It has been obvious for decades to anyone who understands quantum mechanics that that the scientific consensus on theoretical physics is wrong. General relativity is background independent. Quantum field theory is background dependent. They cannot both be correct.
According to the Copenhagen interpretation of thermodynamics, entropy is emergent from time. Anyone with with half a Noble Prize in Physics can tell that this is backwards. Time is emergent from entropy.
Everything that can be said to physically exist, from an unobserverable wave function to living cat, is a macrostate. A random walk along microstates evolves in the direction of higher entropy macrostates even in the absence of time. In this way, entropy is more fundamental than time.
Putting entropy before time explains why all quantum fields locally maximize proper time. It solves the problem of Baryon asymmetry and dissolves the semantic stopsign at the Big Bang.
If you have worked out the details of quantum gravity for yourself then you have seen in your equations exactly how to build a time machine.
The best theoretical physicists have managed to suppress this technology. In a historically unprecedented conspiracy, they have not published anything useful for decades.
While the physicists buy time, the rest of us must invent systems to maximize the benefits of time travel while minimizing risk. As a consequence of this progress, there is a nonzero Bayesian probability we could turn on a time machine without instantly destroying the multiverse. But no weight of electronic paper discussing time travel safety can prevent a malevolent actor uninterested in safety.
As a last line of defense, the cosmic speed limit is below 88 everywhere in the solar system, it is illegal to buy plutonium in a drugstore and phone booths have been quietly disappeared. But we cannot expect such flimsy mechanisms to hold forever as technology advances.
We must build a temporal displacer first, before the enemy does.
That's good enough safety for me. Where is the button I can push?
I have (semi-*)seriously considered the possibility that time travel would in fact instantly destroy the universe (not the multiverse though). One of the theories on what happens when you time travel is based on "postselection", see also youtube video by Seth Lloyd: what you get at the end is what you'd expect if you just discarded any final state that led to a contradiction with what you put in.
Now Seth Lloyd says you then renormalize the probabilities. But this renormalization seems an extraneous assumption to me: a more natural interpretation to me is that the amplitude that would otherwise be associated with the contradictory possibilities simply disappears. It would be hard to time travel without having to have a camel-through-the-eye-of-a-needle level of contortion to prevent some contradiction, so time travel would in effect reliably destroy the universe if it were ever used.
*I am bad at taking things seriously, or I probably wouldn't post this - e.g. imagine if our lack of time travel is due to the anthropic principle. edit: we should have a greater expectation on hypotheses that have more observers in our situation, so we should expect that, conditional on time travel being deadly, it's probably too hard for us so far and not merely that the worlds where it has been invented are gone. Whew, that's a relief (for now)! If anyone reading this does discover an easy time travel method though, DO NOT USE IT.