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By Root 900 0

good questions to which we still do not have the answers. One of the qualities of a good scientist is to select which questions to ask in order to proceed, and which questions should be put aside for another day. So let’s take the ingredients for granted and see if we can figure out how the particles interact with each other. If they did not interact with each other, then the world would be very boring—everything would pass through everything else, nothing would clump together, and we would never get nuclei, atoms, animals, or stars. But physics is so often about taking small steps, and it is not so hard to write down a theory of particles when they do not interact with each other—we just get the second line of the master equation with the W, B, and G bits scratched out. That’s it—a quantum theory of everything but without any interactions. We have taken our first small step. Now here comes the magic. We shall demand that the world, and therefore our equation, have gauge symmetry. The consequence is astonishing: The remainder of the second line and the whole of the first line appear “for free.” In other words, we are mandated to modify the “no interactions” version of the theory if we are to satisfy the demands of gauge symmetry. Suddenly we have gone from the most boring theory in the world to one in which the photon, W, Z, and gluon exist and, moreover, they are responsible for mediating all of the interactions between the particles. In other words, we have arrived at a theory that has the power to describe the structure of atoms, the shining of the stars, and ultimately the assembly of complex objects like human beings, all through the application of the concept of symmetry. We have arrived at the first two lines of our theory of nearly everything. All that remains is to explain what this miraculous symmetry actually is, and then those last two lines.

The symmetry of a snowflake is geometrical and you can see it with your eyes. The symmetry behind Galileo’s principle of relativity isn’t something you can see with your eyes, but it isn’t too hard to comprehend even if it is abstract. Gauge symmetry is rather like Galileo’s principle in that it is abstract, although with a little imagination it is not too hard to grasp. To help tie together the descriptions we offer and the mathematical underpinnings, we have been dipping into the master equation. Let’s do it again. We said that the matter particles are represented by the Greek symbol ψ in the master equation. It’s time now to delve just a little deeper. ψ is called a field. It could be the electron field, or an up-quark field, or indeed any of the matter particle fields in the Standard Model. Wherever it is biggest, that’s where the particle is most likely to be. We’ll focus on electrons for now, but the story runs just the same for all the other particles, from quarks to neutrinos. If the field is zero someplace, then the particle will not be found there. You might even want to imagine a real field, one with grass on it. Or perhaps a rolling landscape would be better, with hills and valleys. Where the hills are, the field is biggest, and in the valleys it is smallest. We are encouraging you to conjure up, in your mind’s eye, an imaginary electron field. It might be surprising that our master equation is so noncommittal. It doesn’t work with certainties and we cannot even track the electron around. All we can do is say that it is more likely to be found over here (where the mountain is) and less likely to be found over there (at base camp in the valley). We can put definite numbers on the chances of finding the electron to be here or there, but that is as good as it gets. This vagueness in our description of the world at the very smallest distance scales occurs because quantum theory reigns supreme there, and quantum theory deals only in the odds of things happening. There really does appear to be a fundamental uncertainty built into concepts such as position and momentum at tiny distances. Incidentally, Einstein really did not like the fact that the world should operate