Mexican hats and a metastable universe

The mass of the Higgs boson may be telling us something profound and puzzling about the future of the universe

Economic announcements, such as interest rate changes or profit warnings, are often discounted by stock markets, meaning that their expected effects are already accounted for in share prices. This can lead to the strange spectacle of an announced increase in profits causing a drop in share price because it doesn’t quite live up to the rumours preceding it. Or indeed, vice versa.

The discovery of the Higgs boson was discounted by many “deep” theorists in a similar way. It was common to assume that the Higgs had to be there and that unless it brought supersymmetry, or other exotic friends, to the party it would be business as usual.

Well, supersymmetry may still show up when we restart the LHC in April 2015. But the fact that the Higgs boson is there, and the fact that we now know its mass - to within a few percent - is in fact causing perturbations even for some “deep” theorists*.

The Higgs boson, and the Brout-Englert-Higgs mechanism, are important because of their role in giving mass to fundamental particles. The mass of the Higgs boson itself is an important number to know because it affects the potential energy level of the universe, which in turn affects how long the universe might last.

Many explanations of the Higgs talk about wine bottles or Mexican hats. The idea is that the universe is rolling around in the lowest bit of an energy surface – in the dip in the brim of the hat, or at the outer edge of the base of the wine bottle, depending on your preferred analogy. The dip is the place where the energy is minimised. This makes the universe stable, since to go anywhere else on the surface would require an enormous amount of energy.

The masses of the fundamental particles, especially of the top quark and the Higgs boson, play a role in determining the shape of this surface. For some values of those masses, the brim of the hat is the lowest possible energy value and the universe is completely stable. For other values, the brim is the wrong shape and the universe is completely unstable. Since the universe seems to have lasted for 13.8 billion years, those values are in quite extreme contradiction with observation, even before you consider the particle masses.

There is a third possibility however, which is that the brim of the hat turns down again and there is another wiggle, another dip, which is even lower than the one the universe currently occupies. To get to this lower state, the universe has to go over a bump, which classically would require lots of energy, so the universe remains stable. But in quantum mechanics, there is a small possibility of "tunneling" through the bump, and finding the new, lower energy region. On a smaller scale, this tunneling effect is seen in radioactive decays and elsewhere.

The probability for this tunneling to actually occur could be very small, meaning the universe could last a long time - 13.8 billion years or (hopefully!) more - a situation called "metastability". But in this configuration, it might at some point pop through into the new energy minimum.

In the new energy state, all the fundamental forces and particles would be completely different from those we experience today, and it's safe to say we wouldn't be around anymore to find out what they were. The whole thing would make total proton reversal look like a picnic. A bubble of weird new universe could appear at any moment and would expand at the speed of light. The timescales involved are huge though, and there's nothing we can do to affect it anyway, so if you need to worry about something, I would advise losing sleep over climate change, war, rogue asteroids and other existential threats way ahead of this one.

Intriguingly, the measured values of the Higgs boson mass and top quark mass put the universe very close to the boundary between metastable and completely stable. So close that we don't know which zone we are in. More precise measurements of the masses may be able to tell us in future. But is the fact that we are so near the boundary a coincidence? Or is it a clue to some underlying principle that we haven't yet worked out?

An example of a critical value that is not a coincidence is the slope of a sand dune. Piles of sand have a critical angle. A pile steeper than that angle will avalanche down. In a field of natural sand dunes, the slopes will all be close to that critical angle, because the wind tries to pile the sand steeper, the sand slides down, and a sort of equilibrium is reached near the critical angle. Is something like that going on in the universe? If so, what plays the role of the wind, pushing us above criticality? How often to avalanches happen? Ok, it's not a very good analogy, just an example.

No one knows where these ideas will take us yet anyway, but the fact that a single mass we have measured is having such deep impact on our ideas of the universe is very exciting. Never discount data.

If you want more explanation on local minina, vacua and the BEH potential I recommend this article by Matt Straessler.

The post was partly inspired by a Science Oxford event yesterday on "The Future of the Universe", chaired by Quentin Cooper, with a theoretical physicist and an astrophysicist (Jim Gates and Jo Dunkley).

* I think “deep” in this context is similar to a secret agent in “deep cover”. You have little idea what they are up to and it is very hard to tell whether they are even on your side. But occasionally they are incredibly valuable.

Jon Butterworth’s book, Smashing Physics, is out now!

A bunch of interesting events where you might be able to hear him talk about it etc are listed here. Also, twitter.

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