Warped Passages - Lisa Randall [93]
When Ike saw the damage, he stormed into Athena’s room and demanded that she watch her owls more carefully in the future. Athena protested that her owls were almost all well-behaved and she need only keep an eye on the bad one. But by that time the owls were back in their cages, and neither Ike nor Athena could identify which one was guilty.
The Standard Model works spectacularly well, but only because it is a theory in which quarks, leptons, and the weak gauge bosons—the charged Ws and the Z that communicate the weak force between weakly charged matter—all have mass. The mass of fundamental particles is, of course, critical to everything in the universe; if matter had been truly massless, it wouldn’t form nice, solid objects, and structure and life in the universe as we know it would never have formed. Yet weak gauge bosons and other fundamental particles in the simplest theory of forces look as if they should be massless and should travel at the speed of light.
You might find it strange that a theory of forces should prefer zero masses. Why shouldn’t any mass be allowed? But the most basic quantum field theory of forces is intolerant in this respect. It ostensibly forbids any nonzero values for the masses of fundamental Standard Model particles. One of the triumphs of the Standard Model is that it shows how to resolve this issue and fashion a theory in which particles have the masses that observations tell us they must have.
In the next chapter we will explore the mechanism by which particles acquire mass—the phenomenon known as the Higgs mechanism. But in this chapter we will discuss the important topic of symmetry. Symmetry and symmetry breaking help to determine how the universe goes from an undifferentiated point to the complex structure we now see. The Higgs mechanism is intimately connected with symmetry, and in particular with broken symmetry. Understanding how the elementary particles acquire mass requires some familiarity with these important ideas.
Things That Change but Remain the Same
Symmetry is a sacred word to most physicists. One might conjecture that other communities value symmetry highly as well, since the Christian cross, the Jewish menorah, the Dharma wheel of Buddhism, the crescent of Islam, and the Hindu mandala all exhibit symmetry (see Figure 56). Something has symmetry if you can manipulate it—for example, by rotating it, reflecting it in a mirror, or interchanging its parts—so that the new configuration is indistinguishable from the initial one. For example, if you were to interchange two identical candles on a menorah, you would see no visible difference. And the mirror image of a cross is identical to the cross itself.
Figure 56. A menorah, a cross, the Dharma wheel of Buddhism, the crescent of Islam, and the Hindu mandala all exhibit symmetry.
Whether we are talking about mathematics, physics, or the world, we can make transformations that appear to do nothing when there is a symmetry. A system has symmetry if someone could exchange its components, reflect it in a mirror, or rotate it while your back was turned without your noticing any difference when you looked at it again.
Symmetry is often a static property: for example, the symmetry of a cross does not involve time. But physicists often prefer to describe symmetries in terms of imagined symmetry transformations—manipulations that one can apply to a system without changing any observable properties. For example, instead of saying that the candles of a menorah are equivalent, I might say instead that a menorah would look the same if I were to interchange two of the candles. I wouldn’t actually have to exchange the candles in order to claim that there was a symmetry. But if, hypothetically, I did interchange the candles, I wouldn’t be able to see any difference. Sometimes I will describe