Читать книгу String Theory For Dummies - Andrew Zimmerman Jones - Страница 80

A symmetry exists when you can take something and transform it in some way, and nothing seems to change about the situation. The principle of symmetry is crucial to the study of physics and has special implications for string theory in particular. Even when a symmetry used to be there, but is then broken by some other effect, physicists find it extremely useful to use it to describe the world. They call those spontaneously broken symmetries.

Symmetries are obvious in geometry. Take a circle and draw a line through its center, as in Figure 4-1. Now picture flipping the circle around that line. The resulting image is identical to the original image when it’s flipped about the line. This is reflection symmetry. If you were to spin the figure 180 degrees, you’d end up with the same image again. This is rotational symmetry. The trapezoid in Figure 4-1, on the other hand, has asymmetry (or lacks symmetry) because no rotation or reflection of the shape will yield the original shape.

FIGURE 4-1: The circle has symmetry, but the trapezoid doesn’t.

The most fundamental form of symmetry in physics is the idea of translational symmetry, which is where you take an object and move it from one location in space to another. If we move from one location to another, the laws of physics should be the same in both places. This principle is how scientists use laws discovered on Earth to study the distant universe. Another familiar symmetry is rotational symmetry: if we make some experiment on a bench facing south or east, we generally do not expect to see a difference.

In physics, though, symmetry means way more than just taking an object and flipping, spinning, or sliding it through space.

The most detailed studies of energy in the universe indicate that, no matter which direction you look, space is basically the same in all directions. The universe itself seems to have been symmetric from the very beginning, at least to a good approximation.

The laws of physics don’t change over time and across space, as far as we can tell. If we perform an experiment today and perform the same experiment tomorrow, we believe that we will be able to interpret the result according to the same fundamental laws. The same is true if we perform the experiment in New York, in Tokyo, or on Mars.

This does not mean that the outcome of the experiment will be necessarily the same! For instance, while the laws of gravity are, as far as we believe, the same now as they were in the distant past, we know that the universe looked very different back then, compared to now.

Symmetries like rotation, translations, and translations through time are seen as central to the study of science, and in fact, many physicists have stated that symmetry is the single most important concept for physics to grasp.

Indeed, symmetry is so important in physics that we can use it even when it’s no longer there. Take a small drop of water, which is a perfect sphere. If we cool it enough, it will become an ice crystal, and as we all know from playing with snowflakes, they are not spherically symmetric. Yet, they do have a beautiful residual symmetry, in many ways richer and more interesting than the original droplet. This is an example of spontaneous symmetry breaking.

Another example is the fact that the equations describing the universe are invariant under time-translations (redefining our clocks), while the universe itself is not: We actually believe that it had a beginning with the Big Bang.

In a much more sophisticated way, the study of how the fundamental symmetries of nature are broken is one of the keys to understanding modern physics. An important example that’s a bit beyond the scope of our discussion is the famous Higgs boson, which is a cornerstone of particle physics and is intimately related to breaking a symmetry — specifically, the symmetry of the electroweak force mentioned in the previous section.

Another type of symmetry which plays a big role in string theory, and has been getting a lot of attention from theoretical physicists, is called supersymmetry. On top of having a catchy name, it is a required ingredient to make sense of string theory. Supersymmetry makes some very strong predictions on the elementary particles that should exist in the universe, and because of that we know that it is not exactly realized in the universe: It can only be one of the spontaneously broken symmetries. We will tell you all about this in Chapter 10.