Time travel violates the law of conservation of energy. By travelling back in time, you yourself are injecting more mass/energy into a system. So it's great as a science fiction trope, but if you're going to talk physics, that needs to be addressed.
that's wrong. Noether's theorem says that "energy is conserved" is equivalent to "the laws of physics are time invariant". If you assert that "energy is conserved" because "the laws are time invariant" that risks begging the question. At the very least you should be asking "ok, then, why are the laws of physics time invariant?"
We know that all of the laws of physics we observe at the local scale are time invariant, but that is not necessarily true for any law we haven't discovered yet. While on the local scale that feels so unlikely as for it to be basically considered "inviolable without extraordinary evidence", that is not necessarily the case in the community for laws at the cosmic scale.
I don’t have the details but I’m pretty sure passage of time is due to a tendency for entropy to increase, and that if I go back in time a second by, say, walking backwards, it is no more a violation of the cons of energy as if I walk forward.
How do you know you aren't walking backwards back in time? To be complete you'll also need to be losing your new memories and becoming younger - it's experimentally undistinguishable.
Always conservation of mass is maintained by broadening the scope of the system under test. You can take matter out of a local system and make that local system less massive, but it’s not a violation of physics because the broader system maintains a steady state.
So isn’t the simple layman’s answer that the “system” also spans the 4th dimension and you are just displacing mass around in a 4D space instead of the typical 3D space?
I dont think conservation of mass works like this between "disparate" points in the 4th dimension. It has to be continuosly connected. Otherwise things could appear out of thin air without causality. Reminds me of this software: https://4dtoys.com/ (4d is time in this case not another spacial dimension but the intuition about discontinuity still applies)
If you could just send information back in time that would not violate conservation of energy. But otherwise would have a similar effect as traveling back yourself. You simply tell your past what to do rather than going back and to do it "with your present yourself". This also avoids a lot of other paradoxes and we already know that the reverse (sending information to the future) is super simple.
