In short, time travel means nothing without space travel. Earth is rotating around the Sun (Sol star), Sol rotates around the galaxy and the galaxy is also moving. So say you want to prevent the assassination of JFK, you’re not just talking about going back 66-67 years, but say you don’t even care where on Earth you end up, where was Earth then? What’s your point of reference? Your point of reference moved.

It's complicated.
We have time at a large scale, and at a small scale. On the small scale, particles interact with time but in a mostly symmetric way, forwards and backwards are the same.

This would and does translate upwards, except it so happens in our "past" is a low entropy state, the "early" universe. Entropy tends to increase, energy spreads out, so what we call time, or more important causality, is the gradient of entropy.

For all we know, another universe could be in the past "before" "the big bang", which has its entropic time running the other way, also towards an expanding universe. (this is kinda adjacent to the big bounce theories, but does not postulate this repeats).

Now, there is a bunch of weird stuff general relativity permits with spacetime, including stuff that time travels (e.g. wormholes, warpdrives). This may or may not be possible to create if it doesn't currently exist, and it also may or may not be possible to use without getting destroyed even if it exists.
But interestingly, even if it were to be usable, be it wormholes, ftl warp stuff, or whatever, it may not break entropic time, only particle time which noone cares about. Causality may simply still be running forwards through that connection. That's still in the theorycrafting stage though.

There is yet more weirdness. For example, when you cross the event horizon of a black hole, you cannot go back, only slow your speed of going forwards, but you can with that travel through things that have fallen in before and after you. So compared to outside, entropic time is now in the direction of a spacial direction. Technically this lets you time travel through the particle-time axis, by some definition, but entropic time is still boringly pointing in one direction, though now by some more definitions that entropic time would causally sit after the end of our universe, so you have very efficiently entropically time-travelled to the end of the universe, infinitely far into the future.

So yeah tldr what we mean by time travel is not looking very possible lately (other than travelling to the future).

From what (i think) i understand about time is, it is a property of space (which is a energy level) that can be locally warped to go faster or slower, but past and future are purely human mind models.
Meaning: there can be a difference in how fast stuff happens but the comparison points don't interfere (can't be low-energy and high-energy level at the same time) and since nobody creates a "savepoint" of the universe, no past exists.

Edit: right, then there's also quantum time, where it depends.

And you meant dilatation?

Time follows geodesics on a curved spacetime manifold, so it’s linear locally but not necessarily globally. In theory a manifold with the right curvature could have geodesics that form loops (which would imply time travel), but there’s no practical way to cause such curvature.

Can I present you PBS Spacetime. In particular this somewhat recent episode explaining time travel is "inevitable under sole assumptions". https://www.youtube.com/watch?v=dZaqLgezRNE Some older episode talk about time travel in some event horizon of rotating black hole.

But in standard normal well understood universe. Nop. Not possible at all.

I think (based on our understanding of the line between the quantum world and thr macro world), time travel is just fantasy.

While mathematically time is reversible for sub-atomic particles (quanta), that breaks down as you gather more particles together.

But it's been a while since I've read deeply on it.

Reguarding black holes. The idea is that things don't go straight into a black hole. Like everything, they orbit. The orbit gets closer and closer, tighter and tighter. As it does the orbital speed increases. Eventually it increases to the speed of light (or near enough practically). For things moving at the speed of light, time effectively stops. So kinda, yah. Subjectively time ceases to exist in a black hole.

There is currently an experiment being conducted where the researchers are attempting to receive a message before sending it.

https://www.youtube.com/watch?v=KZX_c6zfJ2w

Time doesn't exist. Clocks exist.

So basically, our three dimensional universe originated in the formation of a black hole in a four dimensional universe. We're in the event horizon of a black hole. Since we already know the fourth dimension is time, we'd have to escape the event horizon to travel in time. So far, we can hardly escape the gravity well of Earth.

I think we have cracked time travel. I believe it’s happening all the time, but it places you in the same spot in the universe, so going forwards or backwards will just get you floating in space. A good deal of what we see as shooting stars are just the bodies of time travelers who tested it by a few seconds and ended up just outside of the atmosphere and burned up on reentry.