Phase transitions: steam engines, Dark Matter and the Higgs

How the physics of the industrial revolution now connects cosmology and particle physics

Even a watched kettle will induce a phase transition eventually
Even a watched kettle will induce a phase transition eventually Photograph: D. Hurst/Alamy

Phase transitions: steam engines, Dark Matter and the Higgs


We had a particle physics seminar at UCL on Friday; we usually do. This one was from Malcolm Fairbairn and was mainly about Dark Matter.

“Dark Matter” is the mysterious stuff which we postulate to explain several anomalous astrophysical observations. It is mysterious because (as the name suggests) we can’t actually see it - it is dark. To be more precise, it doesn’t interact with photons. So the observations which betray its presence are all indirect. In general they depend upon its gravitational influence. From a particle-physics point of view it is also mysterious because it does not seems to be made of any of the particles we know about in our Standard Model.

One very powerful indirect constraint on Dark Matter comes from considering the development of the universe shortly after the big bang. The Dark Matter around us now is a “relic” from the early stages of the Big Bang. When the universe was hot and dense enough, the assumed Dark Matter particles would have participated in the cosmic mosh-pit, being scattered, annihilated and produced along with everything else. As the universe expanded and cooled, at some point they decoupled, disengaged - drifted towards the bar, if you like - but are still hanging around, distorting the behaviour of the other dancers. The distribution of galaxies, and the cosmic microwave background, depend on Dark Matter. Therefore measurements of them provide further evidence for its existence, and constrain its nature.

I love the way physics allows us to make that kind of connection - in this case, between the distribution of stars in the night sky and the possible existence of a new fundamental particle. Such connections typically require a broad array of apparently disparate pieces of physics. In this case one of the most important links in the chain is thermodynamics - the study of how heat and temperature change, and how they make other things change.

A key idea in thermodynamics is that of a “phase transition”. In a phase transition, some internal property of a system changes (in physics-speak a “system” can be anything from a kettle full of water to the entire universe) and affects its external behaviour. Much of thermodynamics was worked out around the industrial revolution, because the phase transition of boiling water is the driving force behind steam engines.

If you add energy to water, the temperature will in general increase steadily. However, at 100 degrees celsius, that behaviour changes quite dramatically. The temperature stops increasing, even if you carry on adding energy. But the volume (or the pressure, if the water is in a boiler) will suddenly increase as the water undergoes a phase transition from liquid to gas. The pressure can be used to drive an engine. Once the water has boiled, the temperature will start going up again.

There is an important phase transition in the early universe too, connected with the Higgs boson, and called the “electroweak phase transition”. This is the point, in the cooling of the universe, at which the strange “Mexican Hat” shape of the Brout-Englert-Higgs field manifests itself. In simple terms, it is when particles acquire mass; quite a dramatic change.

Boiling water is called a “first order” phase transition, because of the sudden change in behaviour¹. The electroweak phase transition could in principle be first order too, but calculations show that with the Higgs boson now known to have a mass of 125 GeV, the transition is smoother - more continuous, or second order².

As Malcolm descibed in his seminar, this is a bit of a problem for cosmologists, because of another piece of physics which gets dragged in. It is quite difficult to come up with models of the Big Bang which can produce all the matter we see around us, and no antimatter. This is the problem of “baryogenesis”, since the mass that needs to be created here is mostly protons and neutrons, which are baryons. Not anti-baryons.

To make protons and neutrons, without making equal numbers of anti-protons and anti-neutrons, a dramatic shift is required somewhere as the universe cools. The favourite way of achieving this is by having a first-order electroweak phase transition. Which is now ruled out in the Standard Model thanks to the Higgs boson being too heavy, and smoothing out that phase transition into a continuous one.

This is one reason why people like Malcolm are coming up with theoretical extensions of the Standard Model which would both provide a suitable Dark Matter particle, and allow the electroweak phase transition to be first order. It is also one of the reasons the hunt for Dark Matter is so exciting, and in fact difficult, since some of these constraints imply it might be even harder to find than we thought.

It is important to realise that topics like cosmology and particle physics have had huge impact on our technology and our way of life; it’s something I have been known to mention on these pages every now and then.

But it is also pleasing to remember that it goes both ways. The physics that was worked out while struggling to make better steam engines for the industrial revolution now allows us to connect the Big Bang, the behaviour of galaxies, the abundance of matter compared to antimatter, the Higgs boson and Dark Matter; all via the thermodynamics of the early universe.

¹ The label “first order” comes the fact that one of the first derivatives of the energy changes suddenly. See here for more on derivatives.

² If the Higgs boson had a lower mass by a few tens of GeV, this would not be true. Another reason knowing that number is interesting.
