Wednesday, June 18, 2008

Time travel paradoxes

I recently wrote a post about why faster than light communication is impossible. I finished this post showing that such communication would be equivalent to time travel, and it is logical to assume that time travel is impossible.
However, is this indeed true? Time travel is often talked about in science fiction, but is there a reason to think that it is possible?

Photo by jonrawlinson

Firstly we need to distinguish between two types of time travel - to the past and to the future. We all know that it is possible to go to the future. We all do it, it is called living. It is also possible to travel to the future with a "faster speed" than normal life. All you need for this is to accelerate yourself to a high enough speed, and according to relativity you will travel to the future - when you will return to the place you started your travel you will see that your watch is late. How late depends on your speed, it might be a second or 1000 years. This effect is very real, we even have to take it into consideration when we communicate with satellites.

Traveling back to time is a different story. Unlike traveling to the future it was never done. So the only thing we can do is to discuss different theories. There are three main theories about traveling to the past:
1. Time travel is not possible - there are two versions: either there is no way or it will destroy the universe in the process.
2. Time travel is possible but the past cannot be changed.
3. Time travel is possible, but it will destroy part of the universe.

Lets look on all of the three theories:

1. Time travel is not possible:
There are two versions of this theory. The first one comes from a literal understanding of time travel. According to it in order to travel back one second in time, you need somehow to return the whole universe to the exact some state it was one second ago. It means that you need to place every single particle exactly at the same place. However this is clearly an impossible task.
The second version of this theory is based on time travel paradoxes. The paradox I will talk about here is called the grandfather paradox: Lets suppose that time travel is possible. Lets also suppose that someone (Mr X) traveled back in time. While he was in the past he 9accidently) killed his grandfather. In doing so he preventing himself from being born in the first place. But if he wasn't born how could he travel back in time?
There is also a more general version of this paradox - by traveling back in time you change the world past, so in the very moment you will get to the past the world you come from (the future) will no longer exist. And therefore, you never traveled back in time.
The conclusion from this is that if time travel is possible, you will destroy the whole universe by traveling back.

2. The past cannot be changed:
This theory is an answer to the question arising from the previous one. In the grandfather paradox, we assumed that it was possible for Mr X to kill his grandfather and to prevent his own birth. But what if this is not true? What if there is a law that not allows people to influence the past? In this particular example, we can suppose that Mr X will be stopped by police just in the right moment, or it would turn out that the men he killed wasn't his grandfather at all. For the more general version of this paradox, we can assume that either the results of the activities of time travelers just slowly vanish so they don't affect the future in any way, or that there is a fixed time line in which time travel appears together will all other things and nothing can be changed.
This theory allows for time travel and solves the paradoxes I presented, but there is a problem with it. Lets do the following thought experiment: Suppose you have a time machine, and a laser that shoots a bit of light into the time machine. The machine send the light back in time, so it goes out of it on the opposite side and two minutes before the laser was fired. On the wall after the time machine there is a detector that when hit by the laser been will send a signal to put a barrier between the laser and the time machine. It looks like this:Now if the time machine works, the laser will prevent itself from firing, but this would mean that the detector didn't close the barrier so the laser worked - and this is a contradiction. Note that it doesn't matter how the time machine works, and to how long ago the light pulse is sent.
If, as the theory says, we will assume that somehow "it all worked" it follows that something is broken - if for example the detector is broken, no paradox will be created. However, this is a very simple system. The only thing that is likely to always malfunction is the time machine itself. This means that the time machine doesn't work, and therefore time travel is impossible.

3. Local destruction:
This one is the attempt to unite the previous two theories. Basically it says that time travel is possible but because of the paradoxes described above, it will destroy the universe. However, the universe is a very large thing. So only a small part of it will be effected. Time travel will create a "wave of destruction" which will move over some finite distance, destroying everything. As it moves it will slow down and become less distractive, so after some finite distance it will just stop. Beyond this distance (this is, beyond a sphere with the time machine in the center), the universe will remain as it was. Inside this sphere however nothing will exist - a singularity will be formed.
From this is should be obvious that this theory also doesn't allow for time travel - because it can be used only as a weapon, and it is not possible to return or to do anything.

Time travel is not possible, and therefore faster than light communication is also impossible.
But - not always. In the next post about this topic, I will write about some very specific situations in which faster than light travel and time travel are possible.

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