## Tuesday, June 21, 2011

### The limits of the standard model I

After the rather technical discussion in the last few entries let us return this time to a more mundane topic: What is the validity of the standard model. For that purpose assume for the sake of the argument that the Higgs particle will eventually be found.

The question can be paraphrased differently: What is the lowest and the highest energy at which the standard model can be used? This question can also be formulated even more differently: An energy can be associated with a distance. That is very similar to what has been discussed previously in the entry on "Fields, waves, particles, and all that". If you have a very large energy, movement is essentially very rapid. In particular, the fields associated with the particle oscillate very quickly, and thus the distance between the crests of its waves is very small. Hence, changes on very small distances can be sensed by the particle, and thus high energies can be associated with small distances. In the opposite extreme, this means that low energies can be associated with large distances.

Let us then start with the more simple of both limits, the lowest energy. Since the standard model is a quantum theory, this can be also posed as the question when do we no longer observe things, which are distinctively quantum. A quantum theory means associating particles with a field. Thus take again the picture of waves, and let us go again back to the picture of the ocean. If you hover a short distance above it, you can see the individual waves. If you then zoom out, at some point everything blurs together, and you have the impression that only a - more or less - flat surface is there. At this point you do no longer realize the individual particle (wave), but only all of the particles (waves) together, in the form of the ocean as such. Similarly, if you zoom out of the standard model up to, say, the level of your desk, you do not note anymore the particles, but only the surface of the desk.

This is not yet telling you that the standard model is not applicable anymore, just that your are no longer able to distinguish its parts. It is therefore actually a very complicate question, whether the standard model is only valid up to a certain distance scale, because it becomes so hard to see its content. People have tried very hard to see the consequences of the standard model at ever larger distances, but, depending on the part of the standard model you look at, it becomes very hard to make a statement. Once leaving the size of a few times a nuclei, it is essentially only the electromagnetic force we can still test. For that part of the standard model we know that it works at least on the order of our own galaxy, and we have evidence, though far less rigid, that its seems to work rather well even at much larger cosmic distances. Still, answering the question to which distance we can observe the standard model is thus tricky and a persisting challenge. Perhaps even our understanding of the universe would be altered, if we someday would figure out that the standard model is not a suitable description at long distances.

Thus, to the best of our current knowledge, the standard model works (though we have a hard time seeing it) at the largest distance scales, and thus at the lowest energies, we can observe and test. However, it is a technical problem to check whether this is actually true or not: We need very sensitive experiments to check this, and the observation of true quantum effects is up to now limited to very small sizes, like in a Bose-Einstein condensate of atoms. The size of the latter is currently at best below some centimeters. Only some very specific quantum effects can be observed using photons at larger distances, like when using a fiber or making the famous double-slit experiment. But photons are only a very restricted part of the standard model.

The situation will change at high energies. There is also a technical problem, but in addition also a conceptual problem.