Is it possible to go back in time?
I believe that everything is possible in this world. If that can be done then why aren't we receiving any message from the future.
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To go back in time, including sending a message back in time, you need to construct a closed timelike curve (CTC). No-one has even been able to prove this is impossible, and indeed there are solutions of the Einstein equations that have CTCs. One example is the Gödel universe, though that requires the whole universe to be rotating and our universe isn't. There are smaller scale solutions called traversible wormholes, but these can only be formed by exotic matter and as far as we know this does not exist.
So far no-one has found a way to construct a closed timelike curve using physically reasonable methods, and there are good physical reasons to suppose that CTCs cannot exist, e.g. they would mess up causality. Since we observe the universe to be causal it obviously isn't packed with CTCs. I believe, though I wouldn't swear to it, that CTCs also cause problems with unitarity in quantum field theory.