Is time travel possible?
Time travel is the concept of traveling forward and backward to different points in time, much as we do through space.
Unsolved problems in physics: Is time travel theoretically possible? Is it practically possible? If so, what are we to make of the time travel paradoxes, such as going back in time and killing one's own grandfather, etc.?
Humans are in fact always traveling in time - in a linear fashion, from the present to the immediate future, inexorably, until death.
Some theories are predicated on the fact that we move forward in time, and both forward and backward in space. Since time and space have been shown to be intrinsically linked, travelling forwards and backwards through time is not a theoretical impossibility.
Currently, traveling at speeds approaching the speed of light can cause time dilation, the effects of which cause the individual traveling to pass through time more slowly. From the perspective of the traveler, external time would be going much faster, causing the traveler, upon stopping, to arrive at a place farther in the future.
Often it is a plot device used in science fiction and many movies and television shows to set a character in a particular time not their own, and explore the character's interaction with the people and technology of that time - as a kind of culture shock.
Other ramifications explored are change and reactions to it, parallel universes, and alternative history where some little event took place or didn't take place, but causes large changes in the future.
In physics, the concept of time travel has been often used to examine the consequences of physical theories such as special relativity, general relativity and quantum mechanics.
There is no experimental evidence of time travel, and it is not even well understood whether (let alone how) the current physical theories permit any kind of time travel. Although theories do exist about the possiblity of folding time to hop from one point to another.
Einstein's Special Theory of Relativity (and, by extension, the General Theory) very explicitly permits a kind of time dilation that would ordinarily be called time travel. The theory holds that, relative to a stationary observer, time appears to pass more slowly for faster-moving bodies: for example, a moving clock will appear to run slow; as a clock approaches the speed of light its hands will appear to nearly stop moving. However, this effect allows "time travel" only toward the future: never backward. It is not typical of science fiction, and there is little doubt surrounding its existence; "time travel" will hereafter refer to travel with some degree of freedom into the past or future.
Many in the scientific community believe that time travel is highly unlikely. This belief is largely due to Occam's Razor. Any theory which would allow time travel would require that issues of causality be resolved. What happens if you try to go back in time and kill your grandfather. Also, in the absence of any experimental evidence that time travel exists, it is theoretically simpler to assume that it does not happen. Indeed, Stephen Hawking once suggested that the absence of tourists from the future constitutes a strong argument against the existence of time travel - a variant of the Fermi paradox, with time travelers instead of alien visitors. However, assuming that time travel cannot happen is also interesting to physicists because it opens up the question of why and what physical laws exist to prevent time travel from occurring.
The equivalence of time travel and faster-than-light travel
First of all, if one is able to move information from one point to another faster than light, then according to special relativity, there will be an observer who sees this information transfer as allowing information to travel into the past.
The General Theory of Relativity extends the Special Theory to cover gravity. It does this by postulating that matter "curves" the space in its vicinity. But under relativity, properties of space are fairly interchangeable with properties of time, depending on one's perspective, so that a curved path through space can wind up being a curved path through time. In moderate degrees, this allows two straight lines of different length to connect the same points in space; in extreme degrees, theoretically, it could allow timelines to curve around in a circle and reconnect with their own past.
General relativity describes the universe under a complex system of "field equations," and there exist solutions to these equations that permit what are called "closed time-like curves," and hence time travel into the past. The first and most famous of these was proposed by Kurt Godel, but all known current examples require the universe to have physical characteristics that it does not appear to have. Whether general relativity forbids closed time-like curves for all realistic conditions is unknown. Most physicists believe that it does, largely because assuming some principle against time travel prevents paradoxical situations from occurring.