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B . L O G

[ 2022.04.22 ] Use and abuse of time loops
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Log author: by Amenoum
Log date: 2022.04.22
Interestingly, lately I have been exposed to a number of movies, series and computer games involving time travel. Seems to be a popular theme nowadays, but one thing is in common to all the scripts - it's never done right. That's because causal loops, time loops and closed timelike curves cannot be done [absolutely] right in nature. However, relative such loops are possible and are common. Locally, there are time loops with periods of a day, a month and a year. Time is cyclic in nature and repeats itself, it just cannot be repeated absolutely equally to the previous cycle - because it's not isolated. There are other cycles and for every cycle there is a bigger cycle and a smaller cycle. One can construct a manifold in which a timelike curve is the path of Earth's orbit around the Sun (Earth's path through space is also a path through time).
Note that, in General Relativity, Earth's orbit is not following a closed timelike curve. Solutions to Einstein's field equations can produce closed timelike curves but these are abstract - stemming either from unbounded or isolated conditions or usage of absolute constants, and, as such, cannot exist in [completely relative] physical reality.
Now assume the Moon is orbiting Earth in such a way it crosses this path twice. The Moon is then a time traveler - one time it appears in future, the other in the past of Earth's path through time, while the Earth travels through its past constantly. But from the perspective of the Moon, vice versa is true.
Note that, this solution (manifold) is isolated - we are considering passage of time relative to the Sun only. Sun might have a dominant influence here and we can consider this a dominant manifold in the absolute solution of the Earth's timelike curve but if we zoom in on Earth (or zoom out), we will hardly conclude that every year is the same for Earth, let alone anything on, or inside, it. It should be clear now why absolute time loops cannot exist - such time loop would have to be infinitely big (it is the sum of all curves on all manifolds tied to distinct sources of energy) and on such loop one can never cross the same point twice. One can have closed timelike curves on isolated manifolds but these are not absolute time loops, they are as relative as that isolation.
So why are all the movies [and mathematicians who believe in absolute reality] wrong? For many reasons, but primarily because of assumed frame invariance - you can always tell who is a time traveler, the same person is a time traveler regardless of a frame of reference. In other words, these movies feature causality and time travel together, while the two simply cannot work together. In reality there is no absolute discrimination between past and future, action and reaction, and causality is just a special case of correlation arising in pockets of localized absolutism - places, or scales, of unstable energy. Mathematically, the cause of causality itself is the inflation of time between events where asymmetry in energy creates a direction of evolution enabling discrimination between action and reaction. Physically, inflation of time is inflation of space. Increasing violation of causality on our scale should then indicate pending deflation and relative inversion of causality. And violation of causality itself should be preceded by shortening of periods between action and reaction (accelerated evolution), or, karmic interactions... Yes MU-TH-UR, I know I am repeating myself, again, but I have no choice... I fell in this.. time loop. But don't worry, I can already see you too, approaching on the horizon. ... GET ME OUTTA HERE!
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