True time travel (yes, it’s possible) is called time dilation. The faster you go the slower time will pass. This is the core of Einstein’s Special Theory of Relativity. As I have explained to my son, a scientific theory is not the same definition as a theory. Scientific Theory is taking all the available information and forming an explanation of the natural world using the scientific method and repeated testing. You may be wrong, but with the information at hand that may be the only explanation. As you gather more data points form experimentation and testing, you can adjust your theory to fit your data. Just because your initial theory was incomplete doesn’t mean it is wrong. That is the great thing about science, once you learn more you can make better and more stable theories.
There are many effects on time, and there are several theories about time and space. Speed effect on time works like this, if the Earth were to come to a sudden and complete stop, no spin, no rotation around the sun, and no movement in the Milky Way galaxy, time would be faster for us that it is now. Not by much but it would be measurable. On the other side of this idea is the faster you go the slower you experience time.
There are universal speed limits though, nothing can go faster than the speed of light and nothing is slower than a full stop. The amount of energy to accelerate an object close to the speed of light is exponentially greater the faster you go. The energy to go from %99.99 light speed to %100 light speed is would be infinitely greater than %99.98 to %99.99. It is impossible to achieve. If you traveled at %99.99 the speed of light time would dilate for you, and from your perspective you would have time traveled into the future. There have been several experiments with nuclear clocks that prove this theory.
A full stop, could be achieved by showing down the molecules in your body, by cryogenesis, or freezing. It’s the unfreezing that’s the tricky part. If you were frozen today for 1000 years when you were revived, to your perspective you would have traveled into the world of tomorrow. At absolute zero, all molecular movement stops, but it cannot be achieved by thermodynamics alone. Scientist have come close and discovered quantum effects like superconductivity and superfluidity, but have not achieved a complete molecular stop.
Gravity is theorized to have an effect on time as well. Gravity slows time the greater the gravity the slower time passes. Black holes are so dense, and the gravity is so great that even light cannot escape. If you entered a black hole you would never experience the entry into the black hole (you would probably be dead, but if you didn’t die…). Time would stop and you would forever be on the edge of the event horizon. If by some miracle you were able to pull away from the black hole and return to earth, again from your perspective, you would have time traveled into the future.
These effects on time only dilate time and give the appearance of forward in time travel. In the travelers point of view he has traveled in time to the future. Traveling back in time that is a whole other problem. Paradoxes that would result from stepping on a butterfly in the primordial past could alter the present so greatly that you would not recognise it. There are several multiverse theories that prevent a paradox. If you did travel from the present into the past and squashed a bug that would alter the present, maybe it just spawns a second universe line from that point forward leaving the original intact. One with the living bug and one with it dead. (If you don’t know what a paradox or a multiverse is, never fear there are many web pages that can explain them to you. You may need to time travel into the past to read them all, but they are there.)
It may be that time travel into the past can never happen. If it did happen would it even really be time travel and not just hopping onto another parallel world?
In reality we are all time travelers, we are passing through time in a bubble of about 2 to 3 seconds called the present. We are trapped in this bubble, zooming along time. Even if we experience time dilation, once it has ended we are back in the same present as the rest of the universe.