatively stable states (and thus observable) on larger scale from the same reference frame. All components of atoms, photons and all other particles are thus oscillating in mass, with ratios between masses being: $\displaystyle {m_{\mu} \over m_e} = {M_{\mu} \over M_e} = 206.768$ $\displaystyle {m_{\tau} \over m_e} = {M_{\tau} \over M_e} = 3477.22$ Mτ = standard tau [electron] mass = 1776.86 MeV/c2
Mμ = standard muon [electron] mass = 105.6583755 MeV/c2
Me = standard electron mass = 0.511 MeV/c2
where me represents lowest mass eigenstate, mτ represents highest mass eigenstate, while mμ is the intermediate mass eigenstate. Are components of general force (electro-magnetic, gravitational) exchanged with oscillation between sub-major levels as well? Probably, but this may not be observable. Added chapter Oscillation of photon mass. Oscillation of photon mass Mass of all particles should be oscillating and photon cannot be an exception. Its constituent particles (half-photons) should, as standard leptons, oscillate between 3 generations. Assuming calculated mass is the lowest mass, remaining two values can be calculated from tau/muon/electron mass ratios, as established previously. For Mτ = 1776.86 MeV/c2, Mμ = 105.6583755 MeV/c2 and Me = 0.511 MeV/c2: $\displaystyle M_{\gamma \tau} = {M_{\tau} \over M_e} M_{\gamma e} = {1 \over 2} 6.335068208 * 10^{-69}\, kg$ $\displaystyle M_{\gamma \mu} = {M_{\mu} \over M_e} M_{\gamma e} = {1 \over 2} 3.767055455 * 10^{-70}\, kg$ $\displaystyle M_{\gamma e} = {M_p \over 2} = {1 \over 2} 1.821876712 * 10^{-72}\, kg$ $M_{\gamma e}$ = electron half-photon rest mass
$M_{\gamma \mu}$ = muon half-photon rest mass
$M_{\gamma \tau}$ = tau half-photon rest mass

To prevent annihilation, masses of two constituent particles should be equal for 0 time relative to other combinations (relative 0). The oscillation of one half-photon should thus be anti-aligned with the other (phase difference of 180° in ideal case) and the whole system (photon) can be reduced to two-body oscillation. Here the intermediate (0 time) state must be the state with lowest mass (state lifetime is proportional to mass).
Note that, there must exist a threshold frequency - at which point two half-photons will fuse and form a graviton half-particle.
Due to non-zero mass, photon must have a range, roughly equal to [reduced] Compton wavelength, ie.: $\displaystyle r = {\hbar \over {M_p c}} = {\hbar \over c} {1 \over {M_{\gamma \tau} + M_{\gamma \mu}}}$ ℏ = h/(2π) = 1.054573 * 10-34 Js
c = 2.99792458 * 108 m/s
Massive particles will generally either gain or lose energy in motion. There are various interpretations for loss of energy of a particle such as a photon: If motion is orbital, energy may be generally cyclically replenished. However, in reference frames where that motion is linear, loss or gain of energy will exist. However, even if the energy is not replenished, loss of mass may be negligible or unobservable, especially for low rest masses such as that of a photon.
Obviously, r must also be roughly equal to the radius of observable universe (universe that can be observed) - when calculated for lowest rest photon mass at rest frequency. Assuming mass oscillation is synchronized with coupling of photons to gravitons, both photon velocity and frequency will change with gravitational potential. Acceleration of emitted photons must also oscillate but may be effectively constant with high frequency of mass oscillation. For effective mass equal to Mγτ + Mγμ, acceleration is: $\displaystyle a = \pm {1 \over 2} c^2 {c \over \hbar} \left( M_{\gamma \tau} + M_{\gamma \mu} \right) = \pm {1 \over 2} {c^3 \over \hbar} \left( M_{\gamma \tau} + M_{\gamma \mu} \right) = \pm 4.287091748 * 10^{-10}\, {m \over s^2}$ For 2Mγe: $\displaystyle a = \pm {1 \over 2} {c^3 \over \hbar} 2 M_{\gamma e} = \pm {c^3 \over \hbar} M_{\gamma e} = \pm 2.327418326 * 10^{-13}\, {m \over s^2}$ Generally, taking into account phase shift and using relativistic (gravitational) mass, the equation becomes: $\displaystyle a = \pm {1 \over 2} {c^3 \over \hbar} \left({1 \over 2} + {1 \over 2}\sin^2\phi \right) \Delta M {1 \over {\sqrt{1 - {f^2 \over {f_n}^2}}}}$ $\displaystyle \Delta M^2 = 2^2 {{{M_1}^2 + {M_2}^2} \over 2} = 2 \left({{M_1}^2 + {M_2}^2}\right)$ where ΔM is the superposition of mass, f is photon spin frequency, fn is the maximum possible photon spin frequency and ϕ is a mixing angle (equal to 90° for aligned and 0° for anti-aligned oscillation of half-photons). For previously determined 1st order maximum energy of Mn = 1.02413 * 10-16 kg (5.7 * 1019 eV), fn is: $\displaystyle f_n = {c \over {\lambda}_n} = {E_n \over h} = {{M_n c^2} \over h} = 1.389120683 * 10^{34}\, Hz$ Calculated acceleration for various combinations and f << fn is shown in Table \tbl6.
M1M2ϕ [°]a [m/s2]
MγμMγμ90±0.481235302 * 10-10
MγμMγμ0±0.240617651 * 10-10
MγτMγμ90±5.732686887 * 10-10
MγτMγμ0±2.866343444 * 10-10
MγτMγτ90±8.092948194 * 10-10
MγτMγτ0±4.046474097 * 10-10
Table \tbl6: Acceleration for various photon mass eigenstates Acceleration of photons may be misinterpreted as a change in Doppler shift (change in velocity of the source of emission) when mass of the photon is considered to be 0.
There are two interpretations of photon acceleration (deceleration). In one interpretation photon linear momentum remains effectively constant - the change in energy (frequency) is reflected in momenta of its constituent quanta. However, changes in spin momenta are generally correlated with changes in orbital/linear momenta and acceleration of photons will be a superposition of both interpretations, only the dominant component will vary, depending on properties of space.
Indeed, analysis of motion of Pioneer 10/11, Galileo, and Ulysses spacecraft shows anomalous relatively constant weak long-range acceleration of ~ - (8±3) * 10-10 m/s2 (deceleration relative to the Sun) for which no satisfactory explanation has been found, with the assumption that photon mass is 0. Obviously, predicted photon mass oscillation due to gravitational potential can fully explain this anomaly. However, if the anomaly is the result of photons coupling to gravitons (dragging by dark matter), masses - and therefore accelerations, in calculations above should be doubled or paired, depending on interpretation.
There are two interpretations. Either photon mass can be considered as relative 0 while graviton is considered as superposition of two of above calculated masses, or the photon mass is real mass while gravitons inflate to match that mass.
Recently, dark matter was indeed proposed as the solution to the problem. However, in that solution no effect on photons is considered, rather on spacecraft exclusively. It should be questionable, however, whether these gravitons form the gravitational potential of the Solar System, or the galaxy (as proposed, effectively, by the cited work).
Anomalies have been detected on other spacecrafts. Table \tbl7 shows the anomalies and calculated accelerations for matching graviton configurations.
spacecraftdistance [AU]anomaly [m/s2]possible graviton configurations [M1, M2, ϕ]calculated acceleration [m/s2]
Pioneer 10 (<1999)40-608.09±0.20 * 10-102 * [Mγτ, Mγτ, 0°]8.092948194 * 10-10
Pioneer 11 (<1999)<308.56±0.15 * 10-10[Mγτ, Mγτ, 90°] + [Mγμ, Mγμ, 90°]8.574183496 * 10-10
Ulysses (1992-1995)1.3 - 5.212±3 * 10-10[Mγτ, Mγτ, 90°] + [Mγτ, Mγμ, 0°]
[Mγτ, Mγτ, 90°] + [Mγτ, Mγμ, 90°]
12.139422291 * 10-10
13.825635081 * 10-10
Galileo (1993)~38±3 * 10-102 * [Mγτ, Mγτ, 0°]8.092948194 * 10-10
Pioneer 10 (2003)828.74±1.33 * 10-102 * [Mγτ, Mγτ, 0°]
[Mγτ, Mγτ, 90°] + [Mγμ, Mγμ, 90°]
8.092948194 * 10-10
8.574183496 * 10-10
New Horizons (2008)813.2±0.6 * 10-10[Mγτ, Mγτ, 90°] + [Mγτ, Mγμ, 90°]13.825635081 * 10-10
Table \tbl7: Anomalies and proposed solutions (anomaly data sources: a, b) Evidently, the predicted mass oscillation is in remarkable agreement with observations.
Interestingly, the results suggest that in all solutions masses should be equally aligned (both either 0°, or 90°). This would then imply that Ulysses anomaly is the same in value to New Horizons anomaly.

Generally, any particle with finite range (mass > 0) should be converting radial component of velocity to angular orbital velocity with distance relative to the source, although this can be subdued if the range is continuously extended by mass loss. This is a consequence of entanglement (and physical interpretation of that entanglement on particular scale!) of emitted particles with the source, however, entanglements can change (decrease/increase). Added chapters Evidence for photon mass and its oscillation and Photon/graviton range. Additional evidence for photon mass and its oscillation Observed acceleration is a solid evidence for photon rest mass in predicted range (10-68 - 10-72 kg). However, generally, photon mass may be obtained from linear (angular) momentum. Since most of its effective mass is in spin momentum (effective v ≈ 1026 m/s) or constituent spin momenta, experimentally obtained photon mass will be significantly higher than the calculated rest mass. Using conservation of momentum, one can calculate these masses for various pairs of half-photons, ie: $\displaystyle m_1\, v = m_2\, c$ $\displaystyle M_{\tau\tau} = 6.335068208 * 10^{-69} * 3.5 * 10^{26} * {1 \over c} = 7.39603 * 10^{-51}\, kg$ $\displaystyle M_{\mu\mu} = 3.767055455 * 10^{-70} * 3.5 * 10^{26} * {1 \over c} = 4.39794 * 10^{-52}\, kg$ $\displaystyle M_{e e} = 1.821876712 * 10^{-72} * 3.5 * 10^{26} * {1 \over c} = 2.12699 * 10^{-54}\, kg$ c = 2.99792458 * 108 m/s Indeed, experimentally obtained photon masses range from 10-50 to 10-54 kg.
Note that here the same velocity has been used for all photons. In reality, some difference in orbital velocity of half-photons may exist, especially for heavier half-photons where it could result in inflation of photon mass to the order of 10-50 kg or beyond.
Photon/graviton range Obviously, photon can indeed travel vast distances and that would not be possible if its rest mass would range from 10-50 to 10-54 kg. However, as gravitons exist on different scales, this range of masses could represent another vertical sublevel. If so, these would have the following spatial ranges: $\displaystyle r_{\tau\tau} = {\hbar \over c} {1 \over M_{\tau\tau}} = 47561.69\, km$ $\displaystyle r_{\mu\mu} = {\hbar \over c} {1 \over M_{\mu\mu}} = 7.99846493 * 10^8\, m$ $\displaystyle r_{e e} = {\hbar \over c} {1 \over M_{e e}} = 1.653828596 * 10^{11}\, m$ These ranges are interesting because they could be correlated with celestial bodies. Eg. for a photon/graviton mass of 5.52 * 10-50 kg the range would be equal to Earth's radius. I hypothesize that such particles do exist and are carriers of electro-magnetic and gravitational force for large scale (U1) gravitons. Photons of lower rest mass (10-68 - 10-72 kg) are carriers of such force for real mass of U0 scale - standard atoms, which are filling the wells of large scale maxima. In that case, empty large scale gravitational wells should be devoid of, not only standard atoms, but these photons/gravitons too (the wells would be transparent for such photons but would be unable to produce them due to absence of real mass) unless escape velocity of a maximum is > c (black hole maximum). This implies that gravity of such wells has a very limited range. However, there are other interpretations - perhaps the very shielding effect of real mass in a well manifests itself in the reduction of range (rest mass increase) of constituent gravitons of the well once these are absorbed (coupled). Indeed, that would be the most plausible explanation for shielding effect, assuming it exists.
The strong nuclear force then becomes a result of exchange of large source rest mass (~1011 kg black hole) for large force carrier mass, resulting in range decrease (collapse). Proton radius can then be interpreted as a fossilized black hole radius. This has to be one of the most fascinating features of the observable universe - not showing any care for absolute numbers, it's shuffling energies regardless of their magnitudes, all while leaving fossils behind as memories left for someone to process sometime in space and somewhere in time.
Lorentz factor In CR, relativistic corrections must be relative themselves. Scale invariance (vertical energy levels) implies change of metric [units]. Without this change, one must change the value of constants accordingly. Thus, the Lorentz factor cannot be valid for all scales.
In GR, metric may be scaled proportionally to energy, but scaling is limited to space and time dimensions (mass itself doesn't scale in GR, leaving other constants absolute). Another problem is that the constant of proportionality between space and time is interpreted as an absolute constant - invariant to scale. In CR, this cannot be a correct interpretation.
In conventional (absolute) form, the Lorentz factor allows a graviton of infinite mass to move, bound by the same speed limit as any other body of mass. Since such mass requires infinite energy just to start moving, its speed limit is, however, effectively 0. Similarly, a particle of absolute zero mass should have a speed limit equal to infinity as it has absolute 0 mass relative to any scale of space. Of course, one could interpret change in metric of GR as change in energy density - for a non-local observer, infinite mass would indeed not move in GR due to infinite time dilation, while a massless particle in infinitely flat space would have infinite velocity. However, one cannot assume that there exists only one and absolute space-time entanglement (at least not in CR). One can use such reference frame in calculations, but this will lead to misinterpretation of reality on large and small scales. According to CR, space and time both must be quantized (force carrier particles have quantized and non-zero rest masses). This, effectively, makes curvature of space-time relative to scale. Space is thus relatively continuous (due to infinite number of carrier particles) but also relatively quantized (due to quantized ranges and entanglements of carriers with different sources). The infinite number of space-time entanglements only reduces to GR interpretation if the ratio between space and time scales is absolutely equal to c in all the entanglements. This, generally, won't be true, even if it is a good approximation for close scales.
Speed limit may be determined from density and pressure of space. Since density and pressure of space are relative [to scale], for a graviton of infinite mass, density and pressure are such that speed limit is 0. If standard photons are quanta of space they will (or can) travel at the speed limit (c) determined from pressure and density of such space only if they don't have mass relative to that space. However, if they do have kinetic energy relative to that space they must have mass, therefore must travel at speed < c. Effectively, while in motion relative to space, they are no longer quanta of space. Note that this implies that a photon travels at rest velocity as quantum of space, while its own space can spin at higher velocity (>>c, as calculated) although that velocity can be exchanged for radius (which should be the case if photon travels in non-localized wave-form). In CR, c should be interpreted as average velocity of travel (inflation). If rest masses of neutrinos and photons are different, the final radius (range) of inflation will be different and so may be the average velocity unless both photon and neutrino have the same source and are detected [collapsing radius] at the same location. On small enough distances, average velocity should be higher than c, on long enough distances lower than c. Are magnetic field tubes of polarized space half-photons?
Speed limits for particular mass are thus relative to [the scale of] that mass and speed limits can relatively be broken. The relative breaking of a speed limit is synchronized with a change in rest mass energy level, when speed is adjusted to match rest velocity on that level, while speed limit changes to the value associated with the new level. The Lorentz factor should thus have the form: $\displaystyle \gamma = {1 \over \sqrt{1 - {v^2 \over {c_n}^2}}}$ when applied to rest mass: $\displaystyle {\gamma}_m = {m_n \over \sqrt{1 - {v^2 \over {c_n}^2}}}$ $\displaystyle \text{generally, }\, m_n \propto {1 \over c_n}$ where n is the vertical energy level.
Increasing mass [dimension] is thus increasing time dimension while decreasing (quantizing) space dimension (or less likely, keeping one constant while changing other). This can then be interpreted as exchange between space and time which can be correlated with exchange between gravitational potential and electro-magnetic potential or exchange between gravitational mass (range) and carrier mass. Space-time is then an entanglement of quanta or quantum of space orbiting a quantum or quanta of time. Each can be localized at their rest orbital, while in between they may generally travel non-localized (inflating/deflating radii).
Change in speed limit thus requires emission or absorption of a minimum discrete amount (impulse) of energy which can take the body to another vertical energy level. This allows for planetary systems such as the Solar System to be inflated atoms or a system of bound, but individually inflated particles. Note that inflation must be sufficiently fast to preserve the structure, but it cannot be infinitely fast to break the inevitable asymmetry. It is likely that such inflation is triggered by matter/anti-matter annihilation (similar to annihilation/inflation of standard photons into standard electron/positron pairs). Such event is both, the moment of death, and birth, since it likely occurs in the space of a dark matter particle pair (soul, gravitational maximum) where one pair is inflated and the other collapses (exchange of souls) - eg. a collision occurs at U0 energy level, one pair inflates to U1, other collapses to U-1. Since there are no absolute universes, any universe must be inflating in another universe, thus any anomalous energies may have a source in that larger universe. The speed limit of c = 2.99792458 * 108 is the speed limit for U0 particles (eg. standard electrons) in space of U1 bodies, speed limit for U1 scale is generally lower, while for U-1 scale particles (standard photons) in space of U0 bodies it is higher (note that this implies that charge of the electron is rotating in space formed by U-2 scaled quanta). Spin magnetic momentum of electron should be interpreted as evidence of static electron half-photons (U-1 scale electrons) orbiting at velocities faster than c. This is a proper interpretation in CR and it is a proper interpretation if one wants to conserve rationality (intuition). Determination of cn Once the scales of space and time are known, one can easily obtain cn. It was hypothesized previously that U1 scale is entangled with U-1 scale (U-1 gravitons form the space of U1 gravitons). Generally, space of an Un graviton is formed by Un-2 gravitons, thus: $\displaystyle c_n = c_{n-1} {\left( \sqrt{{log{\left( m_{n} \right)}}^2} + \sqrt{{log{\left( m_{n-2} \right)}}^2} \right)}^{-1}$ The speed limit cn on scale U1 (U1.c or c1) is then: $\displaystyle c_1 = c_0 {\left( \sqrt{{log{\left( m_1 \right)}}^2} + \sqrt{{log{\left( m_{-1} \right)}}^2} \right)}^{-1} = c_0 {\left[ log{\left( M_N \right)} - log{\left( M_{p_e} \right)} \right]}^{-1}$ c0 = c = 2.99792458 * 108 m/s
MN = 1.02413 * 1026 kg
Mpe = 9.10938356 * 10-73 kg
which, for c0 equal to standard speed of light (c), m1 equal to Neptune's mass and m-1 equal to calculated half-photon mass gives: $\displaystyle c_1 = 2.99888155 * 10^6\, m/s$ Of course, within any vertical energy levels there are sublevels (mass oscillation). In example, for U1.3 sublevel the speed limit is: $\displaystyle c_{1.3} = c_0 {\left[ log{\left( M_N \right)} + 10^{m-1 \over m} - log{\left( M_{p_e} \right)} \right]}^{-1} = 2.91932312 * 10^6\, m/s$ m = 3 Taking into account horizontal oscillation in the same sublevel, with the assumption of a quantum of energy U1.3.3 lost: $\displaystyle c_{1.3} = c_0 {\left[ log{\left( M_N \right)} + 10^{m-1 \over m} - {\left( {k-1 \over k} \right)}^2 - log{\left( M_{p_e} \right)} \right]}^{-1} = 2.93201263 * 10^6\, m/s$ k = m = 3 Generally, it would probably be useful to limit c to the average value (general reference frame) for a particular level, in this case, the value of 2.93 * 106 m/s may be a valid candidate for the average on U1 level. This speed is confirmed in the follow up paper.
If one is comparing relatively equivalent systems between scales, a precise value can be calculated assuming strongly non-dimensional ratios are well preserved (eg. space/space, not space/time) and knowing precise values of some variables in space and time between two systems, or between one system and the intermediate equivalent.
The limit on scale U-1 can be calculated similarly, assuming entanglement of adjacent scales: $\displaystyle c_{-1} = c_0 \left( \sqrt{{log{\left( m_0 \right)}}^2} + \sqrt{{log{\left( m_{-2} \right)}}^2} \right)$ $\displaystyle m_{-2} = 10^{log\left( M_{p_e} \right) - 6*5} = 9.10938356 * 10^{-103}\, kg$ m0 = Me = 9.10938356 * 10-31 kg $\displaystyle c_{-1} = 3.96 * 10^{10}\, m/s$ Speed limit on U-2: $\displaystyle c_{-2} = c_{-1} \left( \sqrt{{log{\left( m_{-1} \right)}}^2} + \sqrt{{log{\left( m_{-3} \right)}}^2} \right)$ $\displaystyle m_{-3} = 10^{log\left( m_{-2} \right) - 5*4} = 9.10938356 * 10^{-123}\, kg$ $\displaystyle c_{-2} = 7.69 * 10^{12}\, m/s$ This limit is interesting as U-2 particles should form the charge of standard electron (U0.e). The magnetic moment of the electron cannot be formed by rotation of charge exceeding this velocity (without deflating to smaller scale). The magnetic spin angular velocity of electron can be calculated assuming charge radius is known. Assuming this radius is a scaled Neptune charge radius and assuming the Solar System is the carbon atom equivalent (a hypothesis explored in greater detail in follow-up work), the radius is: $\displaystyle R_e = R_0 = {R_1 \over r_1} * r_0 = 3.834298096 * 10^{-16}\, m$ R1 = Neptune charge radius = 24622000 m
r1 = Neptune orbital radius = 4495.06 * 109 m
r0 = orbital radius of the outermost electron in carbon atom = 70 * 10-12 m

Angular velocity of charge forming the quantized momentum of electron is then: $\displaystyle v = {1 \over 2} {1 \over M_e R_e} \hbar = 1.5096 * 10^{11}\, m/s$ The charge is thus rotating at allowed velocity (not exceeding c-2).
Note that electron at standard scale (U0) may not generally orbit the atom as a particle rather as a wave. In that case, due to conservation of momentum, the velocity of its charge is much lower as the radius Re becomes equal to atom radius (r0). Its charge, however, may not be distributed as an orbital wave-line, rather orbital wave-surface, which would then increase velocity somewhat (by 3/2 maximum) but this is negligible compared to initial decrease. Generally, its charge forms a spinning tube. Closer to nucleus the charge velocity may become relativistic but it still won't exceed c-2 and probably won't even exceed c0 (between the innermost electron and atom centre speeds can be greater than c0). Note how using the standard speed of light (c = c0) would produce a picture inconsistent with reality. If electron would in a wave-form orbit the atom at speed c0 the atom radius would have to be 2.9 * 10-13 m, some 241 times smaller than it is in reality.
Applying speed limits Speed limits (cn) are inherently linked to gravitons and depend on their scales. This implies that two bodies of similar mass can have different speed limits, depending on the scale of graviton[s] coupled to the masses. Consider the example illustrated in Fig. \fig7.
Graviton speed limits
Fig. \fig7: Gravitons and associated speed limits (not to scale) The leftmost naked graviton (m1) is an U0 graviton and has a speed limit of c0, the second one from the left (m2) is an U1 graviton and has a speed limit of c1. The m3 represents the same graviton but coupled to real mass of scale U0 (collective of U0 gravitons). This coupling represents a body (or a living body) of mass that, as a whole, has a speed limit of c1 (due to c1 < c0). However, in the rightmost image, showing uncoupled real mass (m4) forming a body (or a dead body), the collective now has a speed limit of c0 even though it may be of similar or even equal total mass (depending on interpretation - mass shielded or not, graviton scales and filled capacities) to the body m3. As noted before, distances between particles are relative and never absolute 0. Electro-magnetic force between two charges, in example, is present over vast distances. This makes the definition of a body relative - due to electro-magnetic connection or entanglement between them, one could consider the two charges as a single body even when greatly separated. We might have our own definitions, in example, considering atoms as individual bodies until they couple to form a molecule, but does it make a difference to nature - unless formation of a molecule is synchronized (or equivalent) with the coupling of the collective of atoms with a distinct graviton of larger scale? Any apparently spontaneous organization of entities into a distinct body should be only relatively spontaneous. Thus, it should be more or less synchronized with a coupling to a distinct graviton correlated with such collective. This coupling may be more or less temporary or relatively long lived, but in any case, stability of this organization should be proportional to the strength of coupling (correlation).
The unification In CR, nothing can be absolute, even continuum of space must be, like all energy, a sum of discrete energies or energy levels. Diversity of energy levels implies it has variable and scale relative properties, such as density and pressure. The number of dimensions of space is in foundations of every theory in physics, here, obviously, such number is relatively infinite. Infinite number of scales (dimensions) might exist, however, in CR, intrinsic limitations on observation of scales of energy exist, effectively, making any infinity relative. Dimensions evolve and one may recognize different species of dimensions where individuals of species often can be represented by the average or relative superposition of individuals. On small scales even different species may be represented by some kind of superposition. Generally, it is convenient to define three or four main species - space, mass, time and charge. These are all entangled, but amounts of entanglement will vary and a difference in superposition of the four may itself warrant classification into different species of superposition. One might use units with different names for the 4 species (m/kg/s/C) but, at some fundamental level, these are generally all units of [angular momenta of] space at some scale and a universe will readily transform one energy into another (exchange space for time, time for mass, etc.). Here thus, there is no intrinsic entanglement between space-time curvature and mass or charge, the space-time-mass entanglement in GR is thus just one possible case of such entanglement. Added chapter The unification: Relativistic time. Relativistic time Everything in nature has an angular momentum relative to something. It is natural then that dimensions of nature are circular and cyclic, quantized into different periods and with different shapes.
Even though these dimensions are cyclic there can be no absolute space, time or mass travel - only relative.
In example, dimension of time (or a quantum of a dimension of time) may be considered as a circular thin tube (or even a relative 1-dimensional ring), a torus, with relatively discrete or relatively continuous degrees of polarization. Space (or a quantum of a dimension of space) may be considered as a thin sphere surface, a torus with significant asymmetry in tube width and height - a relative superposition of time dimensions of various radii. Charge - a superposition (localization) of time dimensions. Mass - a superposition (localization) of spaces. CR implies a relatively simultaneous existence of energy on various vertical scales (self-similarity). If energy existing on one scale can be aware of, or be sensitive to, adjacent discrete vertical energy levels only, direct sensitivity is strongly limited to 3 dimensions. This will be, with implied self-similarity, replicated on all these levels - splitting these into 3 components, hence explaining three generations of particles.
Note that not all universes have to be limited to direct awareness of 3 scales (splitting of energy can result in more than 3 levels) and even those limited to 3 may be aware of other scales indirectly - which might become direct awareness over time. Note also that self-similarity can be interpreted as relatively simultaneous existence of energy on various scales.
If nature does not discriminate between scales of energy (just as it does not between units), then entanglement and operations between adjacent scales should also be natural. In which case, the scaling vector may be normalized. Let A represent a state in time and C a scaling vector, the operation of addition between scales (components of time) could then be represented by the scalar product of vectors: $\displaystyle A \cdot C = \begin{bmatrix} a_1 & a_2 & \cdots & a_n \end{bmatrix} \cdot \begin{bmatrix} c_1\\ c_2\\ \vdots\\ c_n \end{bmatrix} = a_1 \cdot c_1 + a_2 \cdot c_2 +\cdots+ a_n \cdot c_n$ With normalization, the scaling vector C becomes a unit vector: $\displaystyle A \cdot {C \over |C|} = \begin{bmatrix} a_1 & a_2 & \cdots & a_n \end{bmatrix} \cdot \begin{bmatrix} c_1/|c_1|\\ c_2/|c_2|\\ \vdots\\ c_n/|c_n| \end{bmatrix} = a_1 \hat{c_1} + a_2 \hat{c_2} +\cdots+ a_n \hat{c_n}$
Note that, if dimensions here represent scales, geometrical representation of the state with orthogonal unit vectors would be misleading.
and, with no discrimination between scales: $\displaystyle \hat{c_1} = \hat{c_2} = \cdots = \hat{c_n} = \hat{c}$ scales collapse to one dimension: $\displaystyle \vec{A} = \left( a_1 + a_2 + \cdots + a_n \right) \hat{c}$ With no direction, a point in such time becomes a scalar: $\displaystyle A = \left( a_1 + a_2 + \cdots + a_n \right) c$ The collapses of scales in time will have physical interpretations in space and correlations between these may be interpreted as events of synchronicity, however, generally, it should not be assumed that c (speed of change) is absolutely the same between different scales of energy. Relativistic space-time In General Relativity space is treated as non-physical, it has a geometry but no variable physical properties such as density and pressure in common interpretations. Space/time entanglement is treated as absolute which translates to an absolute speed limit, equal to vacuum speed of light in case of massless photons: $\displaystyle c = \sqrt{1 \over {\epsilon_0 \mu_0}}$ ε0 = vacuum electric permittivity = 8.85418782 * 10-12 F/m
μ0 = vacuum magnetic permeability = 4π * 10-7 H/m
However, this can be rewritten in terms of energy density ρ and pressure p: $\begin{aligned}\displaystyle \epsilon_0 = K_{\epsilon}\, {F \over m} = K_{\epsilon}\, {{s^4 A^2} \over {m^3 kg}} = K_{\epsilon}\, {{s^4 N^2} \over {m^3 m^2 kg T^2}} = K_{\epsilon}\, {{s^4 kg^2 m^2} \over {m^3 m^2 kg s^4}} {1 \over T^2} \\ = K_{\epsilon}\, {kg \over m^3}\, {1 \over T^2} = K_{\epsilon}\, {kg \over m^3}\, {1 \over T}\, {C \over N} {m \over s} = \rho_s\, {1 \over B_1}\, {1 \over E_1}\, v_1\end{aligned}$ $\begin{aligned}\displaystyle \mu_0 = K_{\mu}\, {H \over m} = K_{\mu}\, {{m kg} \over {s^2 A^2}} = K_{\mu}\, {{m kg m^2 T^2 s^4} \over {s^2 kg^2 m^2}} \\ = K_{\mu}\, {{m s^2} \over kg} T^2 = K_{\mu}\, {{m s^2} \over kg}\, T\, {N \over C}\, {s \over m} = {1 \over p_s}\, B_2\, E_2\, {1 \over v_2}\end{aligned}$ $\displaystyle \text{for }E_1 B_1 = E_2 B_2\text{:}$ $\displaystyle c = \sqrt{{p_s \over \rho_s} {v_2 \over v_1}} = \sqrt{p_s \over {\omega \rho_s}}$ Kε = 8.85418782 * 10-12
Kμ = 4π * 10-7
and now in terms of energy E and mass m: $\displaystyle \epsilon_0 = \rho_s\, v_1 = {m \over V} v_1$ $\displaystyle {1 \over \mu_0} = p_s v_2 = {E \over V} v_2$ $\displaystyle c = \sqrt{{E/V \over m/V} {v_2 \over v_1}} = \sqrt{{E \over m} {v_2 \over v_1}}$ From this follows: $\displaystyle E = {v_1 \over v_2} m c^2 = \omega m {v_r}^2$ $\displaystyle \omega = {v_1 \over v_2} = {v_r \over \sqrt{{v_r}^2 - v^2}} = {1 \over \sqrt{1 - {v^2 \over {v_r}^2}}}$ Here, factor ω is the non-dimensional relativistic factor. In GR, energy is always relative to an absolute rest frame (vr = c), which may be referred to as vacuum frame or even CMB (Constant Microwave Background) rest frame due to omnipresence of CMB and negligible photon mass. The space/time ratio of that frame is considered intrinsic and non-changeable and, assuming vr = c, with an absolute 0 momentum (v = 0 above). In QM discrete energy is limited to horizontal levels and bound by counter-intuitive limitations of the same absolute rest frame. In CR there are no such restrictions, no rest frame is absolute, each gravitational well has its own space and there are, not only horizontal but vertical energy levels corresponding to scale of discrete packets of energy. In CR, the CMB rest frame is space of a large-scale graviton with [angular] velocity (v) possibly equal to c, relative to a rest frame vr > c, and with a rest mass < mc2/vr2. Space and time of this rest frame may be entangled but information between them cannot travel instantaneously. Also, either may change spin and entangle with another dimension.
Even in weak entanglement, where speed of information transfer increases with distance (due to decrease of particle/wave radii), the speed only becomes infinite at infinite distance between entangled dimensions. Decrease in scale in entanglement is increasing probability for establishment of a bigger entanglement with a closer dimension (switch of context). At infinite distance, entanglement is stable for absolute 0 time.
Therefore, the ratio c is not absolutely intrinsic and it is changeable. Omega factor = relativistic change Omega factor is a non-dimensional relativistic factor, a generalization of the Lorentz factor. It is a necessary modification in order to allow complete relativity of universes. Energy is relative to a specific reference frame and omega factor will generally be relative to a specific graviton in whose space energy is contained. Space of a graviton is characterized by its εμ product (or density and pressure). Omega factor represents change in energy due to momentum: $\displaystyle \omega = {1 \over \sqrt{1 - {v^2 \over {{c_n}^2}}}} = {1 \over \sqrt{1 - {v^2 \over {k^2 c^2}}}}$ c = c0 = standard speed of light where k depends on the vertical energy level (scale of energy).
Note that ω-1 is the eccentricity of the ellipse of width equal to 2kc and height equal to 2v, as shown in Fig. \fig5.
Omega ellipse
Fig. \fig5: Relativistic ellipse With k = 1, width is fixed to c and omega factor degenerates to Lorentz. Note also, if k itself has the form of ω-1, degeneration to Lorentz becomes degeneration of a variable ellipsoid to an ellipse of fixed width. In GR, for an relativistic ellipse it is absolutely forbidden to form a circle (v = kc). However, in CR, this must be only relatively forbidden. Assume v is the angular velocity of a rest frame 1 contained within (or relative to) a rest frame 2 which has angular velocity equal to kc. It is not forbidden for a rest frame 1 to reach velocity kc and no infinite energy for that is needed either (infinity also must be relative) - however, needed energy is equal to energy of rest frame 2 (minus rest frame 1 energy). Thus, rest frame 1 can reach velocity kc by using all available energy of rest frame 2. This is then simply a transformation or exchange of rest frames - rest frame 1 was born (inflated) into rest frame 2, while rest frame 2 died (deflated) into rest frame 1. With rest frame 1 becoming rest frame 2, its velocity is now rest velocity and speed limit now may be increased to angular velocity of rest frame 3 it is entangled with.
Note that entanglement may not be broken. In that case the speed limit now represents a speed minimum and velocity is relativistic if the rest frame slows down. Since entanglements cannot be absolute 0, velocity becomes relativistic when it is either increased or decreased from rest velocity. In that case, rest velocity can be interpreted as a velocity where entanglements cancel.
This is all relative to some remote reference frame. From the perspective of rest frame 1, due to scale change, speed limit may be relatively invariant. Note that energy can also be applied externally, rest frame 2 (generally a graviton) can merge with another such particle, changing its angular velocity and speed limit for rest frame 1.
However, this should be further generalized, to allow polarization of space and summation of (sensitivity to, awareness of) different scales of energy. In a physical reality in which every universe (or distinct form of energy) has a momentum the energy of which is stored into its gravitational maximum and its space, it is appropriate to introduce the concept of rest velocity for rest frames (or rest spaces), equal to: $\displaystyle {v_r}_n = \sqrt{1 \over {\omega \epsilon \mu}}$ ε = rel. const. (eg. 8.854 * 10-12 F/m)
μ = rel. const. (eg. 4π * 10-7 H/m)
where $\displaystyle \omega = {\omega}_n = \omega (n, q_0) = \biggl( {1 \over \sqrt{1 - {\alpha}_n}} \biggr)^{-sgn(q_0)}\, ,$ $\displaystyle \alpha = {\alpha}_n = \sum_{m=1}^{m=\infty} {v^2 \over {{v_r}_{(n-m)}}^2} \approx {v^2 \over {{v_r}_{(n-1)}}^2}\, ,$ n ∈ ℤ
m ∈ ℕ
and n is a discrete (vertical) energy level of the rest frame, v and q0 its velocity and charge (radial polarization), respectively, relative to rest frame chosen by the observer (since awareness of the observer is generally limited to adjacent vertical levels of energy, this frame will usually be n-1, and n-2 for larger scales of energy). Degeneration to Lorentz factor For a negatively polarized rest frame, and Un-2 << Un-1 (vr(n-2) >> vr(n-1)): $\displaystyle {\alpha}_n = {v^2 \over {{v_r}_{(n-1)}}^2}$ Fixing all discrete packets of energy to single scale where vrn-1 = vr = c is the speed limit (speed of light) on that scale, Omega factor becomes Lorentz factor: $\displaystyle \gamma = {1 \over \sqrt{1 - {v^2 \over c^2}}}$ Effect on charge and mass Charge and mass may be commonly exchanged. Generally, charge may be proportional to real mass of the total mass of coupling so this can be interpreted as exchange between real mass and img mass if this is local exchange. Effective electric charge q and mass m now become: $\displaystyle q = q_n = {q_0 \over \omega}$ $\displaystyle M_{img} = M_n = \omega M_0 = {q_0 \over q} M_0$ $\displaystyle M_{re} = M_{n-1} = {M_{0-1} \over \omega} = {q \over q_0} M_{0-1}$ q0 = total rest charge = rel. const. (eg. 1.60217733 * 10-19 C)
M0 = total img rest mass = rel. const.
M0-1 = total real rest mass = rel. const.
$\displaystyle M = \sum_{i=0}^\infty M_{n-i} = \sum_{i=0}^\infty \omega^k M_{0-i} \approx M_{img} + M_{re}$ $\displaystyle k = k(i) = -1^{(i \mod 2)}$
Note 1: All indexed parameters (q0, M0, Mn, etc.) are simply factors of proportion, relative to scale of choice. Since rest state of energy is relative (nothing is absolutely at rest), using recursion, one concludes that the sole intrinsic property of a universe is change (evolution), but in order for it to exist, multiple universes (bigger and smaller scale) are required.

Note 2: Total mass may be decreasing or increasing with relativistic energy, thus, this is generally not a simple local mass exchange. It includes a factor of transformation (ω) which is exchanging scales of real and img dimensions but with emission of energy (inversely proportional to complexity of transformation) and absorption of additional energy - eg. absorption of mn-2 (not previously considered as part of total mass M), into Mn. Relativistic effects are always real at some scale, it is only a question to what degree is the effect local or remote. If the observable moves at rest velocity locally, relativistic effect is generally low (small scale) locally.
Effect on radius Effective radius of a gravitational maximum also depends on ω: $\displaystyle R = \omega R_0$ R0 = rest radius In case of negative polarization it increases with velocity, for positive it decreases. Energy A distinct form of energy can be composed of one or more discrete scales of energy. Total energy is: $\displaystyle E = \sum E_n = \omega m c^2$ where mc2 is rest energy relative to a rest frame with rest velocity c, while ω represents relativistic increase or decrease due to kinetic energy relative to the observer. Since kinetic energy of a system is stored in gravitons (when relativistic relative to space), its distribution will depend on the scale of these gravitons. General force Electro-magnetic and gravitational force are generally entangled and potential should be regularly exchanged between the two. Therefore, it should be useful to couple the two mathematically into a 4-component vector force, ie. general force. General force acting on a particle (eg. moon maximum) of mass m, charge q and velocity v is the sum of polarized (electro-magnetic) and neutral (gravitational) force.
At any moment in space/time the force acting on a body is a superposition of gravitational and electro-magnetic force. In extreme conditions (temperature/pressure) one component may collapse (deflate) as other inflates.
Source of the force is a general rotating graviton with its field spread through the well: $\displaystyle \vec{F} = qm\vec{S} + qm\vec{v}\times\vec{B} + qm\vec{E} + qm\vec{G} = qm\vec{S} + qm\vec{M} + qm\vec{E} + qm\vec{G}$ $\displaystyle \vec{F} = qm(\vec{S} + \vec{M} + \vec{E} + \vec{G})$ with charge/mass radii reduced to infinitesimal value:
Even though the particle has multiple associated charges and real charge/mass radii, to simplify equations, it is useful to reduce it to a point particle, especially in cases where it effectively is a point particle - eg. when space/time resolution is such that real radii or the oscillation in charge/mass distribution cannot be determined.
$\displaystyle \vec{M} = \vec{v} \times \vec{B}$ $\displaystyle \vec{B} = {1 \over m} \mu {q_r \over r^2} \vec{v_r} \times {\vec{r} \over r}$ $\displaystyle \vec{E} = {1 \over m} {1 \over \epsilon} {q_r \over r^2} {\vec{r} \over r}$ $\displaystyle \vec{G} = {1 \over q} {1 \over g} {m_r \over r^2} {\vec{r} \over r} = {1 \over q} {1 \over r} {v_s}^2 {\vec{r} \over r}$ $\displaystyle \vec{S} = \vec{v} \times \biggl({1 \over q} s {1 \over r} \vec{v_s} \times {\vec{r} \over r}\biggr)$ ε = electric permittivity of space (*4π)
μ = magnetic permeability of space (/4π)
g = 1/G = energy density of gravity at the maximum (inverse of the gravitational constant)
s = relativistic factor
M = spin electric field at r
B = magnetic field at r
E = electric field at r
G = gravitational field at r
S = spin gravitational field at r
vs = angular velocity of space (effective graviton) at r
where mr, qr and vr are mass, charge and velocity, respectively, of the field maximum, r is the distance between the graviton and the moon particle.
Note that s is non-dimensional (invariant to scale) and must be equal to: $\displaystyle s = {{v_s v} \over {c_n}^2}$ For n = 0 (c0 = c), using substitution: $\displaystyle {v_s}^2 = {{G m_r} \over r}$ , with the angle φ between v and (vs x r) being equal to the angle between vs and r, the qmS term reduces to: $\displaystyle qm\vec{S} = {{G m_r m v^2} \over {c^2 r^2}} \sin^2{\phi}$ which, when simplified to one-body problem - using reduced (effective inertial) mass (m = μ, mr = M + m), becomes the correction factor to gravitational potential from General Relativity: $\displaystyle V(r) = \int{qm\vec{S} dr} = - {{G(M+m)\mu v^2} \over {c^2 r}} \sin^2{\phi}$
At extreme momentum change, polarized and neutral components can exchange potential - E exchanges with G, while M exchanges with S.
Note that in equilibrium (full capacity) vs = v (vsv becomes vs2), and, using the above substitution for vs2, spin gravitational vector S becomes: $\displaystyle \vec{S} = \vec{v} \times \biggl({1 \over q} {G \over {c_n}^2} {m_r \over r^2} \vec{v_s} \times {\vec{r} \over r}\biggr) = \vec{v} \times \biggl({1 \over q} k {m_r \over r^2} \vec{v_s} \times {\vec{r} \over r}\biggr)$ k = specific vacuum density [m/kg] making vector S the gravitational equivalent of spin electric vector M. Note also that even the ratio between constants of the polarized and neutral force vectors is equal: $\displaystyle {1 \over \epsilon} {1 \over \mu} = {1 \over g} {1 \over k} = G {{c_n}^2 \over G} = {c_n}^2$
Note that if momenta are quantized on one vertical energy level, they must be quantized on all levels - from a proper (scale invariant) reference frame. Due to [relatively] low energy oscillations in vertical scale (eg. lepton oscillation) caused by the splitting of a vertical level, inflation of a system of multiple bodies may inflate different bodies [of the same species] to different [relatively] low energy levels and quantization might not appear conserved (as timescales might be inadequate to detect oscillation). Also note that, with a change in level (eg. oscillation), due to finite speed of propagation of changes in space, distant bodies might not feel the same force as local bodies.
Of course, these equations are valid down to the radius of the field source, below it the field is inverted and can be compressed. Added chapter Exchange of potential. Exchange of quantized potential In the chapter above (General force), it was assumed that force carrier particles are massless, which may be a good approximation generally, however, such interpretation won't always paint an accurate picture of reality. As there are no absolutely massless particles in CR, both gravity and electro-magnetic potentials should be Yukawa type potentials. However, as each carrier particle is a source of force it has its own field with appropriate carrier particle of smaller scale. Even though each field is quantized, recursion leads to infinite ranges and zero mass particles. Thus, each component of general force should be coupled with a sum of Yukawa type terms: $\displaystyle exp\left( {-r \over L_n} \right)$ where Ln is the range of a carrier particle (reduced Compton wavelength).
Note that horizontal energy levels may not be treated equally to vertical energy [sub]levels. In example, carrier rest mass may be treated unchangeable across the horizontal energy levels (levels of the same energy magnitude), it may only be considered [relatively] temporarily excited (or, having excited range). In any case, at stable energy levels, Yukawa term disappears for coupled gravitons.
However, sensitivity (probability for coupling) of real mass to these gravitons will be inversely proportional to difference in scale of energy between the two.
To take this into account, each Yukawa term should be multiplied by the sensitivity factor, proportional to: $\displaystyle {\left({E \over E_n}\right)} \delta_{ij} + {\left( {E_n \over E} \right)} \left( {1 - \delta_{ij}} \right)$ $\displaystyle i = \left\lfloor {E \over E_n} \right\rfloor,\, j = 0$
δij = Kronecker delta
Of course, one should also take into account mass oscillation here.
Therefore, due to quantized ranges, energy levels are quantized, however, due to different scales, quantization is relative. This is evident in planetary systems - planetary orbitals are obviously quantized while quantization for smaller bodies is not as obvious due to greater density of energy levels. Furthermore, the amount of polarization of force carrier particles (gravitons) is likely to change with scale (which may be the source of difference in sensitivity). In that case, distant bodies might effectively feel one force while close bodies would feel another force. Nuclear atomic force, when interpreted as general force, is one such example - on close range gravity dominates, otherwise, electro-magnetic force. Exchange of one potential for the other has two interpretations - either charge of the field source is exchanged with mass, or energy is exchanged between polarized and non-polarized space (mass/charge exchange in carrier particles). In reality, superposition of both, should be present. Added Solution to gravitational anomalies. Solution to gravitational anomalies Previously, it was assumed that angular velocity of space (effective graviton) vs at radius r is equal to Keplerian velocity: $\displaystyle {v_s}^2 = {GM \over r}$ And that velocity is also assumed to be the velocity of standard matter coupled to that graviton. This assumption is equal to the assumption that mass of the effective graviton is always equal to the mass of coupled standard matter. However, this should be valid only at full capacity states - when all constituent quanta of the effective graviton (gravitons of smaller scale) are coupled to matter. Suppose the equation of state is: $\displaystyle GM {m_s \over v_s} = m\, v\, r \tag{G1.1}$ G = gravitational constant
M = mass enclosed within radius r
where the right side is orbital angular momentum of matter, while ms and vs are mass and velocity of the effective graviton, respectively.
The effective graviton is forming the toroidal quantum of space which the matter is traversing, its mass ms is thus the total mass of constituent gravitons while vs is their average velocity.
From (G1.1), orbital velocity of matter is: $\displaystyle v = GM {m_s \over m} {1 \over v_s\, r} \tag{G1.2}$ Assuming vs is for uncoupled gravitons equal (or close) to standard speed of light (c), coupling with standard matter will decrease it but also impart momentum on coupled matter.
Note that such gravitons can't accelerate matter beyond c.
At full capacity, ms = m, vs = v and velocity becomes Keplerian: $\displaystyle v^2 = {GM \over r}$ For m < ms velocity increases, at m << ms, vvsc. With m equal to the mass of a single graviton, v becomes equal to c. For m > ms velocity becomes lower than Keplerian, acting forces are no longer in balance (vacuum pressure prevails), inertia is disturbed and orbital radius decreases - all the way to relative 0 if everything below the original orbit is at full capacity (and if not stopped by accumulated orbiting mass - eg. satellites falling back to Earth are stopped at surface radius). With such mechanism, it should be common for inner orbits to be at full capacity (or over-capacitated near the centre), with probability for under-capacitation increasing with orbital distance. Energy accumulating in the centre will, however, generally be radiated or expelled outwards in some form through various mechanisms.
Note that v and vs are generally vectors, while here it is assumed that the angle between v and vs is 0. This should be fulfilled in equilibrium but may not be fulfilled otherwise and should be taken into account.
Derivation of the equation G1.2 One way to derive the equation G1.2 is through body momentum energy (or total energy with the assumption of zero rest mass in the local reference frame) and gravitational potential energy of the naked graviton, through the following relation: $\displaystyle pv_s + {-GMm_s \over r} = 0$ $\displaystyle mvv_s = {GMm_s \over r}$ $\displaystyle v = GM {m_s \over m} {1 \over v_s\, r}$ Thus, in equilibrium orbital states, momentum energy of the body in the local frame must be equal to the gravitational potential energy of the naked graviton. That way the body cannot escape but will also not de-orbit. Note that in equilibrium v = vs, but the orbital velocity does not have to be Keplerian in this interpretation. Conventionally, however, the ms/m ratio is incorporated into M (why not into G?), as dark matter (if velocity is higher than expected Keplerian velocity). Here, vs is initially equal to c, however, as the body gets entangled with the graviton, vs decreases below c (while v is increasing). For m < ms, gravitons of space are effectively dragging matter, for m > ms (de-orbit occurs), the matter is dragging gravitons toward the centre of the gravitational well (at some point, however, entanglement may be lost, gravitons could decouple and return to the original orbit (range). Note that, when uncoupled, as a constituent particle of local space, static graviton may generally be in a spherical wave form, forming a dark matter halo, or the dark part of the gravitational potential halo. The equation for escape velocity can be derived similarly. Here however, the body is generally already coupled and it must overcome the gravitational potential energy of the total mass (superposition of graviton and body mass) and the momentum energy term must be replaced with kinetic energy term of total mass (because the body now is not at rest relative to space so the momentum energy has a non-zero rest mass term): $\displaystyle {1 \over 2} (m_s+m) v^2 + {-GM(m_s+m) \over r} = 0$ $\displaystyle {1 \over 2} (m_s+m) v^2 = {GM(m_s+m) \over r}$ $\displaystyle v^2 = 2 GM {m_s+m \over m_s+m} {1 \over r} = 2 {GM \over r}$ Proper relativistic treatment The constant c can be interpreted as the constant of proportionality between space and time. Since time dimension is a subspace of space in CR, it is relatively non-dimensional and may be treated invariant in local reference frames. However, in reality space and time dimensions can and will scale differently and the assumption of absolute invariance of c (absolute entanglement of space and time) will lead to misinterpretation (illusion). The difference (oscillation of the constant) may certainly be negligible in horizontal energy levels and vertical sublevels, however, between major energy levels (eg. standard electron/Neptune) significant difference will exist. Generally, c should be inversely proportional to scale. This, of course, applies to all other dimensional constants too. Mechanism of exchange Exchange of electro-magnetic potential for gravitational potential is done through the change of scale. In example, radii of charge maxima may be deflated with inflation of a mass radius of a gravitational maximum. This doesn't affect only orbital radii of gravitons but also spin radii of graviton quanta - effectively, charge is subdued with the inflation of mass (gravity). Note that, seemingly, no extra energy is required as this is simply a change of force flavour, not strength. However, energy is needed to stimulate and process transformation, during which some energy may also be lost. The end product will then have different energy than initial total energy. The triggers of exchange may be: If transformation mechanism exists locally, external energy needed to stimulate exchange can be extremely low. This may simply be resonance or entanglement inversion.
Note that any entanglement decrease must be coupled with another entanglement increase.
The exchange of potentials of general force could thus be common in birth and death of bosons and boson (Bose-Einstein) condensates. The equivalence of bosenovas and supernovas/novas, galaxies and quantum vortices, planetary systems and atoms, in that case, may go far beyond abstract similarity. In any case, it should not be impossible, in any universe, to ensure conditions that would reduce the relativity of self-similarity (similarity to a universe of adjacent vertical scale) to a minimum.
Ten condensed atoms of 10C may just form a U0.Solar System at some moment of oscillation.
Evaluation of G Gravitational constant (G) is not fundamental and may be interpreted as: $\displaystyle G = {1 \over 2} {A_s \over M} {v_s \over T_s} = 2\pi {{R}^2 \over M} {v_s \over T_s} = {3\pi \over \rho} {1 \over {T_s}^2} = {R \over M} {v_s}^2\,\, \left[{m^3 \over {kg s^2}}\right]$ As = surface area of the gravitational maximum [graviton]
R = radius of the maximum
M = gravitational mass of the maximum
ρ = mass density of the maximum
vs = angular velocity of the maximum
Ts = period of rotation of the maximum
It is then relative to a particular graviton (gravitational maximum) and has its properties, such as mass, radius and velocity, built in. These are generally variable properties. Even if, generally, all these variables are correlated in such a way that G remains constant, are they correlated (entangled) at all times and do changes propagate instantly? In CR, instant propagation of information is [absolutely] impossible and some phase difference between changes in [G and] the variables will always exist. The G itself must oscillate. Obviously, a gravitational maximum has a [changeable] spin momentum and this can further be complicated when it is evidently composed of multiple maxima.
Note that vs here is Keplerian velocity. Assuming M is the mass of a graviton, non-Keplerian velocity may be interpreted as a difference in G (due to a difference in graviton mass).
While the 3-dimensional (spherical) form of one maximum may cloud the existence of inner maxima, outer maxima can have different spin momenta. Even if the whole system changes spin, changes cannot be instantaneous across all maxima, rather propagate in a wave-like nature. Gravitational collapse = G collapse Rotational profiles of galaxies show that 1/R is often not proportional to vs2. Even if outer maxima have collapsed (fragmented) to multiple satellite maxima of smaller scale, these cannot acquire [real] mass instantaneously nor they will always acquire [real] mass during collapse. Although collapse requires energy, it doesn't necessarily have to come from real mass. Unlike in GR, gravitational collapse in CR is not reserved for massive bodies, the energy for collapse depends on the initial energy of the maximum. Maxima can thus remain naked for relatively long times, proportionally to scale and inversely proportionally to mass (energy) field density, before [another] equilibrium is established and 1/R becomes proportional to vs2. Gravitational collapse in CR is localization of graviton momentum - eg. a large scale graviton with a spin radius on the order of 106 km can collapse to form a graviton with a spin radius on the order of 103 km, sometimes with a former spin radius fossilized into orbital radius of a new body. Real mass required for equilibrium can be obtained through conservation of angular momenta: $\begin{aligned}\displaystyle \left[m_{img}(n) + m_{re}(n)\right] v_n r_n = \left[m_{img}(n-1) + m_{re}(n-1)\right] v_{n-1} r_{n-1} \\ = M v_s R\end{aligned}$ mimg = mass of the naked gravitational maximum = imaginary mass
v = orbital velocity of the maximum
r = radius of the maximum
mre = acquired smaller scale mass = real mass
vs = vn-1 = spin velocity of the [collapsed] maximum
R = rn-1 = radius of the [collapsed] maximum
M = Mn-1 = total mass of the [collapsed] maximum
where n is the scale of the maximum. In the above, dependence on scale has two equivalent notations: $\displaystyle m_{img}(n) = {m_{img}}_n$ Collapse of a graviton to smaller scale generally can be a high energy or low energy collapse. In case of high energy collapse, accumulated real mass is lost (eg. nova explosions) - decoupled from a collapsing graviton. In case of low energy collapse, the graviton is [relatively] naked and collapse occurs due to localized disturbance of its momentum with sufficient real mass for coupling on smaller scale.
Note that graviton may, instead of deflation, start inflating after decoupling. It will then continue inflating until it reaches maximum range - if it does not collapse and couple to another mass before that point is reached. Maximum range becomes a relative term if graviton is losing energy with inflation - in that case, range would be expanding continuously. However, most energy is lost with coupling. Regardless of interpretation, lost energy at the moment of coupling should be proportional to distance between inflation/emission (decoupling) and absorption/deflation (coupling) due to increasing distance in correlation between entangled constituent quanta of the wave (graviton) - the volume of entanglement cannot remain absolutely constant and it is unlikely to conserve constancy (oscillation average) with distance. Note also that collapse of a wave-form is only a relative collapse of wave nature - difference between a particle and a wave is simply in a radius of a wavelike form. The inverse interpretation is also valid - in some reference frames, the larger wave-form may be interpreted as a particle.
In reference frames where collapse is discrete, low energy collapse occurs when this is established: $\displaystyle m_{img}(n) = m_{re}(n-1)$ In other reference frames, collapse proceeds gradually and can start even before the above relation is established. For a naked maximum, mre(n) is a relative 0. In high energy collapse, mimg(n) must be decreased to match mre(n-1). This is synchronized with increase in vnrn product. There are no fundamental constants. All are fundamentally variable. Reduction The story of forces should probably begin with a single dimension that represents a physical manifestation of correlation (entanglement) between two particles. Attractive force is then a synonym for decreasing distance in correlation, repulsive force - vice versa. However, if wave interpretation prevails, any apparent force may be interpreted as curvature of that dimension. Assuming this is not the only such pair in existence, through interactions with other particles, distance will be randomly increasing or decreasing between pairs. This could then be interpreted as Brownian thermal force. Whether the motion/energy is the result of force (or curvature) or the other way about is completely relative. Now assume distance in correlation in a pair reduces to relative 0, forming a relative superposition. Assuming this entanglement is interpreted as space, the inverse of that entanglement is time. Now that entanglement will be quantized corresponding to number of all other particles in existence. If superposition is oscillating between pairs, this can locally be interpreted as oscillation of mass. However, that superposition is unstable due to thermal motion. And this is where the story would end if the distance would not be relative and if all this wouldn't exist at different scales. Suppose the entanglement between vertical scales is stronger due to stronger anti-alignment in properties. Now the superposition will be harder to break with thermal motion if there is no such motion on the other scale. With that, it becomes clear why the standard strong force is relatively unbreakable and why stable [systems of] quanta of energy have to be inverted between adjacent vertical scales.
Inversion here is commonly represented by inversion of appropriately scaled pressure and temperature.
Assume now that instead of fixed superposition, mass oscillation is fixed to certain frequencies. Obviously, this gives rise to charge - repulsive or attractive force between energies depending on correlation in frequency. Things get increasingly complicated with the number of discrete masses in oscillation.
Opposite (anti-aligned) charges are decreasing spatial distance due to increasing correlation manifested in sharing of coupled carrier particles (eg. half-photons) between them. Coupling of these particles increases carrier mass, decreasing range. This contraction of a radius of one dimension (eg. time, or magnetic field tube) is then synchronized with contraction of spatial distance. Decrease of distance will be accelerated due to positive feedback (the rate of fusion of carriers increases inversely proportionally to distance). The [superposition of] carrier particles is thus alternating in entanglement between two sources of force (synchronized with mass oscillation). If charges (frequencies of mass oscillation) are aligned there can be no sharing and carriers will be annihilating or deflating into smaller scale, increasing range. Note that difference in velocities between two charges can affect mass oscillation and, therefore, alignment of frequencies, when relativistic effects are manifested locally. This implies that rates of nuclear fusion should increase if fusing protons have different velocities.
One interpretation of strong force could then be oscillation of particles between 2*3 different mass (colour charge) oscillations, giving 23 combinations for gluons (coupled carriers).
Scale and centre of the observable universe For every universe there must exist a reference frame that universe is revolving about.
Given the determined scales of discrete vertical energy levels, it is reasonable to assume that the centre of the observable universe (point it is revolving about) is outside of it. Thus, all observable galaxies collectively orbit a barycentre outside of the observable universe. This can be confirmed and approximated by observing galaxies on a different energy level of the same system. Momenta of such galaxies should be correlated - in equilibrium state they orbit the centre in the same direction but with a calculable difference in speed and distance from the centre. Eg. If one considers Milky way as a bound electron, the atom which Milky way is a part of should have a diameter on the order of 10 trillion (1013) light years, 103 times the diameter of the observable universe. In that case, all other energy levels are outside of the observable universe. However, considering the number of galaxies and the state of evolution, this is not the best interpretation (although some layering may be present). Considering distances between atoms (planetary systems) and molecules (binaries and other strongly correlated systems) the observable universe is a gas bubble of extremely low density with particles concentrated in quantum vortices (galaxies). This bubble or soup, however, cannot be completely homogeneous and it is only a matter of technology and proper interpretation whether one can observe the difference between the closest and the furthest layers of this gas (layer) relative to the external central point. The most appropriate interpretation of observable universe is a part of space of a large scale graviton, in a form of a torus - as stated already. It may have been deflated from an even larger scale, however, evidence suggests it has been inflated from smaller scale, probably in an annihilation event.
Atomic property differentiation between systems Vertical energy levels are entangled. This implies entanglement between equal species, but entanglement between different species of different scales is not forbidden either. Increasing number of protons and electrons in an atom is splitting (or increasing) energy levels (layers) of the atom. What if properties of standard scale atoms are strongly correlated with properties of U1/U-1 systems (atoms) they are co-evolving with? For example, radii of atoms might be correlated with [a density of] the gravitational well they are in. Consider the Lyman (or any other) series for a hydrogen [like] atom - if density of series is not invariant to such correlation, one could have a distorted image of non-local reality, as the spectrum lines of standard atomic elements would be variable across time and planetary systems. Eg. in the Nitrogen system the Lyman series for hydrogen would have red-shifted frequencies.
One might even argue there are 6 distinct wavelengths (after 6th, the spectrum becomes continuous) in Lyman series and that such differentiation is a direct consequence of the Solar System being an atom with 6 protons and 6 electrons (carbon), or that series beyond the 6th may be influenced by more distant systems.

Wave-particle duality


All particles having a momentum always generate waves. A particle itself may be in wavelike or corpuscular form. This form, like everything, is relative. One observer might detect a wave while other may observe a particle form (both forms can even be observed at the same time). Forms are dependent on properties of local space, which may be affected by the observer too. Generally, with more energy density, a corpuscular form is more likely to be detected. These are coherent waves which have more concentrated mass due to wave collapses initiated by self interference. Waves may be coherent in space (laser waves) and/or in time (high frequency waves). Coherence in both, space and time, will thus produce the most dense energy. A wave collapse may also be initiated by interaction with other waves (particles). From human perspective, wave nature prevails on U-1 scale, particle/wave on U0, while on U1 scale nature is observed generally as corpuscular. New particles can be formed with two species of a single particle/wave (eg. half-photon) in coherence, fused (concentrated, with range decrease) to form a particle of larger scale (mass).
Evidence Some evidence for complete relativity is presented in this paper. Additional evidence confirming complete relativity of universes is presented in follow-up papers. Mainly in the analysis of the Solar System in CR context. Of course, other researchers are welcome to confirm or refute the presented predictions and hypotheses in this and follow-up papers. Due to inherent limits in observation, however, different interpretations are sometimes possible and some might prefer a less-intuitive interpretation of reality. This does not have to be an issue - there's no reason we should all believe in the same reality, especially that which we cannot observe directly. Some views, however, may be limiting the observer of that reality. Conclusion Angular momentum seems to form the fundamental signature of energy. All energy is thus fundamentally correlated with frequency. Evolution might concentrate these energies into corpuscular forms of different scale, however, oscillation will always be relatively conserved and observable at all scales of space taking dilated time into account. But the single absolutely intrinsic property of a universe is relativity. It appears that everything must be relative in order to exist, and conservation of energy through transformation (evolution) is inevitably equivalent to conservation of relativity. Small updates/revision throughout the paper. Small updates/fixes. Paper, effectively, rewritten. Chapter Discrete states of invariance revised. Paper revised. Chapter On absolute scale everything is conserved, relatively - everything is exchangeable updated. Chapter Graviton revised. Revision in some postulates. Small, but important update in Discrete states of invariance. Paper heavily revised and updated. Some small but some important revisions and updates. Paper revised. Acknowledgement This would not be possible without all the work of all the observers of observables of different scale, theorists describing physics of such universes and promoters and propagators of knowledge. This would also not be possible without Earth providing souls and energy for all these creatures, without the Sun providing soul and energy for Earth and without the galaxy providing soul and energy to Sun. ... Last, but not least, this would not be possible without the universes of my body entangled with my soul, often enduring sleepless nights with understanding rather than rebellion. Thus, I thank everything for every thing and every thing for everything.

References


Inverse references (Signals)

Poison was the cure (1990), D. Mustaine Psychotron (1992), D. Mustaine Tornado of souls (1990), Megadeth Earth My last words (1986), D. Mustaine Countdown to extinction (1992), Megadeth Ludwig van Beethoven Albert Einstein Red Dwarf (1988-1999), C. Barrie et al False existence (2000), M. Ljubičić Ode to joy (1785 - 1824), F. Schiller et L. v. Beethoven Jim Carey Mars Vedran Ljubičić Elysian fields (1994), Megadeth 7th son of a 7th son (1988), S. Harris David Attenborough Alien, S. Weaver et al Venus The number of the beast (1982), S. Harris This is the new shit (2003), Marilyn Manson Jaws, S. Spielberg et al Pantera 'Oumuamua Rondo ala turca (1780), W. A. Mozart I thought I knew it all (1994), Megadeth Wolfgang Amadeus Mozart John Carpenter Dubioza kolektiv Call of the wild (1987), Deep Purple Clint Eastwood Majke Neptune Manowar Kurt Russell Anthony Hopkins Metallica Leo Cimbal Mariamne Apophis Isaac Newton Stephen King Katarina Perić Rough stuff (1988), AC/DC We're from America (2009), Marilyn Manson John Lithgow Rammstein Predator, A. Schwarzenegger Rihanna Sirius B Marko Prišuta Fuck the system (2002), System of a down Jesus Christ Father Ted Alice Cooper Ameno (1997), Era Nikola Tesla AC/DC, M. Young et al Megadeth, D. Mustaine et al Iron Maiden, S. Harris et al Antonio Vivaldi Sun Monty Python Christiano Cimbal Marilyn Manson, M. Manson et al F. F. Chopin Claude Debussy System of a down, S. Tankian et al J. Pachelbel

Addendum


Some additional, old, unformatted, unchecked and possibly incorrect data stemming from delusion.

SUM photon
--------
The SUM photon is a system of multiple photons fused into one body. 

SUM proton
----------
The SUM proton is a system of multiple protons fused into one body. These protons are in the form of distinct layers of the SUM proton:
	sun outer core layers, sun mantle, planetary cores and outer space, comets, dwarf planets between asteroid belts.
The mantle layers of the sun are terrestrial planets (SM UP quarks). The sun itself is the core (SUM SM DOWN quark).

SUM neutron
-----------
The SUM neutron is a system of multiple neutrons fused into one body. These neutrons are in the form of distinct layers of the SUM neutron: 
	sun inner core layers, planetary mantles, planetary and sun atmospheres, asteroids, dwarf planets between cometary belts.

The Solar system
----------------
Sun and the terrestrial planets form one SUM proton composed of 6 standard protons.
Solar system contains 6 protons and 4 neutrons making it a Carbon atom (10C).
	Solar inner core   (-)	= SUM SM UP quark (4 SM UP quarks - 4 neutron parts) = 					*NEW, pending addition of one 1 SM UP quark
		|   													*The inner and outer core have inverted (exchanged position) as part of 6p4n -> 4p6n conversion
	Solar outer core   (+) 	= SUM SM DOWN quark (6 SM DOWN quarks - 6 proton parts)					*NEW, pending loss of dwarf planet (1 SM DOWN quark = 1 proton part)
	Solar inner mantle (-)	= SUM SM UP quark (6 SM UP quarks = 3 proton parts) = +2/3 -1/3
		
	Solar outer mantle (-) 	= SUM SM UP quark (6 SM UP quarks = 3 proton parts) = -2/3 +1/3
		Mercury (AJ) 	(-) 	= SUM SM UP quark (2 SM UP quarks - 1 proton parts)
		Venus 	(AN)	(-)	= SM UP quark (1 SM UP quark - 1/2 proton part)
		*Earth/Moon (AU)(-)	= SM UP quark (1 SM UP quark - 1/2 proton part)						*pending conversion to SM DOWN quark, orbital changes
		Mars	(AS)	(+)	= SUM SM UP quark (2 SM UP quarks - 1 proton parts)
	Solar crust	   (-+) = SUM SM DOWN quark = 
	  Asteroid belts 	(-+) = SUM e + anti e neutrinos (6 proton parts)							*pending loss of asteroids in 2 belts (1 proton part) about 2.66' AU
	  Inner dwarfs
		Vesta		(-) = SUM SM UP quark [2 SM UP quarks - 1 neutron parts (2/3 of the SM DOWN quark)]
		*2.66 AU	(+) = SM UP quark [1 SM UP quark = 1/2 neutron part (1/3 of SM DOWN quark)]		*NEW, forming dwarf planet (1 neutron part)
		Ceres		(+) = SUM SM UP quark [2 SM UP quarks - 1 neutron parts (2/3 of the SM DOWN quark)]
		*3.00 AU	(+) = SM UP quark [1 SM UP quark = 1/2 neutron part (1/3 of SM DOWN quark)]		*NEW^2, forming dwarf planet (1 neutron part)
		Pallas		(-) = SM UP quark [1 SM UP quark = 1/2 neutron part (1/3 of the SM DOWN quark)]
		Hygiea		(-) = SM UP quark [1 SM UP quark = 1/2 neutron part (1/3 of the SM DOWN quark)]
	Solar atmosphere = (+) SUM electron = +2/3 -1/3
		Jupiter		(+)	= SUM electron (2 electrons)
		*Saturn		(-)	= SUM electron (2 electrons)								*pending loss of 1 electron planet + 1/2 rings
		Uranus		(+)	= electron (1 electron)
		Neptune		(+)	= electron (1 electron)
	Solar outer space
		Cometary belts = SUM anti e + e neutrinos (6 proton parts)							*pending loss of comets in 2 belts (1 proton part) about 66.42 AU
		Outer dwarfs	= SUM SM DOWN quark (5 SM DOWN quarks - 5/2 neutron parts)
					Pluto/Charon (2 SM DOWN quarks - 2 neutron parts)
					Haumea (1 SM DOWN quark - 1 neutron part)
					MakeMake (1 SM DOWN quark - 1 neutron part)
					Eris (1 SM DOWN quark - 1 neutron part)
					*66.42 AU (1 SM DOWN quark - 1 neutron part)					*NEW, forming dwarf planet (1 neutron part)
		Outer g-spheres	= SUM anti e neutrinos + e neutrino (4 neutron parts)
				= *SUM anti e neutrinos + e neutrino (1 neutron part)					*NEW, forming whole (1 neutron part)


The notation:
	The expression in braces after the expression denotes relation.
	Eg. counter-clockwise(Polaris) = counter-clockwise relative to Polaris

	Rotation of Solar system space
	------------------------------
	The Solar system space is rotating in the same direction as the planets, counter-clockwise(Polaris). The rotation speed decreases with distance from the Sun.
	This space is layered both horizontally and vertically. Vertically it corresponds to layers of the Sun, but it is losing density with distance so the layers expand vertically 
	and horizontally.
	However in matter dominated space, due to coupling with matter
	The space of planets rotates in the same direction as the planets


The Solar system is entangled with Sirius system.

Spin change
-----------
Spin change radiates energy - more spin changes = more energy radiated. Jumps from higher to lower orbit include multiple spin changes.
Spin momentum gives energy to matter, angular momentum gives energy to space.

The Earth-Moon system
---------------------
The Earth and Moon are one body. Together they form one of the SM UP quarks in Sun total proton.
When both were neutral they were almost touching each other, rotating about the barycentre.
Both cores had a radius of current Moon radius. As they moved away from each other (losing charge) 
they were shrinking accelerating spin and acquiring mass, forming:
								* Solar system nova
								* Ejection of outer comets and dwarfs
								* Ejection of electrons (current gas giants)
								* Ejection of main asteroids and dwarfs
								* Ejection of quarks (current terrestrial planets)
								* Neutron 1 completely unpacked
	1. outer space (Earth hill sphere)			+ Proton 1 unpacked
								* Neutron 2 unpacked
	2. atmosphere						+ Proton 2 unpacked
	3. upper mantle
	----- 	Event horizon					* Neutron 3 unpacked
		Here they started losing spin, getting closer to the Sun
								+ Proton 3 unpacked
								* Neutron 4 unpacked
	-----	Event horizon					+ Proton 4 unpacked
	4. lower mantle
								+ Proton 5 unpacked
	5. outer core
								+ Proton 6 unpacked
	6. inner core

The Moon core capacity relative to Earth core is empty (and vice versa) - they have opposite charges and attract, and they are fully entangled as the capacities match each other.
When the Moon and Earth core were closest together (at the Earth-Moon barycentre - Earth mantle)
Since these charges were at full capacity they started discharging by exchanging orbital momentum (charge) for a spin momentum (mass) - thus moving away from each other.
The discharge of electric energy is through magnetic (spin) radiation. We are at the end of the discharge process - the magnetic field of the Moon is fully contained inside the Moon, while 
the magnetic field of earth is rapidly declining to interior.
The magnetic fields are created and maintained by the difference in rotation velocities of the layers:

	The Earth-Moon entanglements
	----------------------------
	E inner core 	<=> Moon core
	E outer core 	<=> Outer space (beyond atmosphere to the Moon)
	E lower mantle 	<=> E thermosphere					CHANGING TO
	E upper mantle	<=> E upper atmosphere - mesosphere			----------->
	E astenosphere 	<=> E lower atmosphere - Stratosphere
	E litosphere	<=> E troposphere

	General entanglements
	---------------------
	Entanglements are not constant (they oscillate too). Entangled entities are connected by wormholes which periodically and relatively open and close.
	As Earth rotates entanglements change.
	The side of Earth facing the Sun is entangled with the Sun and the planets it can see.
	
	
Evolution
---------
The evolution is a change in "rest" energy ("rest" frequency of oscillation) of the species.
The evolution can be weak or strong, it is oscillating and it has a half-life.
Each evolution is composed of weak and strong evolutions. Currently for our universe, after 2 weak evolutions 
comes 1 strong.
The evolution cannot result in new species if there is no overlap of multiple evolutions.
When the overlap is low (no strong gravitational changes) the dominant driver of evolution is natural 
selection = fine tuning of species = weak property change.
When the overlap is high (strong gravitational interactions - cataclysmic events) the dominant driver of 
evolution is mutation = strong change of properties.

Weak evolution is the evolution in a weakly interacting gravity field (such as current Earth).

	Evolution overlap (mutation)
	----------------------------
	When the end of previous and the start of next evolutionary period overlap, the evolutions themselves mutate 
	causing mutations of gravity fields and matter,
	resulting in stable mutated species. The strength of the mutation depends on the overlap and strength of 
	interacting evolutions.
	Generally, the strength is increased when evolution periods forcibly (unnaturally) shorten.

		The extinction (annihilation)
		-----------------------------
		If the evolutions are oppositely charged the overlap results in inversion of species - transforming larger 
		species to smaller [1:n] (and vice versa), inverting sex (chirality).
		The overlap of evolutions of the same sex increases size of the species.
		The extinction can be relatively total or partial, but no annihilation results in extinction of life - 
		rather transformation of life (death).
		In compressed evolutionary periods the mutations can progress in a much faster chain reaction.

		The opposite sex (charge=chirality) overlap (mutation)
		------------------------------------------------------
		The overlap of species of opposite sex (chirality) reduces the size by 2/3.
			New mass radius = (FC) * m

		The opposite spin (mass) overlap (mutation)
		-------------------------------------------

		The same sex overlap (mutation)
		-------------------------------
		The same sex overlap results in species almost doubled in size, with annihilation of differences between the 
		interacting forms causing less variation of species properties.

			New mass radius = 2^n - ΣA

		Strong overlap (mutation)
		-------------------------
		Eg. fusion of human with cattle 					  	=> a hairy humanoid creature with horns, a tail and 
																	hoofs, popularly known as devil
		    fusion of devils of the same sex						=> a larger (2^1) devil
		    fusion of two great white sharks (Carcharodon carcharias) of the same sex 	=> Carcharocles 
													megalodon (2^1) = Carcharodon carcharias (2^1), of opposite sex

		Weak overlap (mutation)
		-----------------------
		Eg. fusion 
A universe is a relatively complete, relatively deterministic, relative chaos. A truth hard to accept is still truth. Failure to accept it only prolongs the due pain. Treating time as money is the abuse of time. Abuse time and you will be abused by time, in space. Treating space as a resource is the abuse of space. Abuse space and you will be abused by space, in time. Humanity. A bug, at first, in otherwise perfect software. Evolved into a malicious virus, a malware of epic proportions, spreading into every pore of perfection. Destroying and consuming reality. Chemists.. always cooking something. If only they would know what it is. Mathematicians.. should stay away from physics. Unless they are prepared to get physical. Everything is physical. Thoughts are bodies. Every body hurts. Sometime. Someone. Polarized by fear of the unknown, a master of science is transforming into a monster of religion. And the science fades into Prisca Sapientia. Simple explanation often requires complex imagination. Temples, shrines, pantheons and deities. One can only laugh at all the ingenious forms of human epitaphs, to the waste of energy. All shall be recycled, by the recycled tears, of recycled earth, in recycled universe. Another year, another dimension for a mathematician. General Relativity is a good theory, it's just not relative enough. Most selfish addiction is the food addiction. All humans have it. None are fighting it. Slavery. Safety. Salvation. Starvation. Stupidity. I have been given life, I gave life. I have been given knowledge, I gave knowledge. The legal and illegal. Ridiculous. At the period of contraction tornadoes become so strong and charged they strip flesh from the bodies. At certain point it becomes a vortex of dark space. The tornado of souls.
#EXTM3U F:\MP3\(computer) emily_howell_sample_1.mp3 F:\MP3\02_Beethoven_-__Moonlight__Sonata__1st_movement.flac
#EXTM3U E:\MUSIC\Bruce Dickinson - Man Of Sorrows - YouTube.MP4