Causality and Paradox
The idea of causality is that a cause must always precede its effect. This seems logical. But time travel would allow someone to travel back in time to a point before they were born. How can someone live before they were born? This point seems subtle but I do not think that it is a strong argument. If I can go back in time to meet a younger version of myself, why can't I go back before I even existed. The laws of physics do not state anywhere that moving at different rates in time should affect my biology in any way. In fact, from a relativistic point of view, it is perfectly valid for me to seem to experience the normal flow of time while the outside world changes. Even though I may step through a wormhole that has its other mouth 33 years in the past I should still remain the same age that I am when I step through the wormhole. I would then appear in the past, a person of approximately 23 years old. There is no physical reason why I could not live 10 years before I was born. The real trouble happens if I do something to prevent my time travel in the future, which is my past.
There are some rather standard time travel paradoxes that are often presented. They usually involve the killing of an ancestor in the past in order to prevent the time traveler's own birth. However, I find no reason to be so morbid. There are many mind bending scenarios that can be invoked to illustrate the problem of paradox. Let us imagine that I have discovered a wormhole time machine created by some ancient race of spacetime explorers and can travel to the past and back to the present. Now suppose that I decide that I want to change history. I want to go back to Dallas, Texas on November 22, 1963 and prevent President Kennedy from being assassinated. I go back in time and I manage to warn the proper authorities of the danger to the President. They catch Lee Harvey Oswald and any conspirators before they are able to accomplish their deadly mission. I am successful and the assassination is averted. Now all of the history books change. When I go to school and take history there will be no mention of the assassination of President Kennedy, because it never happened. That being the case, when I find my time machine and decide to step back in time and change history I will not go back to prevent his murder. Since I do not go back to stop the assassination it will occur again, and by now the paradox is obvious. So while I may have started off with good intentions, saving a life, I end up creating an irreconcilable paradox. Are there any ways out of this paradox or have I doomed the spacetime continuum to destruction?