Wednesday, October 24, 2012

Hiding our ignorance

The radiative corrections discussed last time have another important aspect. For this, it is useful to recall the entry on Einstein's famous relation E=m*c*c. This relation told us that you can convert energy to mass, and thus to particles.

Now, quantum physics is a cheater. Always was, always will be. One of the most basic things it cheats about is knowledge. It tells you that certain pairs exist of which you cannot know both at the same time with certainty. If you know one very precisely, you can have only little knowledge about the other. The most important and fundamental such pair is position and speed. If you know the position of a particle well, you cannot know its speed very well. And the other way around. This is an observation of nature, which has been confirmed in numerous experiments. We cannot yet really explain why this is so, and have to accept it for the time being as an experimental fact. What we can do is derive an enormous amount of knowledge from this fact.

Among this is that a very similar relation holds for energy and time. If we know time very precisely, we do not know the energy very precisely. If you combine this with Einstein's formula, you get a very interesting consequence: For very short periods of time, energy is not very well defined, and may be much larger than assumed. Since this energy is equivalent to mass, this means that for very short periods of time you can have particles pop out of nowhere and vanish again. To be precise, you can have a pair of a particle and an anti-particle for very brief moments in time.

This seem to be almost unbelievable: Something hops into and out of existence, just like this. However, you can measure actually this effect, and it has been experimental confirmed very well. Also, it should not be taken too literally. What really happens is that quantum physics does something, and in our mathematical description it appears like you would have these pairs.

So what does this have to do with the radiative corrections? Radiative corrections are quantum corrections. As such they involve precisely this type of process: Something hoping out of the vacuum. It then briefly interacts with whatever you are actually looking at. Then it vanishes again. Therefore, radiative corrections include all the possible interactions of some particle with all other possible particles. Now comes the real boon of this: In reality this happens with all particles, not only those we know of. This has been used in the past to predict new particles, like the top quark, some of the neutrinos, and, yes, also the Higgs.

Great, so I can get everything from it! you may say. Unfortunately, it is not that simple. The heavier the particles, the less their contributions to radiative corrections, and thus the more precise an experiment has to be to detect their influence. As a consequence, the Higgs was the last particle for which we had strong such indirect evidence. And this was already experimentally challenging.

But it is much more troublesome for theory. Since we do not actually know what is there, our calculations have a problem. We create at very short times a lot of energy, but we do not know where to put it, since we do not know all the particles. Our theories thus lack something. And this something haunts us as failures of our theories, when we try to calculate radiative corrections. This was a very big problem for theories for a while, but we finally managed it. The key concept was named 'renormalization', which is again somewhat of a misnomer. Anyway, it gives a name to the process of hiding our ignorance. In fact, what we do is that we introduce in our theories placeholders for all these unknown particles. These placeholders are designed on purpose to remove all the problems we have. The way we designed them they can never described something of nature, but they absorb all the problems we encounter with our ignorance.

Since we know that we have these problems, it also tells us that the standard model cannot be the end - or for that matter any theory having such problems. They only describe our world at (relatively) low energies: The standard model is a low-energy effective theory, as was briefly indicated before. Here, you now have a better view of what the reason for the infinities encountered back then is: That we do not know what particles may appear in our radiative corrections, and thus that we do not know where to direct our energy to. And that the parameters used back then just mock up the unknown particles.

You may wonder whether this is a generic sickness of quantum theories. This is very hard to tell for a realistic theory. Of course, we assume that if we would know the theory of everything, it should not have these problems. We can indeed construct toy theories of toy worlds, which do not have these problems, so we think it is possible. Whether this is true in the end or not, we cannot say yet - perhaps we will need in the end a whole new theoretical concept to deal with the real world. For now, renormalization prevents us from the need to know everything already. This permits us to discover nature step by step.