From Ethan Siegel at Forbes:
This might seem like out-and-out science fiction, but not all of it belongs to the “fiction” category: traveling through time is the one thing in science that you can’t help yourself from doing no matter what you do! The question is how much you can manipulate it for your own ends, and control your motion through time.
Physicist Siegel offers theories that enable forward or backward motion through tme but says
But that’s a mathematical solution; does that mathematics describe our physical Universe, though? It appears not to be the case. The curvatures and/or discontinuities we’d need our Universe to have are wildly incompatible with what we observe, even near neutron stars and black holes: the most extreme examples of curvature in our Universe. More.
Yes, that’s the difficulty. We can imagine things that cannot exist. Reality is constrained but imagination is not. At some point, science must make peace with reality.
See also: Does a Time Travel Simulation Resolve the “Grandfather Paradox”?
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I’d like to think some cute stuff like “quantum time travel” e.g. “extra temporal coherence” and maybe some elegant but all but useless bigger effects exist, with respect to our access of the structure of time. But Back To The Future style time travel, while dramatically engaging, is analytically disgusting.