Paradoxes of Time Travel
If one where to travel back in time, there would be a few paradoxes that would have to be resolved. Granted, that this is a hypothetical thought experiment. Because at the current time of this writing time travel in the backward direction has not been achieved yet. However time travel to the future is possible and happens all the time. The time dilation effect due to Einstein's theory of relativity can be measured even in commercial airliners.
Time travel in the backwards direction quite a bit more difficult and is when these paradoxes often occurs. While it is highly unlikely that we will ever be able to travel back in time. Physicists are unable to rule out that possibility. See Hub article Is time travel possible?
Although realistically very difficult to achieve, there is no physical law that has been discovered yet that forbids the possibility of time travel. So if time travel did occur, these would be just some paradoxes that arises.
The Grandfather paradox
The paradox that comes to mind first and is probably the most often cited is the grandfather paradox.
The grandfather paradox supposes that you travel back in time and killed your grandfather before your father was born. So if your grandfather had been killed, he would not have been able to give rise to your father. If your father did not exist, then how can you. But if you don't exist, then how can you go back in time and kill your grandfather? Hence the paradox.
In effect, you have altered the past in such a way that makes the present impossible.
The information paradox is often seen in science fiction movies where a person from the future goes into that past and gives advanced technology or information to someone in that past. From the point of view of the person in the past, that advanced technology / information appears to have come out of nowhere. In fact that, that technology or information simply appeared when it has not even been invented yet. How can that be?
In this paradox, you travel to the future. Suppose that you do that and then you saw the future and do not like it. Now you come back to the present and decide to alter history such that the future that you saw does not materialize. As a concrete example, suppose you went into the future and saw that you were a doctor but were unhappy with your profession. Now after coming back to the present, you decided to major in art history instead -- thereby eliminating the possibility of you becoming a doctor. (I'm not saying that art history majors cannot be doctors, but you get the point).
This is similar to the grandfather paradox, but this time you altered the present in such a way that the future does not happen. In effect, you have altered the future that you had already seen.
Resolution of the Paradox
Of course physicists whose job is to think about time travel and these problems have come up with some explanations to resolve these paradoxes.
The first explanation is the "self-consistency" school of thought. Here the time traveler is inevitably forced and constrained in his/her actions in such a way as to not produce a paradox. So if you travel back in time to try to kill your grandfather, you will inevitably fail. For example, the gun would miss its mark, or something. This implies that we do not truly have free will. this may not sound so unreasonable when you consider that physical laws actually constrains our actions. For example we may have the "free will" to want to float in the air. But due to gravity and other physical constraints we are unable to do so.
The second explanation is the "many worlds theory". Many physicists believe that our universe is not the only universe. Our universe is just one of many universes out there in a bigger multiverse. There are multiple universes. The many worlds theory states that there are as many universes as there are possibilities. So in one universe, your grandfather lives in which you are born. In another universe, your grandfather is killed and you were never born. When you time travel, you are traveling between these universes.
Sounds far-fetched, right? But many notable physicists are seriously considering these possibilities. See some references below.
- Chapter 5 of "Parallel Worlds" by Michio Kaku
- The Hidden Reality by Brian Greene