Time travel has fascinated me since I was a little kid. The possibility of traveling through time would have a big influence in our life. But it this possible?
Let's think of the following situation. John goes back in time and kills his grandfather before he has children. Now, since his grandfather doesn't have children John's father isn't born, but if his father isn't born this means that, you guessed it, John isn't born. But wait.. if he wasn't born, there's no one to go back in time and murder his grandfather; and if his grandfather isn't murdered he will have children and.. I'm telling the whole story all over again. You get the idea.. this creates a loop you can't get out of.
How can we solve this?
Let's presume that John wants to kill his grandfather. He will try multiple times, but will fail. Maybe he will miss, or there would be something to stop him from achieving his goal.
Or, he might manage to kill him, but later find out that he was adopted :). So no problem if his father wasn't born in the first place.
Another theory is the multiple universe theory (which I think is the right one). Let's presume that John has a time machine and can travel through time. This theory states that when he travels through time, he opens a "gate" to a parallel universe. So he would actually modify a different reality than his own. Doesn't really matter what he does here, because his original time (which is in another reality) won't be affected.
In other words, time travel is something fascinating, but I don't think that we would ever be able to change the past.
Another example was in the movie "The time machine". The character builds a time machine to prevent the death of his girlfriend, but every time he saves her she dies in another way. This happens for a very simple reason: if she doesn't die he doesn't build the time machine to prevent her death.. and we have another paradox.
I once saw a very interesting movie directed by Steven Spielberg. Here is the main idea.. the police has some sophisticated equipment to predict the future. Every time a criminal has the intention of doing something against the law, the system would predict that and he would be arrested before committing the crime. One day, the system predicts that one of the policeman is going to kill someone. Normal procedures says that in cases like this, the person that is going to commit the crime must be arrested immediately, since someones life is at stake. However, the police man has no intention of killing nobody, and doesn't even know the person that the system says he whats to murder.
So let's revise.. there is a system that can predict the future, and it says that a police man wants to kill someone, but the police man doesn't even know that person, and surely has no apparent intention of killing him.
Because he wants to know the truth, he tries to find that person. When he finds him, he discovers that his child was kidnapped by this person when he was little. Now, all of the sudden, he has an impulse to kill.. but he knows that doing so will result him being arrested, so he decides to let him live, defying the prediction.
This is a very interesting situation. It is a self-fulfilling prophecy. The events are triggered by the prediction of the same event.
Another example of this: someone goes back in time to prevent a car accident, but his actions make the accident happen in the first place.
A very good movie about time travel was "Back to the future". If was a nice movie, but nothing about time travel mentioned there is true:). The characters systematically change the course of time, change events in the past, but no paradoxes occur.
Well, that's all about time travel for today.