Symmetry Not

The enhanced symmetry of unification does some great things. It assembles the scattered pieces of the Core into well-proportioned wholes. Once our vision accommodates to that dazzling first impression, however, and we begin to look more carefully, things don’t seem right.

In fact, something very basic appears to be wrong. If the strong, weak, and electromagnetic forces are aspects of a common underlying master force, then symmetry requires that they should all have the same strength. But they don’t. Figure 18.1 shows this.

Figure 18.1 Perfect symmetry would require the strong, weak, and electromagnetic forces to have equal strengths. They don’t. For later convenience, here I’ve used the inverse square of the couplings as the quantitative measure of their relative power. So the strong interaction, which is the strongest, appears on the bottom.

There’s a reason why the strong interaction is called strong and the electromagnetic interaction isn’t. The strong interaction really is stronger! One manifestation of the difference is that atomic nuclei, bound together by strong-interaction forces, are much smaller than atoms, held together by electromagnetic forces. The strong forces hold nuclei together more tightly.

The mathematics of the Core theory enables us to give a precise numerical measure of the relative strength of different interactions. Each of its interactions—strong, weak, electromagnetic—has what we call a coupling parameter, or simply a coupling.

In terms of Feynman graphs, the coupling is a factor by which we multiply each hub. (These universal, overall coupling factors come on top of the purely numerical values of the color or electromagnetic charges of the particular particles involved, as encoded in the Charge Account.) So each time a color gluon appears in a hub, we multiply the contribution of the process depicted by the strong coupling; each time a photon appears, we multiply by the electromagnetic coupling. The basic electromagnetic force comes from exchanging a photon (Figure 7.4), so it has the square of the electromagnetic coupling. Similarly, the basic strong force comes from exchanging a gluon, so it has the square of the strong coupling.

Complete symmetry among the forces requires every hub to be related to every other. It leaves no room for differences among the couplings. The observed differences, therefore, pose a critical challenge to the whole idea of achieving unification through symmetry.

Correcting Our Vision

A great lesson from the Core is that the entity we perceive as empty space is in reality a dynamic medium full of structure and activity. The Grid, as we’ve called it, affects the properties of everything within it—that is, everything. We see things not as they are, but as through a glass, darkly. In particular, the Grid is aboil with virtual particles, and these can screen or antiscreen a source. That phenomenon, for the strong force, was central to the stories that unfolded in Parts I and II. It occurs for the other forces too.

So the coupling values we see depend on how we look. If we look crudely, we will not discern the basic sources themselves, but will see their image as distorted by the Grid. We will, in other words, see the basic sources mixed together with the cloud of virtual particles that surround them, unresolved. To judge whether perfect symmetry and unity of the forces occurs, we should correct for the distortions.

To see down to the basics, we may need to resolve very short distances and very short times. That’s an oft-repeated lesson, from van Leeuwenhoek and his microscopes, to Friedman, Kendall, and Taylor using their ultrastroboscopic nanomicroscope at SLAC to look inside protons, to experimenters using the creative destruction machine LEP to dig into Grid. As we saw in connection with those two recent projects, to resolve extremely short distances and times, where quantum theory comes into play, it’s necessary to use probes that actively transfer large amounts of momentum and energy to the object being probed. That’s why high-energy accelerators, despite their expense and complexity, are the instruments of choice.

A Near Miss

As we discussed in Chapter 16, the virtual particle clouds can be slow to build. For the cloud around a quark to grow from a reasonable-sized seed to threatening proportions, it had to evolve from the Planck length to the proton’s size: a factor of 10¹⁸ in distance!

Given that experience, we should not be surprised to find that to get to the basics—to see down to the distances where unification might take place—we might need to transfer outlandish amounts of momentum and energy. The next great accelerator, the LHC, will give us ten times better resolution—that is, a factor of 10¹—at a cost of roughly ten billion euros. And after that, it gets really difficult.

Figure 18.2 Correcting for Grid distortions, to see whether the forces unify. If we plot things in this way—with inverse couplings squared ascending in the vertical direction versus logarithm of energy or (equivalently) of inverse distance in the horizontal direction—then the corrected couplings, viewed at better and better resolution,track straight lines. The size of the experimental errors is indicated by the width of the lines. It almost works, but not quite.

So we have to use our noodles instead. Though not as foolproof, they’re relatively cheap, and ready at hand (so to speak). With a few strokes of a pen, we can calculate the effects of Grid distortion and correct for them.

The result is displayed in Figure 18.2.

As Homer Simpson might say:

D’Oh!

It doesn’t quite work. Close, but no cigar.

What to do?