Time Reversal

A friend of mine watches his wedding videos saturday afternoons but he looks at them in reverse. He says he always cries at the part where he gives his bride back to her father.
~

In everyday language and in effect of experience, a type of time-travel will be described that has none of the obvious contradictions but it turns out really not very exciting. This is the type of evolution I will discuss here, and in this stricter setting is there are no inherent paradoxes. 

Our approach is of purely philosophy and obviously would not be of practical value. We are looking at an evolution in time where the past can be known and is unique and fixed, as of observation of any previous instant indefinitely, so that a so-called time inverse exists giving any given previous state. In mathematics such an evolution would be called a dynamical system and warrants serious consideration.

Semi-groups

The alternative is when there doesn't have to be only one single history, and thus the evolution is not invertible and it is called a semi-group. Apart from relaxation of this requirement the basic properties are the same but now it might be possible that two past states converge and meet in the same “present”. It would not be hard mathematically to demonstrate with an example. Two distinct past states can lead to the same “now”, or two different histories could result in the same present.

However with the invertability assumption made, very interesting recurrence theorems amongst more can be proved, where given enough time, with a googleplex and closer to infinity a given state will return and be revisited. The study of chaos theory is also in the framework of dynamical systems and in the results perturbations and probability effects can be incorporated.

Many more possibilities now arise. As a reality the evolution idea of a semi-group becomes scientifically more feasible as well as desirable and is much more acceptable to everyday experience, where even now a beginning, a Big Bang can be accommodated. Unfortunately this allows contradictions involving time-travel.

For a dynamical system there could be only one history for each given state, only one.

Probabilistic considerations

In a purely deterministic evolution without uncertainties, occurrences inherently random do not exist and probabilities even for such as in gambling for example, all of it is pre-determined in principle there isn't a problem.

Whereas in turn if the deterministic property does not apply entirely, for example with existence of fundamental probabilistic influence as an element of chance, it would probably make amongst others my quantum mechanics colleagues very happy and all of this reasoning does not apply. So that for or a semi-group and a dynamical system in principle there cannot be any true probabilistic effects.

Reversing time

Thus for a dynamical system the requirements are stricter, for any given time the state of the universe is determined, thus there is a history that is (can be) “known” unique and fixed. For any time in space one can see and “return” to any earlier time and indefinitely backward, but this must imply that there was no beginning, at the time equal to zero, and that time is negative also. This says that there exists no element of chance or such and only one possible history, you might call it backward determinism, as a total and complete determinism, both forwards and backwards.

Reality

The Universe as described would be a repetitive monotonous boring place indeed, and I claim that in such a setting free will cannot exist and I would say consciousness itself cannot exist and God neither, I feel these cannot be accommodated.  The time-inversion assumption has to be scrapped leaving us with a semi-group.

The concepts of time and reality must definitely be radically different from our experience and I don't believe it works like this, I do believe in a free will and a soul.