Time travel is impossible because it offends reason. Time is fixed, and is not a malleable “dimension”. There was one 1960 and that’s it. You can’t go fast enough and live through last week again. Where does it exist? This alternate Nebraska, with an alternate family, cooking last weeks dinner.
It should be way past obvious that sci-fi and string hypothesis (not a theory since no repeatable experiments demonstrate it) have taken physics into a deep error.
We have flipped the model and made a grave error. When the math does not describe the observable universe we should look at the math model and look for the errors. Instead, we decide the math model is accurate if the calculations are right, and try to make the observations fit the math.
In 500 years they will laugh at us.
At the quantum level lots of things offend reason. Experiments have demonstrated that entangled particles are linked not just across infinite space but also infinite time. It's possible for an event in the present to alter an entangled event that occurred in the past. Unfortunately for some unknown reason there doesn't seem to be a way to use this to pass non-random information, but the effect is real. It's a clue that time and space as we perceive them are illusions of some kind.
Particles can be quantum entangled through time as well as space