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 metric 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 with each orbit.
The Moon is then a time traveller - 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 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
factor 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 associated with all 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 traveller, the same person is a time traveller 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.
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 the shortening of
periods between action and reaction (accelerated evolution), or, karmic interactions...