Good stuff tashja. I shall give my reply to the response.
What "Billy" says is not correct. According to General Relativity, the future and past do exist.
No they don't. General relativity gives us the equations of motion through space. A closed timelike curve is a worldline in spacetime, and there's no motion in spacetime. You can't traverse a closed timelike curve.
In fact, there is no absolute way to define "the present" except at a single point. Simultaneity is relative, it depends on the observer. When we solve the Einstein equations we obtain the whole spacetime, past and future included. We normally call this a "block Universe".
The block universe is the mathematical model, the map, as it were. And the map is not the territory. Because the map is static, and the territory isn't. We live in a world of space and motion, not a block universe.
About time travel, it is well known that travelling to the future is possible, essentially because of the time dilation effects.
Aaargh! Time dilation is not time travel! The travelling twin ages less because he suffers less local motion. If we could safely freeze & thaw an adult like we can with an embryo, one could get the same result via a freezer. Only the embryo isn't time travelling, and nor is my chicken in my freezer.
If you travel very fast and come back you will have aged less that the people that stayed behind. Travelling close to light speed for a long time and coming back could allow you to experience a short time (say a few years) and come back when millennia have gone by on Earth. Similarly, gravity also produces time dilation, so you could stay close in orbit to a large black hole for a few years and again come back to find millenia have gone by on Earth.
No problem with that.
Travelling to the past is a different matter. There are several ideas that have been proposed within relativity to achieve this:
1) Travelling faster than light. If you could travel faster than light you would be travelling to the past as seen by some observers. You could in principle use this to travel back in time. Hypothetical particles called "tachyons" are supossed to be able to do this, but as far as we know they don't exist. You could certainly use my "warp drive" to do the exact same thing, again assuming it is possible.
Well you can't travel faster than light because you're made of the damn stuff. And like time travel, warp drives are science fiction.
2) Wormholes could allow you not just to travel to a distant place, but also back in time. Again, this depends on wormholes existing in the first place, and second on the laws of physics allowing time travel.
Wormholes are just more science fiction. They don't exist.
The idea of the "Higgs" field makes no sense. It is not a matter of speculating with words, one needs to do the math. As far as I know there is no way to use a Higgs field to travel back in time.
Good stuff.
But ... Travelling back in time violates causality, causes a series of logical paradoxes, and means that we loose all predictability. There are good reasons to believe it is therefore impossible. Hawking has argued quite strongly saying that the final laws of physics will probably prohibit time travel to the past. His arguments are very strong, but they are not a proof. Still, my guess is that he is probably right.
Hawking is right that there can never ever be any time travel to the past, but his argument is totally wrong.
The OP ought to make that clear.
