Relativity gives us a simple method to sort through the thorniest of these paradoxes. We will make use of the "world line" method, pioneered by Einstein.
...Our world line never really begins or ends. Even when we die, the world lines of the molecules in our bodies keep going. These molecules may disperse into the air or soil, but they will trace out their own never-ending world lines. Similarly, when we are born, the world lines of the molecules coming from our mother coalesce into a baby. At no point do world lines break off or appear from nothing.
...Our world line thus contains the entire body of information concerning our history. Everything that has ever happened to us--from our first bicycle, to our first date, to our first job--is recorded in our world line...
...With the aid of the world line, we can now picture what happens when we go back in time. Let's say we enter a time machine and meet our mother before we are born. Unfortunately, she falls in love with us and jilts our father. Do we really disappear, as depicted in Back to the Future? On a world line, we now see why this is impossible. When we disappear, our world line disappears. However, according to Einstein, world lines cannot be cut. Thus, altering the past is not possible in relativity.
The second paradox, involving re-creating the past, poses interesting problems, however. For example, by going back in time, we are fulfilling the past, not destroying it. Thus the world line of the inventor of time travel is a closed loop. His world line fulfills, rather than changes, the past.
...Thus perhaps we can fulfill the past, but never alter it. World lines, as we have stressed, cannot be cut and cannot end. They can perform loops in time, but never alter it.
