Can we tell when unification works?

Some time ago, I wrote about the idea that the three forces of the standard model, the electromagnetic force, the weak force, and the strong force, could all be just different parts of one unified force. In the group I am building I have now a PhD student working on such a theory, using simulations.

Together, we would like to answer a number of questions. The most important one is, whether such a theory is consistent with what we see around us. That is necessary to make such a theory relevant.

Now, there is almost an infinite number of versions of such unified theories. We could never hope to check each and every one of them. We could pick one. But hoping it would be the right one is somewhat too optimistic. We therefore take a different approach. We aim to get a general criterion such that we can check out many of the candidate theories at the same time.

For this reason, we ignore for the moment that we would like to reproduce experiments. Rather, we ask ourselves what are common traits of these theories. We have done that. What we are currently doing is to construct the simplest possible theory which has as many of these traits as possible. We have almost completed that. This reduced theory will become indeed very simple. Of known physics, it contains the weak force and the Higgs. As with every unified theory, it also contains a number of additional particles. But they are not dangerous, if they will be too heavy to be visible to us. At least, as long as we do not have more powerful experiments. The last ingredient are the interactions between the different particles. That is what we are working on now. Having the simplest possible theory has also another benefit - it demands small enough computer resources to be manageable.

After fixing the theory, how do the questions look like? One of the traits of such theories is that there are many new particles. What is there fate? How is it arranged that we cannot see them? If we think of the theory describing only rather small changes to the standard model, we can use perturbation theory. With this, we would just follow pretty old footsteps, and the answer can essentially be guessed form the experience of other people. The answer will be that all the surplus stuff is indeed very, very heavy. In fact, so heavy that our experiments will not be able to see it in any foreseeable future, except as very indirect effects. We get out what we put in.

But here comes the new stuff. As I have described earlier, there are many subtleties when it comes to the Higgs of the standard model. But in the end, everything collapses to a rather simple picture. Almost a miracle. Almost, but not quite. The reason is the structure of the standard model, which is very special in the number and properties of particles. The other one is that the parameters, things like masses, just fits.

The natural question is hence: Does the miracle repeats itself for this type of unified theory? Is the new stuff really heavy? Is the known stuff light enough? If the almost-miracle repeats itself, the answer is yes. Should it repeat itself? Well, we will test under which conditions it repeats itself, by playing around both with the number of particles, their structures, and the parameters. We assume right now that we can get it to work, but that we can also break it. And we would like to understand very precisely when it breaks and why it breaks. And finally, the most obvious question, do we want that it repeats itself? Probably the most obvious question, arguably the hardest to answer. If it does not repeat itself, a whole class of ideas becomes more problematic. Ideas, which are conceptually pretty attractive. So, in principle, we would like to see it repeating itself. But then, would it not be more interesting if we needed to start afresh? Probably also true. But in the end, our preference should not play a role. After all, nature decides, and we are just the spectators, trying to figuring out what goes on. And our preferences have nothing to do with it, and therefore we should keep them out of the game.