Warped Passages - Lisa Randall [101]
The symmetry exists until the moment someone picks up a glass. At that moment the left-right symmetry is spontaneously broken. No law of physics dictates that anyone has to choose left or right. But one has to be chosen, and after that, left and right are no longer the same in that there is no longer a symmetry that interchanges the two.
Here’s another example. Imagine a pencil standing on end at the center of a circle. For the split second in which it rests on its tip and is exactly vertical, all directions are equivalent and a rotational symmetry exists. But a pencil standing on end won’t just stay there: it will spontaneously fall in some direction. As soon as the pencil topples over, the original rotational symmetry is broken.
Notice that it would not be the physical laws themselves that determined the direction. The physics of the pencil falling over would be exactly the same no matter the direction in which it fell. What would break the symmetry would be the pencil itself, the state of the system. The pencil simply cannot fall in all directions at once. It has to fall in one particular direction.
A wall that is infinitely long and high would also look the same everywhere and in all directions along it. But because an actual wall has boundaries, if you are to see the symmetries you will have to get close enough to it that the boundaries are out of your field of vision. The wall’s ends tell you that not everywhere along the wall is the same, but if you were to press your nose up against it so that you could see only a short distance away, the symmetry would appear to be preserved. You might want to briefly reflect on this example, which shows that a symmetry can appear to be preserved when viewed on one distance scale, even though it appears to be broken on another—a concept whose importance will become apparent very soon.
Almost any symmetry you care to name is not preserved in the world. For example, there are many symmetries that would be present in empty space, such as rotational or translational invariance, which tell us that all directions and positions are the same. But space is not empty: it is punctuated by structures such as stars and the solar system, which occupy particular positions and are oriented in particular ways that no longer preserve the underlying symmetry. They could have been anywhere, but they can’t be everywhere. The underlying symmetries must be broken, although they remain implicit in the physical laws describing the world.
The symmetry associated with the weak force is also spontaneously broken. In the rest of this chapter I’ll explain how we know this and discuss some of the consequences. We’ll see that spontaneously breaking the weak force symmetry is the only way to explain massive particles while avoiding incorrect predictions for high-energy particles that cannot be avoided in any other candidate theory. The Higgs mechanism acknowledges both the requirement of an internal symmetry associated with the weak force and the necessity for it being broken.
The Problem
The weak force has one especially bizarre property. Unlike the electromagnetic force, which travels over large distances—which you benefit from each time you turn on the radio—the weak force affects only matter that is within extremely close range. Two particles must be within one ten thousand trillionth of a centimeter to influence each other via the weak force.
For the physicists who studied quantum field theory and quantum electrodynamics (QED, the quantum field theory of electromagnetism) in its earliest days, this restricted range was a mystery. QED made it look as if forces, such as the well-understood electromagnetic force, should be transmitted arbitrarily far away from a charged source. Why wasn’t the weak force also communicated to particles at any distance and not just to those nearby?
Quantum