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.