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By Root 898 0

again at the second line of the master equation. Without knowing any mathematics, you can “see” the interactions between matter particles. The portions of the second line involving W, B, and G (for gluon) are sandwiched between two matter particles, ψ, and that means that here are the bits of the master equation that tell us how matter particles “couple” with the force mediators but with a punch line. The photon lives partly in the symbol “W” and partly in “B,” and that is where the Z lives too! The W particle lives entirely in “W.” It is as if the mathematics regards the fundamental objects as W and B, but they mix up to conjure the photon and the Z. The result is that the electromagnetic force (mediated by the photon) and the weak force (mediated by the W and Z particles) are intertwined. In experiments, it means that properties that can be measured in experiments on electromagnetic phenomena should be related to properties measured in experiments on weak phenomena. That is a very impressive prediction of the Standard Model. And it was a prediction: The architects of the Standard Model, Sheldon Glashow, Steven Weinberg, and Abdus Salam, shared a Nobel Prize for their efforts, for their theory was able to predict the masses of the W and Z particles well before they were discovered at CERN in the 1980s. The whole thing hangs together beautifully. But how did Glashow, Weinberg, and Salam know what to write down? How did they come to realize that “W and B mix up to produce the photon and the Z”? To answer that question is to catch a glimpse of the beautiful heart of modern particle physics. They did not simply guess, they had a big clue: Nature is symmetrical.

Symmetry is evident all around us. Catch a snowflake in your hand and look closely at this most beautiful of nature’s sculptures. Its patterns repeat in a mathematically regular way, as if reflected in a mirror. More mundane, a ball looks unchanged as you turn it around, and a square can be flipped along its diagonal or along an axis that slices through its center without changing its appearance. In physics, symmetry manifests in much the same way. If we do something to an equation but the equation doesn’t change, then the thing we did is said to be a symmetry of the equation. That’s a little abstract, but remember that equations are the way physicists express how real things relate to one another. A simple but important symmetry possessed by all of the important equations in physics expresses the fact that if we pick up an experiment and put it on a moving train, then, provided the train isn’t accelerating, the experiment will return the same results. This idea is familiar to us: It is Galileo’s principle of relativity that lies at the heart of Einstein’s theory. In the language of symmetry, the equations describing our experiment do not depend on whether the experiment is sitting on the station platform or onboard the train, so the act of moving the experiment is a symmetry of the equations. We have seen that this simple fact ultimately led Einstein to discover his theory of relativity. That is often the case: Simple symmetries can lead to profound consequences.

We’re ready to talk about the symmetry that Glashow, Weinberg, and Salam exploited when they discovered the Standard Model of particle physics. The symmetry has a fancy name: gauge symmetry. So what is a gauge? Before we attempt to explain what it is, let’s just say what it does for us. Let’s imagine we are Glashow or Weinberg or Salam, scratching our heads as we look for a theory of how things interact with other things. We’ll start by deciding we are going to build a theory of tiny, indivisible particles. Experiment has told us which particles exist, so we’d better have a theory that includes them all; otherwise, it will be only a half-baked theory. Of course, we could scratch our heads even more and try to figure out why those particular particles should be the ones that make up everything in the universe, or why they should be indivisible, but that would be a distraction. In fact, they are two very