Lost in Math by Hossenfelder Sabine

Author:Hossenfelder, Sabine
Language: eng
Format: epub
Publisher: Hachette Book Group
Published: 2018-06-12T04:00:00+00:00

FIGURE 12. A spinning top, as long as it is in motion, is rotationally symmetric. As it loses energy through friction, the symmetry is broken.

The symmetry of the electroweak interaction, for example, is restored at just about LHC energies, a signal of which is the production of the Higgs-boson.

THE STANDARD model needs three different symmetry groups—U(1) and SU(2) for the electroweak interaction, and SU(3) for the strong nuclear force. These are small groups, as you can tell by the small numbers. But larger symmetry groups often contain several smaller groups, and therefore one large group whose symmetry is broken at high energy could give rise to the standard model at the energies we observe. In this picture, the grand unified symmetry is like an elephant, of which we have presently, at low energies, only an ear, a tail, and a leg. The full elephant would be restored only at the unification energy, estimated to be about 1016 GeV, or 15 orders of magnitude above LHC energies.

The first proposal for such a unified symmetry used the smallest group that contains the symmetry groups of the standard model, SU(5). Unified forces like this, however, generically enable new interactions that allow protons to decay. And if protons are unstable, so are all atomic nuclei. In such unified theories, the proton’s lifetime could be as high as 1031 years, much exceeding the present age of the universe. But because of quantum mechanics, this would merely mean that the protons’ average lifetime was that high. Once protons can decay at all, it can also happen quickly; it’s just that quick decays are rare.

There are 10 protons in every water molecule, and 1025 water molecules in every liter of water. And so, instead of waiting 1031 years to see a single proton decay, we can monitor a large tank of water and wait for one of its protons to decay. Experiments like this have run since the mid-1980s, but to date nobody has seen a proton decay. The current observations (or lack thereof) imply that the average lifetime of protons is longer than 1033 years. With that, SU(5) unification is ruled out.

The next attempt at unification used a larger group, SO(10), in which the upper bound on the proton lifetime is higher. Since then, several other symmetry groups have been tried, some of which push the proton lifetime up to 1036 years, orders beyond even upcoming experiments.

Besides proton decay, grand unified theories also predict new particles because the large groups contain more than what’s in the standard model. These new particles, as usual, are assumed to be too heavy to have been detected yet. And so theoretical physicists now have a selection of unified theories that are safe from being experimentally ruled out in the foreseeable future.

Grand unification alone, however, doesn’t solve the problem with the Higgs mass. For that, physicists also supersymmetrize the grand unification. We know that supersymmetry—if it is a symmetry of nature—must be broken at energies above what we have tested so far, because we haven’t yet seen susy particles.

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