What is strong and what is weak?

Given the previous discussion that things we measure depend on the energy at which we measure them, one could reasonably ask whether names like a strong force or a weak force are justified, or whether the strength of a force may not also depend on the energy.

Actually, it is precisely like this. An this is something which is at the same time a blessing and a bane to theoretical calculations.

When we measure the strength of an interaction, what we do is actually rather indirect. We start out with two particles. These we accelerate by some means, e.g. a particle accelerator like the LHC at CERN. Then we aim them at each other and let them collide. Afterwards, we measure what is left of them, and whether something new has been created in the process.

A practical complication is actually quantum physics. The latter tells us that when we perform an experiment more than once, we cannot perform it such that it will produce precisely the same result. However, this does not mean that physics is arbitrary. Lets make the experiment many times. Then we get an average result. Furthermore, if we build a second experiment to make the same collision, on the average it will yield the same result. In this sense it is reproducible. However, for many things we have to make very many collisions such that we get a precise enough average. That is one of the reasons why we not can just make one experiment at LHC and have immediately the answer whether the Higgs is there or not. We have to perform our averages in this case very precisely.

Well, lets return from this detour. Just keep in mind that when I talk here about an experimental result, it is actually more than the simple picture I will draw.

So, we measured what is left after the two particles collide. Then we may either get the result that the two particles after the collision are essentially unscathed, maybe a bit deflected, but that is it. Or, we may end up with new particles, and a serious redistribution of energy among them. Obviously, in the first case the interaction is not so very strong between the particles, wile it is rather strong in the later case. When looking at the details, it is not that simple, but this should illustrate the point that we can learn something about the strength of an interaction when we let particles collide.

We did this, and what we found is that the strength of the forces is indeed dependent on the energy. These findings are rather remarkably, and where of the following nature:

When we did this with the electromagnetic force, we found that the electromagnetic interaction becomes stronger and stronger the higher the energy. However, the increase is very, very slow. But we were able to measure it very accurately, and it also agrees with the theory to an extremely good precision. The increase of the strength of the electromagnetic force is such that by increasing the energy by a factor of 100, we get only an effect of a few percent. Thus, no man-made experiment is just yet able to test how strong the electromagnetic force is really becoming before we run into the problem that the standard model is just a a low-energy approximation.

The opposite turns out to be the case with the strong nuclear force. At low energies it is actually very strong, the strongest force we know so far, making all the nuclear physics, and keeping our protons and neutrons together in the nuclei, and the quarks even more deeply hidden. However, when increasing the energy, the strength of this force quickly decreases. If we would be able to look at arbitrary large energies, it would become arbitrarily small. This feature is called asymptotic freedom. As a consequence, the strong force becomes the simpler to deal with in theory the higher the energies. Therefore, our best tests of our theory of the strong force comes actually from high energies rather then from nuclear physics, as one would expect.

The weak force is actually very similar to the strong force, and it becomes weaker the higher the energy. The difference is that it starts out already rather weak, at least superficially, and thus its consequences are not nearly as spectacular as the ones of the strong force.

And there is the last remaining set of forces in the standard model. These are the ones associated with the Higgs, which provide the mass to all particles. This is a force we could not yet measure reliably in experiment, since we were not yet able to find the Higgs. Thus, we can make only a statement based on indirect evidence, and theoretical expectations. If they are true, then we expect that the interactions due to the Higgs will, like the electromagnetic interactions, also strengthen with energy. However, it turns out that the question of when these forces become strong depends very much on the mass of the Higgs. If the Higgs is as light as currently still permitted by the experiments, the corresponding interactions will rise very slowly, just like for electromagnetism. Then this rise can be ignored also for most purposes. If the Higgs would be only ten times heavier then the situation would be completely different. We would then expect to see relatively strong interactions between the Higgs and the other particles in the standard model at the LHC. That we did not see them yet does not mean they are not there - it is still hard to produce a Higgs which could interact strongly. Thus such potentially strong interactions are very rare even at such an experiment like the LHC.

Thus, the names of the forces are what they are just because at the low energies, where we first encountered them historically, they were weak and strong. And then these names just stuck, as they always do.

Why mass depends on energy

One of the fascinating topics one is confronted with in particle physics is the fact that quantities depend on our perspective. For example, masses and the strengths, with which particles interact, depend on the energy we use to probe them. That may sound strange at first. However, it is not so surprising that such quantities may depend on our way of looking at them.

Take an apple. It has a certain mass, say 100 gram. However, if you put yourself inside the apple, the amount of apple you see before your (if you look towards the pit) is less than the whole apple, and its mass is thus less. In a very cartoon idea, you could also say that this depends on the energy: If you ride a (rather slow) bullet, its penetration depth will depend on its initial energy, and thus the higher the energy, the less of the apple mass remains in front of you.

Of course, things can get not only less, but also more. Talk a light bulb (or LED, if you like it more modern). Put veils upon it. The amount of light you perceive depends then on the number of veils between you and the bulb. The more veils are already behind you, and the less before you, the brighter the bulb. Of course, the idea with the bullet applies here, too. Just avoid hitting the bulb.

Well, for particles you do not have veils or outer shells of an apple. So what is going on there? What is going on is that the vacuum around a particle is actually a rather thick soup than really empty. This seems surprising at first - after all, we have been thinking that the space in, e.g., an atom is essentially empty. The reason for this apparent contradiction is quantum physics. In quantum physics, we got used to the fact that we cannot really say what is going on, and everything becomes fuzzy. In particular, we cannot say whether a portion of the vacuum is really empty or contains particles, as long as we do not make a very precise measurement. In the head of theoretical physicists, this observation of nature has formed the picture of so-called virtual particles.

Virtual particles are particles which appear and disappear all the time. They may either be emitted by a source, like another particle, or may even pop out randomly (though necessarily at least in pairs) from the vacuum. They only exist for a very brief glimpse, and are then reabsorbed by the source, or annihilate again into nothing. Only, if we look close enough, i.e. short distances and thus high energies, we can check whether such particles are there or not.

In particular, if we want to look at one particle, or the interaction of two or more particles, they are surrounded by a cloud of such virtual particles. Only if we get close enough to them, and that means at high energies, we can dive through this cloud. However, to really see the pure and unaltered particle (or process), we would need to resolve it with a wave-length of its size, but this is zero. Hence, this would require infinite energy, because we want to measure them at zero distance. So we cannot.

However, the more energy we invest, the deeper we get into the cloud, and the more we see of the particle's or process' properties. Measuring these accurately, we can even extrapolate to the real properties of the particles. Then we find that, e.g., the masses of particles become less and less the closer we get and thus most of their mass is made up by this cloud of virtual particles. Also, we find that some of the interactions become less, and others become stronger. Since these quantities change with energy, a physicists also calls them running quantities. Running means here that they change comparatively quickly with a change of energy. We also know the concept of walking quantities which change slowly, but we do not know an example of such theories (yet) in nature.

When thinking about such things, we should always keep in mind that the standard model of particle physics is, as discussed previously, just a low-energy effective description. Hence, when we try to extrapolate, we use our theory as input, meaning that our extrapolation necessary will fail at some higher energy, and we do not even know precisely when. So this running is telling us just how things change in a certain range of energies we can test. However, this is actually useful: By looking for deviations from what we think should happen, we can find something new.