The internal contradiction of the Identity Principle is that in order for two entities to be the same they must be distinguishable as two therefore there must be some difference, some element that distinguishes them and at the same time in order for them to be different there must be some element of the two that are the same in order to even compare them, to even relate them. Some element of the two entities must be exactly the same, equivalent in order to even relate them since any comparison between the two must be hinged on some reference point, some invariant that serves as the starting point, the zero of the coordinate system so to say from which to measure the two and obtain two different measurements and some element must be infinitely different in order to distinguish them, to declare them as two entities upon which the Identity Principle can be declared, the values V1, V2 that are plugged into the function "Identity Principle(V1, V2)".
So they are the same and different at the same time, a pure total contradiction, thought paths and processes break down, logic breaks down, this is the end of the line for our Man Brain as it is presently configured and designed. You must change the design of the present Man Brain to eliminate the contradiction...
Also, time is the constant change of the configuration of bits describing the entire universe, and since this configuration is always changing no matter what, in a sense time travel is impossible because each time instant is one configuration of bits that will never come back again and can never be obtained again, each instant is a unique number that can never be written down again no matter what, a fleeting number that was and will never be again no matter what, no matter how infinite the universe is in size and time or anything else, infinity in time and space and anything cannot ever make that fleeting instant appear again, no matter what. So this can be a definition of time.
Of course you can locally configure the bits of a chunk of matter in a cube to be exactly like New Jersey in 1953 with all the people there and reproduce the exact same "Information Relationships" between people and their minds and memories and all and actually really travel back in time, at least as far as our Man Brain experience can tell and distinguish (let alone play around with it inserting new memories and mixing different time slots and elements, different time periods (a year 2000 model car in NJ of 1953 and such) to see how people react and such). But the chunk of matter in the cube that is configured accordingly to make believe and simulate that it is an environment that "once was" is delimited in space, maybe a chunk of matter, a cube of matter 100 km wide and long and high where the simulation of that exact past is being performed in such a way that the actors within that "fake past" could never tell that they are in a fake reality, since the only thing that counts is the Experience and Reciprocal Information Relationships between the actors and their interaction with the material items and people surrounding them. However, outside of the cube of matter playing out the simulation, time would still be flowing forward, the configuration of the universe as a whole would still be ever changing, just that cube would be repeating a sequence that was performed previously for only some very small and insignificant subset of the universe as a whole, a small chunk of matter returning back to a configuration it once had, but only for that very small chunk of matter, it can easily be done and performed and played out. So it wouldn't contradict the laws of the never returning numbers again.
That would beg the question: is there a metaphysical entity, property of matter that makes it deeply different from itself, from another configuration of matter exactly equivalent, mathematically equivalent being billions of light years across, even if just one photon millions of light years away is different as compared to an exactly equivalent chunk of matter inside a cube of hundreds of millions of light years across ? In other words, take two cubes of matter 100 million light years wide and high and long, make them 100 % exactly equivalent and then change just one photon: does that change the two chunks in such a way as to express the flow of time ? is time hinged only on change no matter how small, and change is constant if only because particles are never at thermal rest ?