Time travel is more than just possible, it is inevitable. If one gets out of bed at seven a.m. and then one drinks coffee, or tea, at seven-thirty a.m., then obviously, one has just traveled forward in time. The question of time travel then, refers not to whether organisms move forward in time, but whether it may be possible to ever go back to things that are already in the past, or to go far ahead to future times Could a person exist who leaves the present and goes back (or forward) to a time when they previously existed, or will exist?
Time is called the fourth dimension. That time is relative, and that organisms can experience this for themselves, is the reason that many believe it must be possible to then re-arrange human relations to time just enough to slip between the slight differences, somehow. The idea of a worm-hole allows that very tiny wrinkles, dips or voids in time could be taken advantage of for people to slow, or speed up time. The same sort of warping of time is probable near black holes. Time travel by means of incredible mass that drags time, is possible.
In space, time moves faster, so it is theorized that at close to the speed of light, were such speeds attainable, people would experience time as going more quickly. People could travel in one hour, close to the speed of light, and would experience in each of their one hour intervals, what would take two hours on earth.
The problem of time travel paradox is that in nature’s laws, there are strict limits. The speed of light itself, 186,000 miles per second is one such limit.
Another is that effect cannot occur before cause. When one tries to reverse cause and effect, the resulting chaos allows there is no consistency, and no way to verify anything. That is why so very often although scientists can conjecture into the past, and into the future time travel, they are very limited as to what rules apply. Without consistent cause and effect, there are no rules.
To travel into the past, where one has already died, seems impossible then. But to travel forward is another thing altogether.
There is one version of “time travel” that of Futurama, that is very feasible. This is because our humble pizza delivery guy does not really jump ahead to the future world of 3.000. He simply sleeps in suspended animation while one thousand years actually go by. He just does not experience them. When people and organisms are routinely frozen, then the sense of time travel will be quite real, but for now, though many are cold, few are frozen.