Albert Einstein discovered the theory of relativity in the 1920's after starting thinking about it at the age of around 16. Albert Einstein's theory of time travel is basically theory of relativity. They are linked side-by-side.
Relativity is only a theory because it cannot be proven. If it were a law it would have to be proven. In order to prove that relativity is a true we would need to conduct an experiment in which we would send an rocket with a person in it at 99.99% the speed of light then come back to earth and told us the information he reordered, then maybe we'll know for sure.
Now, according to Einstein you can't travel at 100% the speed of light because He predicted that objects gain mass as they accelerate to greater and greater speeds. Now, to get an object to move faster, you need to give it some sort of push.
An object that has more mass needs a bigger push than an object with less mass. If an object reached the speed of light, it would have an infinite amount of mass and need an infinite amount of push, or acceleration, to keep it moving. No rocket engine could do this. Also, in fact, as far as we know nothing can match, or exceed the speed of light.
Plus, there are many theories on quantum mechanics, which disproves Einstein's theory. We may never know for sure which theory is correct. It's possible that these theories are BOTH wrong. But who could say for sure. I really can't say. Yet again, it's very possible that the answer could be discovered tomorrow. For instance here are some quotes that prove that someday we could have machines that could travel through time.
"Heavier-than-air flying machines are impossible." (Lord Kelvin,