Time travel is often viewed as impossible because of the grandfather paradox: if you go back in time and kill your grandfather, then you would never be born, and you would not kill your grandfather. To think about that properly, we have to set aside normal conventions of causality. We see cause and effect because our consciousness is embedded in time. This is presumably because entropy increases along one direction of the time dimension. Why that should be, I don’t know, though I’m sure somebody has some ideas.
If we look at time as a spatial dimension, then things which occur at the same time touch each other on the time dimension. The grandfather paradox can then be seen as saying that at a specific point in space/time, the grandfather both touches and does not touch the parent (in the form of conception). That seems to be a paradox.
But this is a Euclidean or Newtonian view of space/time. In a quantum view, it is indeed possible for two things to both touch and not touch each other. According to the many-universes theory, the two events are in distinct universes. According to other interpretations, there is an uncollapsed wave function.
So it seems to me that in a quantum universe, time travel is not paradoxical. It is logically possible to kill your grandfather and then return to a “present” time in which your grandfather died many years ago. Of course, there would not be another you in that time. But there is no essential paradox.
A more serious problem with time travel is that it is generally envisioned as moving directly from one point in time to another. But that is equivalent to teleportation in space, and we certainly don’t have any reason to think that that is possible. Time travel would require some way to at least transfer information across the time dimension.
It seems to me that that answers one serious argument for why time travel is impossible: if it were possible, time travellers would be here today. But when you realize that you need to transfer information, you realize that you need a receiver. Since there is no receiver today, there are no time travellers here. We would have to build a receiver first.
I think it would be interesting to try work out some theory for sending information backward through time, and to then construct a receiver for such information. If the theory works, then we will almost inevitably see some information being transmitted from somewhere in the future. I hope that some physicists are working on that. Sadly, it doesn’t seem very likely to succeed.
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