According to Dr Michio Kaku, time travel might be possible as long as, we can achieve sufficiently high energies. We might even be able to travel into parralel Universes, and he supports that advanced aliens might have actually already achieved that. In particular the many worlds interpretation of the quantum theory allows for such a possibility. Any ideas on that?
My opinion is that what we call "time", has no existence in nature in the same way that matter and energy exist. There is no past or future in the real sense, they only exist as a theoretical construction. Of course time appears in the mathematical equations, and to make things worse there is no absolute time.
In mathematics I can define infinite points on a line, however this idea has no application in the real world, as there are no infinite physical quantities in nature.
What Einstein taught us is that there is no absolute time. Experiments have proven him correct. There are only two ways that we can play with time, but it would be unfair to call this game a real time travel. The first way is what Einstein called "Special Theory of Relativity or SR", and the second way is the "General Theory of Relativity or GR". According to the SR, time is relative with respect to the position, and according to the GR time is relative with respect to the position and gravity. If we therefore change our position, time will become relative. Time is also relative for different strengths of gravity. For a photon time freezes. The same is true for an object near enough a black hole. These are both examples of limiting values of position change and gravity strength. We know that it is impossible for a massive object to reach the speed of light (as this would require infinite amount of energy), but it is in theory possible to go near a black hole and slow down our time. However, in reality the tidal forces near a black hole would be so strong that would tear our bodies apart. In addition to that, our only advantage would be that we could go back to Earth or to an other planet, and find them to be far ahead in the future, since time in the meantime, time would flow faster there. However, we can still reach speeds such as the 9/10th of the speed of light, and cause a significant time dilation that will allow us to travel to other galaxies, and still be alive.