Tuesday, August 21, 2012

The speed of light - and its consquences

So far, I did not say anything about gravity. This will remain so. However, I will have to say something about special relativity. Somehow, special relativity is often associated with gravity. This is actual not the case. Einstein's theory of special relativity does not make any reference to gravity. Only the theory of general relativity, of which special relativity is just a small subset, does so.

If special relativity is not about gravity, what is it about? Well, it is about the fact that our universe is a bit more weird than one expects.

What do you expect of a law of nature? One property is likely that it is always valid. This simple requirement has quite profound consequences. Assume for a second that you and your experiment are alone in the universe. This means ta you have no point of reference. If now the experiment moves, you could not say whether it is moving, or you. Still, you would expect that it gives the same results, irrespective of whether it or you are moving. We made experiments to test this idea, and it was confirmed beautifully. This fact that experiments are independent of relative motion, is one of the basic observations leading to special relativity.

The next ingredient is much more harder to believe. Take a light beam. What speed does it have? Well, the speed of light, of course. Now, if you move the thing creating the light at a fixed speed, how fast should the light move? Naively, one would expect that the light would now move faster. Unfortunately, our universe does not tick that way: The light still moves with the same speed. Actually, the light is actually made up out of massless photons, which travel at the speed of light. And this observation is the same for anything which is massless: All massless particles move at the speed of light. And the speed of light is always the same, no matter how fast the light source moves.

This is nothing we can really explain. It is an experimental fact. Our universe is like this. But this observation is the second basic fact underlying special relativity.

If we cannot explain why this second fact comes about, can we at least describe it? We can, and that is what leads to special relativity.

Now, how do we describe this? Well, this is a bit more involved. Take the universe. Then at each instance you have three directions in space. Distances you measure do not depend on the direction in space. You can also measure time elapsing. Works out also nicely. But now, try to measure a space-time distance. You do this by measuring a distance in the space direction. Then you take the elapsed time, and calculate what distance a light ray would have moved during this time. By this, you can talk about a distance in time direction.

The speed of an object is given (if the speed does not change) by the ratio of distance over time required to move over this distance. If you now want that the speed of light is independent of whether the light source moves or not, something peculiar is found: To get this, a distance in space-time direction is obtained by subtracting the distance in the time direction and in the space direction, when you do your Phytagorean geometry. That is completely different than what you have in the three time directions, but the only way to get the light speed to agree with experiment. The geometry of space-time is hence quite different from the one we know just from space.

As a theoretician, I say that the way we measure the distances is not like the ordinary one in three space directions (a so-called Euclidean measure), but we have rather a Lorentz measure. This is in honor to the first one who has described it. Again, we cannot yet explain why this is the case, it just is an experimental fact.

You may wonder why you never noticed this in real lifer. The answer is that when the light source moves very slowly compared to the light ray, the effect is negligible. This becomes only relevant, if you move at a considerable fraction of the speed of light. But then all the nice effects result of which you may have heard in Science Fiction movies or novels: Things like the twin paradox, time dilatation, length contraction, and so on. All of these result from these two basic observations. And are described by the theory of special relativity.

This all sound pretty weird, and it is. It is nothing we have a real handle on with our everyday experience. Just like the quantum effects. The universe is just this way.

As you see, gravity enters here nowhere. And also no quantum stuff. If you add gravity, you get to the theory of general relativity. If you add quantum stuff, you end up with quantum field theory. The standard model is of the latter kind. And this combination leads to very interesting effects, which I will discuss in more detail next time.