Why Does E=mc2_ - Brian Cox [73]
As far as the Standard Model goes, the twelve are all elementary particles, by which we mean that the particles cannot be split up into smaller parts; they are the ultimate building blocks. That does seem to go against the grain of common sense—it seems perfectly natural to suppose that a little particle could, in principle, be chopped in half. But quantum theory doesn’t work like that—once again our common sense is not a good guide to fundamental physics. As far as the Standard Model goes, the particles have no substructure. They are said to be “pointlike” and that is the end of the matter. In due course, it might well turn out that an experiment reveals that quarks can be split into smaller parts, but the point is that it does not have to be like that; pointlike particles could be the end of the story and questions of substructure might be meaningless. In short, we have a whole bunch of particles that make up our world and the master equation is the key to understanding how they all interact with each other.
One subtlety we haven’t mentioned is that although we keep speaking of particles, it really is something of a misnomer. These are not particles in the usual sense of the word. They don’t go around bouncing off each other like miniature billiard balls. Instead they interact with each other much more like the way surface waves can interact to produce shadows on the bottom of a swimming pool. It is as if the particles have a wavelike character while remaining particles nonetheless. This is again a very counterintuitive picture and it arises out of the quantum theory. It is the precise nature of those wavelike interactions that is rigorously (i.e., mathematically) specified by the master equation. But how did we know what to write down when we wrote the master equation? According to what principles does it arise? Before tackling these obviously very important questions, let’s look a little more deeply at the master equation and try to gain some insight into what it actually means.
The first line represents the kinetic energy carried by the W and Z particles, the photon and the gluon, and it tells us how they interact with each other. We didn’t mention that possibility yet but it is there: Gluons can interact with other gluons and W and Z particles can interact with each other; the W can also interact with the photon. Missing from the list is the possibility that photons can interact with photons, because they do not interact with each other. It is fortunate that they don’t, because if they did it would be very difficult to see things. In a sense it is a remarkable fact that you can read this book. The remarkable thing is that the light coming from the page does not get bounced off-track on the way to your eyes by all the light that cuts across it from all the other things around you, things you could see if you turned your head. The photons literally slip past, oblivious to each other.
The second line of the master equation is where much of the action is. It tells us how every matter particle in the universe interacts with every other one. It contains the interactions that are mediated by the photons, the W and Z particles, and the gluons. The second line also contains the kinetic energies of all the matter particles. We’ll leave the third and fourth lines for the time being.
As we have stressed, buried within the master equation are, bar gravity, all the fundamental laws of physics we know of. The law of electrostatic repulsion, as quantified by Charles Augustin de Coulomb in the late eighteenth century is in there (lurking in the first two lines), as is the entirety of electricity and magnetism, for that matter. All of Faraday’s understanding and Maxwell’s beautiful