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Symmetry: A ‘Key to Nature’s Secrets’

The recognition of accidental symmetry not only resolved the old puzzle about approximate symmetries; it also opened up exciting new possibilities. It turned out that there are certain symmetries that could not be violated in any theory that has the same particles and the same exact local symmetries as the Standard Model and that is simple enough to be renormalizable.8 If really valid, these symmetries, known as lepton and baryon conservation,9 would dictate that neutrinos (particles that feel only the weak and gravitational forces) have no mass, and that protons and many atomic nuclei are absolutely stable. Now, on experimental grounds these symmetries had been known long before the advent of the Standard Model, and had generally been thought to be exactly valid. But if they are actually accidental symmetries of the Standard Model, like the accidental proton–neutron symmetry of the strong forces, then they too might be only approximate. As I mentioned earlier, we now understand that interactions that make the theory nonrenormalizable are not impossible, though they are likely to be extremely weak. Once one admits such more complicated nonrenormalizable interactions, the neutrino no longer has to be strictly massless, and the proton no longer has to be absolutely stable.

There are in fact possible nonrenormalizable interactions that would give the neutrino a tiny mass, of the order of one hundred millionth of the electron mass, and give protons a finite average lifetime, though one so long that typical protons in matter today will last much longer than the universe already has. Experiments in recent years have revealed that neutrinos do indeed have such masses. Experiments are under way to detect the tiny fraction of protons that decay in a year or so, and I would bet that these decays will eventually be observed. If protons do decay, the universe will eventually contain only lighter particles like neutrinos and photons. Matter as we know it will be gone.

I said that I would be concerned here with the symmetries of laws, not of objects, but there is one thing that is so important that I need to say a bit about it. It is the universe. As far as we can see, when averaged over sufficiently large scales containing many galaxies, the universe seems to have no preferred position, and no preferred directions—it is symmetrical. But this too may be an accident.

There is an attractive theory, called chaotic inflation, according to which the universe began without any special spatial symmetries, in a completely chaotic state. Here and there by accident the fields pervading the universe were more or less uniform, and according to the gravitational field equations it is these patches of space that then underwent an exponentially rapid expansion, known as inflation, leading to something like our present universe, with all nonuniformities in these patches smoothed out by the expansion. In different patches of space the symmetries of the laws of nature would be broken in different ways. Much of the universe is still chaotic, and it is only in the patches that inflated sufficiently (and in which symmetries were broken in the right ways) that life could arise, so any beings who study the universe will find themselves in such patches.

This is all quite speculative. There is observational evidence for an exponential early expansion, which has left its traces in the microwave radiation filling the universe, but as yet no evidence for an earlier period of chaos. If it turns out that chaotic inflation is correct, then much of what we observe in nature will be due to the accident of our particular location, an accident that can never be explained, except by the fact that it is only in such locations that anyone could live.

  1. 8

    Again, I admit to passing over some technical complications. 

  2. 9

    Lepton number is defined as the number of electrons and similar heavier charged particles plus the number of neutrinos, minus the number of their antiparticles. (This conservation law requires the neutrino to be massless because neutrinos and antineutrinos, respectively, spin only counterclockwise and clockwise around their directions of motion. If neutrinos have any mass then they travel at less than the speed of light, so it is possible to reverse their apparent direction of motion by travelling faster past them, hence converting the spin from counterclockwise to clockwise, and neutrinos to antineutrinos, which changes the lepton number.) Baryon number is proportional to the number of quarks minus the number of antiquarks. 

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