Complete Relativity

Nature of observables

Definitions

Here are the definitions of terms and expressions that may be used here and other papers and articles in CR context.

n_th 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. Measurement affects all interacting entities.

n_th order interaction = n_th 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). 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 might 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 a 1st order interaction, and the interaction between two bodies as a 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). 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), and the identity/strength of interacting forces is strongly localized (even absolutely in common interpretations, where the value of zero is interpreted as an absolute constant):

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

The equation (1.1) is equivalent to momentum pulse (energy) reflection:

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

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 (e.g., 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. 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.

Superposition

Superposition is a relatively special state of a system which can be described as a combination (generally sum) of correlated (entangled) multiple base states. Mathematically, superposition may be formulated as a sum of probabilities for particular states of particles. 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. E.g., on the scale of standard electrons, spin momenta is generally measured as discrete (e.g., up or down, not something in between). This is usually because intermediate states are unstable in the context, and the measurement itself may collapse the system into a discrete (stable) state. Base states of superposition are context-dependent. In one example, two base states may represent two anti-aligned spin momenta. In another example, two base states may represent the nature of a particle (wave-like and corpuscular-like). If intermediate states cannot be observed, the values assigned to individual base states may be understood as probabilities for that state to be observed after measurement is performed. However, between measurements, the particles will commonly oscillate between base states and common physical interpretation will be the averaged superposition - e.g., in case of its nature, the particle may effectively exhibit both the corpuscular/localized and wavelike/delocalized nature simultaneously which may be interpreted as partial localization/delocalization. The interpretation in the form of averaged superposition is commonly a consequence of inherently limited observation/interaction. However, instability is scale relative. An unstable state (such as the averaged superposition) on one scale may be interpreted as physically stable on another. This is generally a consequence of effective time dilation and exchange of nature of potential between vertical scales of energy.

Universe (U)

In relativity lacking theories, Universe may be 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, relatively finite and relatively 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 rest 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 another scale. However, rules exist in the association of energy with specific scale (vertical energy level). A localized group of energies of particular scale, no matter how large, should only be associated with a larger scale [as well] if the group is spatio-temporally entangled with a distinct graviton of larger scale. This distinction is generally a distinction between a simple aggregate of entities and a collective of entities representing something more than the sum of these entities. In other words, it is the emergent phenomena that represent a likely signal for the coupling of the collective with a graviton of larger scale. The coupling may be periodic, occasional, stable or unstable, and, due to time dilation between scales or relativistic causality, the rate of emergence/decay of emergent phenomena can only be relatively synchronized with the rate of coupling/decoupling. On one scale transition may appear continuous, on the other discrete.

Polarization and scale of a universe

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

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

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 but it becomes more complex with emergence of phenomena between discrete vertical energy levels). 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, e.g., 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 U_n.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 (e.g., 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, since unresolvable properties effectively do not exist for the observer, the concept of elementariness is certainly useful. Even in cases where the structure can be resolved but is inaccessible, for pragmatic reasons it may be disregarded. Both, standard protons and electrons, for example, may be treated as elementary as the constituent particles are strongly confined. Even on large scales, depending on context, 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. Preservation of existence on particular scale 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 although not always observable. For elementary particles (on any scale) the observable momentum will commonly be angular:

$L = m v r$

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 x_i 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
a_j = amplitude of j^th order oscillation
ω_j = frequency of j^th order oscillation
φ_j = phase shift of j^th order oscillation

where, generally, a_j < 1 for j > 1. Multiple dimensions are generally entangled, so f may be f(x_i, ..., x_n). Of course, not all oscillation will be resolvable in space/time.

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 T_x, 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 T_x 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 the time of decoupling (death) the large scale graviton inverts scale (and some other properties, e.g., spin), and this 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.

Relativistic uncertainty = conservation of relativity

Generally, particles are waves whose properties like position and velocity are more or less spread, or more or less localized. Some properties are entangled in such a way that localization of one property results in the spreading of the other. Besides position and velocity, commonly mutually entangled properties are lifetime and energy, where a particle with higher energy has a lower lifetime. As all observation is physical on some scale, no measurement can be performed without affecting the subject of measurement. This measurement will affect the spreading of the measured property, producing the inverse effect on the entangled property. No localization can be absolute, therefore, measurements are inherently limited in resolution. The entanglement of the spread of values is commonly formulated as the Heisenberg uncertainty principle. Relativistic uncertainty is a generalization of that uncertainty:

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

${\hbar}_n > 0$

where ℏ_n is a constant of uncertainty relative to scale n. The sigma (σ) values represent the spreading of entangled properties x and y.

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

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

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

can be interpreted as:

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

$\displaystyle \Delta p \Delta r \ge \hbar$

Exchange of the angular period or the period of oscillation t (by the increase in v and a proportional decrease in r) for energy may result in a jump to a higher discrete vertical energy level - appearance of energy on a larger scale (its spread beyond the inherent limit of resolution/stability on that scale). If the rest energy on that particular scale was previously considered as a relative 0, this may be interpreted as a relative violation of energy conservation, allowed as long as the increase in energy (inflation/spreading of E) is inversely proportional to particle stability (Δt) on that scale. However, period of stability here is the period of angular momentum, and in reality, energy is obviously conserved - it has simply changed scale [of spreading]. In CR, any rest mass is only relatively at rest and should be interpreted as energy in conserved/localized momenta. Note that oscillation between entangled properties is common in reality. Note that the postulated exchange between gravitational and electro-magnetic force can be formulated as a relativistic uncertainty. In its simplest form, in the limiting case:

$\displaystyle m v r = {\hbar}_n$

Suppose this is the spin momentum of charge. With the increase of mass m, vr decreases proportionally, exchanging electro-magnetic dominance for gravitational. Note also that the relativistic uncertainty is one formulation of conservation and exchange of [the amount of] relativity. Not only is the absolute precision or absolute localization impossible, since everything is multidimensional, confinement of [relativity in] one dimension results in the spreading of [relativity in] the other. This relationship is common for the dimensions of space (wavelength) and time inverse (frequency), e.g., in flat space-time:

$\displaystyle \Delta x {\Delta t}^{-1} \le c_n$

Which, for c_n = c₀ = c reduces to the absolute reference frame of GR.

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. 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). 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 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. The force (curvature in some interpretations) is greatest at the real graviton radius and generally decreases exponentially with distance of effective gravitons from the real one, however the gradient of potential will depend on the shape (dimensionality, or complexity) and energy of effective gravitons so it can progress linearly as well. Effective gravitons can be of different species or flavour so their ranges will differ. This can result in relatively sudden transformation from exponential to linear progression. The associated well of gravitational potential of a graviton may be considered its private space, however, that privacy falls off with distance. Elementary graviton has an intrinsic spin momentum, which can be quantized from some reference frames. This spin momentum is also 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. 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.

Physical interpretation

Assuming the scale of a graviton is U_n, constituent quanta of space forming the associated gravitational well will be of scale U_n-2. With an locally empty gravitational well, graviton is considered to be naked (as such, it may be interpreted as a dark matter particle of certain scale). However, attracted particles of scale U_n-1 will be coupling with quanta forming graviton's space (U_n-2 scale gravitons) and such couplings will be considered as coupled mass or real mass forming the body of the U_n graviton. Mass of the naked graviton may be referred to as imaginary (img) mass. Total mass of the body-soul coupling is then the sum of img and real mass. In some interpretations, however, real mass may be shielding the img mass, in which case total mass will effectively be equal to real mass. Elementary 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) of certain scale. The ground shape of a simple localized graviton is generally a torus. Relativistic momenta may distort the shape of a graviton, however, shape and distribution of mass of a graviton generally depends on its excitation state (which in some cases may be defined by 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 potential density maxima corresponding to the maxima of [the square of] the associated wave-function. In a highly polarized graviton, structure may be highly ordered, with oppositely polarized inner components separated towards different sides of the membrane. Fig. \fig1: General shape of a simple graviton in ground state (no radial/angular nodes in the waveform) Shape of a graviton is shown in Fig. \fig1, where the surface of a torus represents its effective boundary. 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. Charged gravitons, in addition to gravitational field tubes (which have ring-like and spherical eigenstates), possess both electric and magnetic field tubes. What are magnetic field tubes? 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 U_n-1 scale, space in the associated magnetic field lines is formed by particles of U_n-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.

Space-forming gravitons

Space-forming gravitons of an U_n graviton are of U_n-2 scale. These space-forming gravitons are hypothesized to orbit the centre of the larger (U_n) graviton. If the U_n graviton is completely naked, all the U_n-2 gravitons are uncoupled/non-localized and form radially standing waves (the semi-major orbital radius is relatively constant) of angular velocity equal to c_n-1. Once localized (with coupling to real mass), some of the angular velocity is exchanged for spin momentum, thus, the orbital velocity of the coupling becomes lower than c_n-1. The space-forming gravitons have different ranges (energies) and the density of these gravitons falls of with distance (generally exponentially). Different interpretations exist for why these particles remain in orbit, rather than being radiated away. In one interpretation, the reason is their non-zero rest mass and, thus, a finite range. In other words, they are confined, and once the range is reached, there is no more energy for additional expansion and they form a standing wave. In another interpretation, the encircled mass for them represents an effective or relative black hole so they cannot travel further and instead form a relative equivalent of a photon circle correlated with conventional black holes (where the surface tension is 1/2 of the surface density in a thin-shell approximation, in GR framework). Both of the interpretations can be true simultaneously. In case of the latter, however, obviously it is not the radially acting gravitational force that's keeping the particles in orbit (which would require escape velocity greater than the speed of light). Instead they could be considered as being part of the large scale graviton (U_n) - they are, in any case, entangled with it and are spatially extending its presence (in a wave form, spin momentum is certainly a more appropriate interpretation than an orbital momentum). This can be interpreted as a physical manifestation of a quantum wavefunction of the large scale graviton, where its location probability decreases with distance (square of distance, usually). The entanglement between the graviton of a larger scale (U_n) and U_n-2 gravitons can be lost (e.g., when the U_n graviton itself is delocalized or changes scale), which is then interpreted as decoupling of the U_n graviton from local space and the body of real mass that may exist in the well. The fate of U_n-2 gravitons will depend on the local environment and whether they are localized or not. Due to their standing (static) nature and confinement to a particular potential well associated with a parent graviton of larger scale, the space-forming gravitons will generally be referred to as static particles.

Effects of graviton interaction and oscillation

The constituent quanta of one graviton will weakly interact with constituent quanta of another graviton. However, in case of stronger entanglement the two may form a superposition in space and probability for interaction may increase. Superposition is, of course, relative, and if gravitons are of different scale, orbital radii of constituent quanta will be different. What happens to the gravity of a graviton confined within another graviton, assuming both are of similar energy (of the same or similar magnitude)? It is possible that extroverted gravity simply becomes the sum of gravity of all gravitational sources, however, relative confinement of inner gravity (inner effective gravitons) is possible as well. The reason for this is the non-zero mass of effective gravitons, which implies the limited range of gravity. Thus, those with shorter range can be confined within the radius of an outer graviton. In the extreme case of confinement, the outer real graviton may be effectively shielding the gravity of the inner real graviton. 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 graviton oscillating between different radii, 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 other work, I hypothesize that large scale gravitons (which may be 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 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 may have to be filled with fluids to ensure long-term stability. Note that Earth's surface gravity is greater on the poles, but that is a consequence of the reduction of the surface radius due to redistribution of mass towards the equator. Directly below poles mass density is lower than elsewhere. Are there tunnels below? Long-lived tunnels, except near gravitons, seem unlikely due to generally 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 (solids 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). It is questionable whether impacts alone can cause such large volcanism on the other side of the planet (although they can certainly cause widespread earthquakes and smaller volcanism). However, the recreation of tunnels with graviton oscillation (likely correlated with impacts) could result in such phenomena at antipodal locations - [enhancing] depression on the side of impact (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) and/or stronger impacts, 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 a result of unusually high alignment.

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

A naked (uncoupled) U_n graviton will effectively attract particles of U_n-1 scale. There are now two possibilities on the effect of total gravity:

1. with inflation and coupling of an U_n.space constituent U_n-2 graviton with an U_n-1 particle (U_n-1 graviton, which may be naked or coupled to real mass itself), one graviton is shielding the other, energy equal to the energy of the U_n-1 particle is confined and there is no increase in gravity of the well with acquisition of U_n-1 matter,
2. there is no shielding and total gravity of the well is increased with acquired matter.

Note that the 1. possibility may be interpreted as one particle giving mass to the other. Regardless of the outcome, the interaction could affect the range of gravity of the system. Constituent gravitons of space of U_n-1 gravitons are of U_n-3 scale which are orders of magnitude less massive, thus, with no significant shielding, the range of gravity is extended. 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 (e.g., 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 graviton of larger mass, 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 coupled 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. Here, thus, the energy of this large scale effective graviton is proportional to the intensity of the gravitational coupling with matter.

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, 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, e.g., 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 has a ring-like form, 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. 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.

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. Conventional theories on planetary formation have troubles explaining how larger bodies actually form from the dust grains. Another problem for conventional theories is the fast formation of these bodies, e.g., 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 absolute point sources of energy are impossible, 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 Newtonian 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
δ_ij = Kronecker delta

Obviously, if there are any sources of gravity inside and these are not balanced by the outer forces, the graviton would collapse. To prevent this collapse, a repulsive force must exist - either fictional (e.g., provided by the graviton angular momentum) or real (in case of specific entanglement, e.g., charge). In reality, both should be present to some degree. 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. 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.

Graviton flavour

Since all particles have mass, all are prone to the oscillation of flavour between couplings. Different flavours can be interpreted as different discrete local vertical energy levels. Generally, 3 major flavours exist for any particle (not counting the flavour corresponding to a naked graviton), and a non-localized particle (graviton) may be considered to be in a superposition of the 3 basis states. There is no change of energy during flavour oscillation, however, there is a change in the size of the gravitational imprint proportional to the mass associated with certain flavour. At the time of graviton localization, assuming there is enough energy, rest mass of the graviton can be changed, when it will, depending on the current flavour, settle in one of the 3 mass eigenstates. The gravitational imprint can be interpreted as curvature of space, or dark matter, of scale U_n-2 for a graviton of U_n scale. Gravitational imprint (space) is, thus, stretching and compressing with the oscillation of the graviton radius. Note that this allows for the graviton to acquire and shed real mass during flight, which may be interpreted as partial localization. The magnitude of this effect will depend on the properties of the medium. In high vacuum the effect may be negligible, however, in some media the speed of propagation may be significantly affected, due to momentum conservation. If, at the point of localization, there is not enough energy for the graviton to settle into the mass eigenstate associated with the current flavour, the graviton is most likely to settle into one of the possible flavours. However, the speed of time is scale dependent and time dilation will thus exist between scales, so the transition will appear continuous from some reference frames. In such frames, total mass (which includes acquired real mass) can deviate from the mass associated with the eigenstate. Locally stored kinetic energy may also be interpreted as gravitational mass from these frames. Since flavour and mass eigenstates cannot be absolutely synchronized, gravitons inflated on large scale (where time is significantly slowed down compared to the reference frame) may have long-lived unfilled gravitational wells (real mass capacitance). The unfilled capacity may generally be more likely to be concentrated in the outer regions of the well, however, this will depend on the graviton radius and whether multiple gravitons are present (which generally should be the case). Indeed, this naked gravitational imprint is commonly detectable in galaxies, as dark matter. However, these imprints should be present in planetary systems as well, although any unfilled capacity may be mostly concentrated within the bodies. However, rather than unfilled capacity, flat velocity curves can be explained by the change in the intensity differential of gravitational coupling with distance (e.g., change of graviton energy and shape from the 2-dimensional spherical form into a ring-like form).

Proper interpretation of kinetic energy

The value of kinetic energy is relative, however, energy will be locally acquired and released during changes in velocity (acceleration). Absolutely constant velocities do not exist and, since space is physical, any motion relative to space will involve absorption and emission of energy, but this may be interpreted as relatively constant motion if absorption and emission are equal and cannot be resolved. Momentum is coupled to energy, however, in cases where there is no motion relative to certain [scale of] space, one may consider kinetic energy as fictional and manifested only at the time of interaction (localization) when the interaction results in local increase in energy, when some energy may be inflated from smaller scale. All energy thus consists of real and imaginary parts of some scale, but, unlike in conventionally common complete reductionism, in CR, neither may have an absolute zero value, only a relative one. Whether the [part of] kinetic energy is produced upon interaction or is carried by momentum, it probably should be associated with flavour of gravitons, and thus [inflation of] physical gravitational imprints (img mass) proportional to the kinetic energy. Note that this does not forbid the inflation of flavour beyond the mass eigenstates, such inflation only implies relative instability.

Energy in the gravitational imprint, reality and illusion of a universe

For a simple graviton in orbital motion, this is generally satisfied:

$\displaystyle m \left({1 \over \sqrt{1 - {{v_s}^2 \over {c_s}^2}}} {1 \over \sqrt{1 - {{v_a}^2 \over {c_a}^2}}}\right) v_a r_a = n \hbar$

m = rest mass
v_s = spin velocity
c_s = spin velocity limit = information speed limit in spin space
v_a = orbital velocity
c_a = orbital velocity limit = information speed limit in orbital space
r_a = orbital radius
ℏ = quantization constant

The first relativistic term (enclosed in parentheses) here represents the energy in the gravitational imprint due to angular motion relative to spin space (space associated with the source of the spin momentum), the other relativistic term represents the energy in the gravitational imprint due to angular motion relative to the orbital space (space associated with the source of the orbital momentum). The n may be an integer, half-integer, or something more complex, depending on graviton nature and interpretation (reference frame of quantization). Reduced orbital wavelength of the graviton is:

$\displaystyle {\lambda}_r = {r_a \over n}$

Which is, for v_a = c₀ = c, c_s >> v_s, c_a >> c, and n = 1, equal to reduced Compton wavelength, which is the reduced wavelength of a photon whose energy is equal to the rest energy of the particle. But, in general, it is a reduced wavelength of a non-excited particle in a non-relativistic uniform motion, at standard light speed. For a particle with no orbital momentum:

$\displaystyle m \left({1 \over \sqrt{1 - {{v_s}^2 \over {c_s}^2}}}\right) v_s r_s = n_s \hbar$

r_s = spin radius

Reduced wavelength (or, reduced spin wavelength) of the graviton is:

$\displaystyle {\lambda}_r = {r_s \over n_s}$

With v_s = c and c_s >> c, this reduces to a Compton wavelength. It is obvious here that a realistic result requires c_s >> c, otherwise (with c_s = c), one has to reduce rest mass or radius to 0 in order not to obtain infinite spin momentum. Experiments have shown that the radius of a localized electron must be much smaller than its reduced Compton wavelength, and even much smaller than its classical radius. This implies that the contribution of electron charge energy to electron's rest mass is very small, even negligible, as according to some experiments the upper limit to electron's radius is 10^-22 m. Thus, its rest mass effectively originates in the spin momentum of its body mass, not charge. For an electron at rest, taking into account spin momentum magnitude, rather than its projection, this should then be satisfied:

$\displaystyle {1 \over \sqrt{1 - {{v_s}^2 \over {c_s}^2}}} = {{\sqrt{3} \hbar} \over {2 m_e r_s v_s}} = k$

$\displaystyle {{v_s}^2 \over {c_s}^2} = 1 - {1 \over k^2}$

$\displaystyle {c_s}^2 = {{v_s}^2 \over {1 - {1 \over k^2}}}$

m_e = electron rest mass = 9.10938356 × 10^-31 kg
ℏ = reduced Planck's constant = 1.054571817 × 10^-34 Js

For the mass radius r_s = 1 × 10^-22 m, and assuming v_s = c₀ = c = 2.99792458 × 10⁸ m/s, one obtains c_s ≈ c (only slightly larger than c). But what are the actual values of r_s, v_s, and c_s in reality? For practical purposes, one might assume that v_s = c_s = c and, thus, r_s = 0, but in reality r_s must be larger than 0 and both v_s and c_s may be larger than c rather than c_s alone. In case of particles of this scale, however, c_s may be equal to c, with v_s being slightly smaller. Thus, the assumption of a locally relativistic spin does not require for the electron to rotate faster than c (classically, for this radius, v_s would simply have to be larger than c by about 10 orders of magnitude). For the force carrier particles, v_a is generally fixed to c_n (or, close to c_n - in reality), which represents information transfer limit in space associated with the vertical energy level (scale) n. Reduced Compton wavelength for such particles is also their range. It is clear that in particles of variable wavelength, with fixed v_a (which can now be interpreted as propagation velocity) and fixed spin momentum, spin momentum components must be variable (in such way to conserve the spin momentum). For particles like photons, spin velocity v_s should be proportional to frequency and r_s should be inversely proportional to frequency. If flavour (gravitational imprint) oscillates between different eigenstates (and it does in reality for any particle), it is the velocity v_s that should oscillate as well (proportionally). If v_a remains fixed (in reality it too should oscillate but this may be negligible), to conserve total momentum, the range must oscillate as well (and should be inversely proportional to mass and frequency). Generally, for any naked graviton (graviton coupled to relatively negligible mass), v_n ≈ c_n. Once graviton couples to matter (higher mass, associated with particular eigenstate), v_n decreases significantly. Knowing the radius (range) of the observable universe, one can obtain the upper limit for photon rest mass. Its relativistic mass is:

$\displaystyle m = {\hbar \over {r c}} = 8 \times {10}^{-70}\, kg$

r = radius of the observable universe = 46.508 × 10⁹ ly = 4.4 × 10²⁶ m
c = standard speed of light = 2.99792458 × 10⁸ m/s

Thus, its rest mass must be lower than that.

Gravitons as force/momentum carriers

Gravitons are also force carrier particles, where dimensionality (complexity) of such gravitons will depend on the complexity of force. In case of the, so called, fundamental forces, gravitons usually have simple shapes, which may be interpreted as ground shapes of spherical harmonics. Forces are present on different scales and act on different bodies. In any case, intensity of force coupling (strength of force acting on a particular body) is directly proportional to the intensity of gravitons coupling to the body. And this intensity will depend on distance but also on the shape of gravitons, which can be further correlated with mass/range of gravitons. Generally, intensity depends not only on the density but on the dimensionality of the gravitons as well. Consider, for example, a force carrier graviton in the form of a 2-dimensional sphere [surface]. The strength of this force will decrease inversely proportionally to r², where r is the distance from the source. In case of 1-dimensional gravitons, in the form of rings, the force will decrease inversely proportionally to r. The same force can be carried by gravitons of different mass (range) and shape. Generally thus, the force decreases inversely proportionally to rⁿ, where n can be interpreted as denoting energy levels due to discrete ranges of gravitons (n may thus change with distance, but generally not continuously, rather at discrete points). Note that this can explain all cases of anomalous gravity (e.g., gravitons farther from a supermassive black hole have not only exchanged their energy for the energy of the supermassive black hole with universe's expansion, in the process they have reduced dimensionality). Gravitons can be more or less localized (they generally localize with coupling to bodies). The maxima of wavefunctions associated with gravitons represent maxima of potential of the associated force. This explains why electrons in the atoms, for example, generally can be found at these maxima. However, energy levels can be associated with any graviton of any scale, although these levels can be well confined and undetectable, especially on smaller scales. Particles localized to the maxima of another graviton (e.g., electron coupled to a proton) generally do not lose energy in these states. There are multiple interpretations of this. A particle may be in the form of a standing wave. However, since this particle is also coupled with gravitons forming [private] space of the parent graviton, the particle is not losing energy because it is, in equilibrium, rotating with space. On smaller scales this rotation can, and will, at some scale exceed the speed of standard light. This allows for more intuitive interpretation of spin momenta of particles such as electrons. However, since speeds larger than the speed of light are confined to smaller scales of space, the electron itself cannot travel faster than light unless it is itself confined below the radius at which the speed of light is exceeded. This, of course, implies that relativistic effects depend on scale as well (speed of information transfer is not absolutely invariant to scale, only relatively, as transitions are discrete).

Static particle

Particles forming space (effective gravitons) of a graviton of scale U_n are particles of scale U_n-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 U_n-1 scale. However, the particles will get bound (coupled) to U_n-1 scale matter captured by the gravitational well, exchanging orbital velocity for spin (U_n-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 space-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.

Rest = uniform motion = uniform ageing

A body (e.g., graviton) is at rest relative to local space if the coupling of constituent particles of space with the body is in the equilibrium state. This equilibrium is accomplished when the amount of coupled particles (strength or intensity of coupling) does not change over time (d/dt = 0). There are two ways to achieve equilibrium - the absence of motion and uniform motion. The two states are equivalent in a sense that motion through time is uniform in both. But there is a difference in the strength (intensity) of coupling, which is proportional to the amount of motion through space. This then implies a difference in the speed through time (rate of ageing). Stronger coupling (note that this is usually gravitational coupling) implies slower passage through time. Wherever motion relative to local space exists, relativistic effects on the body will be, at least in part, real. The degree, or the amount, of reality (physicality) in a relativistic effect will be proportional to the amount of physical motion through local space. To change the rate of ageing work must be done, energy must be transformed. Obviously, this is done through [real] acceleration, when the intensity of coupling is changing - growing proportionally to acceleration.

Reality and illusion of rest

The intensity of coupling (and, thus, the rate of ageing), for different reasons, can change [to a degree] even if the body is apparently at rest. This is particularly evident in living bodies, in which the rate of ageing measurably varies over the lifetime even when uncorrelated with changes in mass. Note also, however, that the coupling with complex bodies is more complex itself and variability can be limited to certain scales of coupling. Most complex coupling is lost at the time of death of a complex body, however, the effect on body weight may be negligible. The effect certainly is small in case of living bodies on Earth, but this is unlikely the case generally. The effect is inversely proportional to complexity, proportional to the number and magnitude of scales on which death (decoupling) occurs (e.g., a death of a human body is also a certain death of its organs, and will be followed by death of organelles and cells after certain time, but it's not the death of all the smaller components, such as microbes, molecules and atoms), and the intensity of the coupling(s) during life. Note that it is not hard to relatively quantify the complexity/intensity of coupling between different bodies at rest. If two bodies of the same mass age differently, the coupling is stronger and/or more complex in case of slower ageing. The intensity/complexity of coupling is probably highly correlated with the intensity/complexity of consciousness. In more massive brains, for example, the amount of consciousness is probably generally higher than in less massive brains (although one must here distinguish between extroverted and introverted consciousness - depending on sensitivity to the external and internal reality), but not necessarily the complexity of consciousness - which may further be correlated with intelligence. Neither consciousness nor intelligence require brains, the purpose of compressed neural networks is probably the focus/localization of intelligence/consciousness in space/time. Consider plants/fungi for example, in these systems both, intelligence and consciousness, are spread over space and time. Correlated with the intensity/complexity of coupling (rate of ageing) is the resolution of experience. Here, plants/fungi are more conscious of long-term effects than of short-term disturbances. A reaction of a plant to occasional disturbance (cutting of a branch for example) may be interpreted as subconscious or even fully reflexive (unconscious), but a frequent disturbance may be resolved (experienced) on a higher level of consciousness and may induce a more complex response (which may be evident in its progeny, if not in the plant itself). This complex response may be interpreted as emergent phenomena, but all emergent phenomena are, as noted before, probably correlated with distinct coupling. However, as rest can be illusionary, so can emergence. Emergence is, however, usually real in living bodies.

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 the 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.

Gluon

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

Gluon tube

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

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

Gravitational maximum is the n-dimensional area of a maximum of the gravitational potential in a gravitational well, with n corresponding to the dimensionality of the maximum. 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 can be considered as a 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. Energy of a gravitational maximum is proportional to the capacity (gravitational imprint) of the associated gravitational well for coupling with matter. 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 a naked particle (soul) can be interpreted as an act towards 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 [the 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. 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 (dark matter) 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. 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

One possible mechanism of induction (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.

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. More charged a graviton is, more two-dimensional it will be and the density of the gravitational field will be decreasing from the equator to the pole. Thus, the gravitational escape velocity (without taking rotation into account) can be significantly lower at the poles. This restricts the feeding potential of a black hole, as, instead of being trapped, some matter may simply be accelerated towards the centre only to be 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 (e.g., in young stars, where they concentrate 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 have 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 the Solar System confirmed with the 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.

Body	Inclination (ecliptic) [°]	Inclination (Sun's equator) [°]	Inclination (invariable plane) [°]
Mercury	7.01	3.38	6.34
Venus	3.39	3.86	2.19
Earth	0	7.25	1.57
Mars	1.85	5.65	1.67
Vesta	7.14	3.48	7.13
Ceres	10.59	3.40	9.20
Pallas	34.93	36.45	34.21
Hygiea	3.83	10.79	-
Jupiter	1.31	6.09	0.32
Saturn	2.49	5.50	0.93
Uranus	0.77	6.48	1.02
Neptune	1.77	6.43	0.72
Pluto	17.14	11.86	15.55

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 the 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 (e.g., 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 that these are youngest and were formed after system stabilization, however, more likely, as decreasing inclination (relative to the invariable plane) of dwarf planets in the main asteroid belt (and increasing alignment with the current equatorial plane) towards 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).

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. 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 (e.g., 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 kind of 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. 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. Pragmatically, 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 equation 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 the 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, e.g., electro-magnetic force might regress to gravitational force with inflation of energy, but also vice versa, depending on the scales in question. This is exactly what I hypothesize had happened with the inflation of energy in the observable universe.

Strong entanglement, interaction probabilities, 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. 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 an accelerated change in distance between charges will result in emission of photons, the photon can be interpreted as a product of a change in [the strength of] entanglement between charges. It then must be a composite particle, at minimum, a pair of particles produced with inflation of polarized space-forming gravitons of charged particles. Obviously, if the two charges are fermions (having half-integer spin momenta), the inflated particle (photon) must be a boson (full-integer spin momentum) - elementary for some observers. The composite particles of a photon (half-photons) are then fermions of scale U_-1, which may be interpreted as an inflated U_-2 electron-positron pair (or, perhaps electron-proton pair) - since electrons/protons are of scale U₀, their space-forming particles must be of scale U_-2. Absorption of that photon by an 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, even though one may dominate and the energy can be decomposed into electro-magnetic and gravitational waves and energy may even be exchanging between these during travel. Considering the apparently oscillating force dominance between vertical energy levels, the dominant force on the U_-1 scale should be neutral, suggesting that even the half-photons should not be electrically charged. Why do the photons, being neutral, interact strongly with the standard charged particles? In one interpretation, this is due to the difference in vertical scale (photons are of U_-1 scale, standard charged particles are of U₀ scale). Recall that adjacent vertical scales are entangled. This difference in scale can be interpreted as polarization and, thus, results in high probability of interaction in case of strong entanglement. Generally, a non-localized photon is, like a gravitational wave, a more or less spherical wave (energy distribution depending on conditions during emission and photon dimensionality), 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, e.g., in non-flat gravitational space).

Implications on evolution

Regardless of the physical manifestation of photon propagation, it obviously carries information on the source, including original location in flat space (which may be locally manifested as a recoil in specific direction at the 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, relative 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. 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, self-organization or free will.

Weak entanglement

Graviton tubes are always physical at some scale, however, with increasing distance and no additional energy applied to the tube, entanglement weakens. 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 a remote observer could measure superluminal transfer - assuming tube (subspace) is resolvable by that observer. 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 (e.g., 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 sufficiently limited observer, these relative values (e.g., zero, infinity and invariance), may be effectively equal to being absolute. However, any observer that assumes this is an inherent limitation of reality, rather than its own, will, by that, limit its own understanding of reality as well.

Layers of entanglement, background entanglement

Since entanglement in space/time is never broken absolutely, entanglement is layered and certain hierarchy in dominance can exist. On may thus introduce a concept of "background entanglement". Consider a simple case of gravitational and electro-magnetic entanglement, where the two are coupled through the uncertainty principle. One component may explode at the expense of the other, but the other is never lost absolutely. If dominance oscillates between the two, one of these can be considered the background [level of] entanglement.

Electric polarization and charge/mass exchange

In the standard model of physics particles have fixed (intrinsic and unchangeable) properties (e.g., 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). 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. 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).

particle	charge 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 m_g for the graviton (assuming unscaled gravitational constant G) as follows:

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

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

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

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

For r = 1 * 10^-15 m and mass of a down quark M = m_d = 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 m_g = 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. 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). 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 (m_e):

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

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):

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

Is it a coincidence that graviton momentum is quantized by [the inverse of] 2/3 electron mass? Down quark mass (m_d) 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:

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

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). 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 (m_e) 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].

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

input particle (mass m, charge)	charge fraction Q	n	output mass M (charge)	correlated standard model particle (mass, charge)
up quark (2.2 MeV/c2, 2/3 e+)	1/3	0	5.2741 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	-1	4.7467 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	-1	4.5069 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+)	4/3	1	1.8028 GeV/c2 (1 e-)	tau electron (1.7769 GeV/c2, 1 e-)
anti-strange quark (96 MeV/c2, 1/3 e+)	2/3	-1	92.0566 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	-3	2.0713 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	-2	1.7836 GeV/c2 (1 e-)	tau electron (1.7769 GeV/c2, 1 e-)
positron (0.511 MeV/c2, 1 e+)	1/3	3	1.225 GeV/c2 (2/3 e+)	charm quark (1.27 ±0.02 GeV/c2, 2/3 e+)
positron (0.511 MeV/c2, 1 e+)	2/3	0	4.9 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	-2	2.533 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	-1	101.3198 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). 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):

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

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

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:

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

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. 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:

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

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:

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

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 m_img.

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 U_n, coupled real mass is of scale U_n-1, while particles (gravitons) forming space associated with the graviton are of scale U_n-2. 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. Real mass is usually denoted with m_re. 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). 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:

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

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 r_s), which at full capacity is Keplerian:

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

However, evidently, angular velocities in gravitational wells are not always Keplerian (e.g., 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). In case of lack of velocity, the well is over-capacitated (real mass is greater than img mass). 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 (m_re < m_img) at the same radius velocity must increase. Decoupling can be simply achieved with the inversion of a spin of a graviton (e.g., 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:

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

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

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

Here, of course, v_re and T_re should be relative to rest velocity (expected Keplerian velocity) and period when calculating local excess energy. 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:

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

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

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

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

Excess mass is:

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

body	total 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]
Mercury	0.330	4.8728	567028	1407.6	6231.6	0.1588	6232.3	0.3203 (97%)
Venus	4.868	63.6013	3079911	5832.6	10269.8	0.5234	10270.7	4.7408 (97%)
Earth	5.972	534.1110	1206084	23.935	18090.9	0.1158	18178.8	4.9038 (82%)
Mars	0.642	109.8515	1581777	24.623	5092.5	0.5304	5204.6	0.4223 (66%)
Pluto	0.01303	0.6371	224993	153.293	1963.4	0.1997	1966.0	0.0118 (91%)

Table \tbl3: Spin momentum components and excess energy of terrestrial bodies* 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. 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 (r_s). Apparently, complexity (excess mass percentage) of terrestrial bodies can be determined by the following equation:

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

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

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

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

with parameters shown in Table \tbl4.

n	j	i	body	distance from the Sun d [109 m]	complexity p (%)
1	0	0	Mercury	57.9	97.0
3	1	1	Venus	108.2	97.2
3	2	3	Earth	149.6	82.2
1	3	6	Mars	227.9	66.2
3	17	153	Pluto	5906.4	91.1

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. Calculated distances are shown in Table \tbl5.

n	j	body	distance from the Sun d [109 m]	calculated distance dn [109 m]
1	0	Mercury	57.9	53.7
3	1	Venus	108.2	107.5
4	2	Earth	149.6	152.0
5	3	Mars	227.9	215.0
19	17	Pluto	5906.4	5937.4

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. Such splitting (entanglement) may be described by the splitting operator, or, perturbation 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:

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

Hallucination

Hallucination is the experience of reality. Hallucinations can differ in intensity, coherence and consistence and all these are variable. In living/conscious beings, experience of reality is generally a superposition of different types of hallucinations where some may be subdued, others intensified, depending on which level of consciousness is dominantly active. Human experience of reality, for example, generally can be reduced to two distinct types of hallucinations. One dominates during sleep (introversion) - when the extroverted senses and interactions are subdued, other dominates during extroversion - when the activity of external senses is intensified and interaction with the environment dominates the experience of reality. Certain aspects of sentient experience of reality may be simulated or emulated by artificial machines. One may refer to this simulation/emulation as an artificial or non-conscious hallucination. Conscious experience of reality requires souls, whose coupling (specific entanglement) with the body acts as a catalyst for the experience. However, this entanglement does not have to have a physical interpretation on a scale accessible to the observer. Experience of reality does not depend directly on the sense, rather the interpretation of that sense. This allows for dominantly extroverted and dominantly introverted beings to experience equivalent realities.

Intelligence = general intelligence

Intelligence is the ability of an entity to focus its processing power and produce logical and unbiased conclusions based on optimally correlated and coherent information and information processing, in problem solving. Intelligence can be biological (coupled with consciousness) or mechanical (e.g., artificial). Generally, intelligence is a mixture of conscious and mechanical intelligence, however one or the other component may be negligible and the amounts of each are relative. Consider a human being, a lot of brain activity highly correlates with conscious intelligence from a human perspective, however, many physiological processes are highly automated and do not involve highly conscious processing of information.

Conscious intelligence

Conscious intelligence is the ability of an individual to focus its consciousness and produce logical and unbiased conclusions based on optimally correlated and coherent thoughts, 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 considered as 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. Introverted organisms can be highly intelligent, but with subdued extroverted expression may not be considered as such by extroverted organisms, and 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 in a highly conscious and energetic way. However, near-death experiences show that introversion can feel more real than conventionally perceived (extroverted) reality. Generally, life-forms are hybrids (superposition) of extroverted and introverted intelligence. This is evident through the existence of dreams in extroverted species, however, lack of conscious control, consistency and coherence make these experiences virtual for most. It is evident on the level of organs as well - while the organism may be expressing extroversion, some internal organs may be introverted. Intelligence is polarized when one component is higher than the other. Generally, thus, any particular species of intelligence may have polarized and neutral subspecies of individuals. Survival of a body during evolution generally requires usage of the body. Similarly, survival of a soul during evolution requires usage of mental capacity. Extroverted intelligence is generally more concerned with the former, introverted with the latter.

Extroverted intelligence = physical intelligence = material intelligence

Extroverted intelligence (I_M) is the amount of intellectual capacity generally used to ensure survival of the body of a living being (consciously or subconsciously), its own species or entangled (symbiotic) species and the living environment. In highly extroverted beings conscious care for the soul is highly subdued and use of the mind may be limited to short-term excitations usually highly correlated with physical activity. Extroversion does not imply low intelligence of the mind, only an mechanistic intelligence (subconscious bias towards reductionism and close-mindedness).

Introverted intelligence = mental intelligence = spiritual intelligence

Introverted intelligence (I_S) is the amount of intellectual capacity generally used to ensure survival of the soul of a living being (consciously or subconsciously), including the entangled (symbiotic) species. In highly introverted beings conscious care for the physical body and its use is highly subdued, it may be outsourced to the environment (external entities) or delegated to the constituent entities of the body (local ecosystem), more or less influenced by the host through the subconscious levels of the mind. Introversion does not imply high intelligence of the mind, only a spiritual intelligence (subconscious bias towards holism and open-mindedness).

Intelligence potential

Biased intelligence will favour beliefs of interest (illusion of truth), rather than the actual truth (reality of truth). The truth is, however, essential for real scientific progress and long-term sustainability. The intelligence potential (IP) is a measure of neutral (non-biased) intelligence, generally concerned with truth and the sustainability of truth. The IP is plastic, and, in polarized (disease prone) individuals, can be strongly affected by diseases (such as depression). In any case, generally, the lower the IP the more it can be correlated with short-term interests. A function for the determination of IP should have this form:

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

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

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

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 (e.g., EQ) are a measure of such intelligence projected to (entangled with) external reality. While IQ might correlate well with IP for extroverted species with significant introversion, it is not well suited for extremes and is completely inadequate for measurement of intelligence of highly introverted species.

Artificial intelligence = non-conscious intelligence

Artificial intelligence is the ability of a machine to focus its processing power and produce logical and unbiased conclusions based on optimally correlated and coherent information and information processing in problem solving. Even if individual atoms the computer is made of possess consciousness (i.e., 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 exist for a long time now, their processing power and complexity have been increasing exponentially, 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 (illusion of consciousness is increasing). 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 - e.g., by replacing neurons with transistors, however, transistors are not living cells and this replacement may be diluting, or reducing the amount of, human consciousness (at least initially). In other words, human consciousness could be delocalizing gradually and conscious 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 artificially 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.

Life

A living being or 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 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 the 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 may 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. Planets, in example, appear to be extremely introverted lifeforms (evidence for this, however, is provided mostly in other works of the author) - 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).

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.
	E.g., 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)
		-------------------------
		E.g., 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)
		-----------------------
		E.g., fusion