Today the 2008 Nobel Prize winners were announced for physics. It was given to three physicists who described something called *symmetry breaking*. Since most people don’t know what symmetry breaking is, but people remember me writing about group theory and symmetry, I’ve been getting questions about what it means.

I don’t pretend to completely understand it; or even to mostly understand it. But I mostly understand the very basic idea behind it, and I’ll try to pass that understanding on to you.

We’ll start with the idea of symmetry. Intuitively, we think of symmetry as a situation where something is identical on both sides of a line. Another way of saying that is that reflecting it in a mirror won’t change what we see. Symmetry is really something much more general than that. Mathematically, we say that symmetry is an *immunity to transformation*. What that means is that for something symmetric, there is some kind of transformation you can do to it, and the result is indistinguishable from what you started with.

The intuitive symmetry – mirror (or *reflective*) symmetry – is one example of this: flipping a reflectively symmetric image around a line in indistinguishable from the original image. Another easy example is *translational symmetry*: imagine that you’ve got an infinite sheet of graph paper. If you move that paper to the left the width of one square, you can’t tell that it was moved: it’s completely indistinguishable.

So what is symmetry breaking?

Sometimes you have a symmetric configuration which has to go through a transformation that results in it becoming non-symmetric. A canonical example of this is a ball on a hill. Imaging a perfectly round hill, with a spherical ball sitting on top of it. It’s completely symmetric reflexively and rotationally. But in gravity, it’s very unstable. Eventually something is going to perturb it, and the ball is going to roll down the hill. Once it does that, it’s no longer symmetric. The symmetry was *broken* by

the motion of the ball. This is called *spontaneous symmetry breaking*: the system has what is in some sense an inevitable state transition, and after that state transition, the system is no longer symmetric.

In deep physics and cosmology, there are a lot of basic symmetries. There are also a lot of things that appear like they *should* be symmetric, but aren’t. For example, if the universe started with a big bang, then *at some moment* immediately after the big bang, space was uniform. But that basic symmetry broke; space is now *very* non-uniform.

From looking at some of the basic rules of how things work, and it

seems like the quantities of matter and antimatter should be equivalent, which reflects a basic symmetry in the structure of the basic particles that make up the universe. But from what we can observe, that’s very much *not* true: there’s a lot more matter than antimatter. At some

point when particles were condensing out of the energy cloud after the big bang, the symmetry broke, and we wound up with a lot more matter than

antimatter.

Finally, the basic fundamental forces in the universe appear to be related on a very deep level. They’re really the same thing, but operating at different scales and different energy levels. At very high energy levels, electromagnetic forces, and the two atomic forces are all really the same thing. There’s a deep symmetry between them. But as the energy level of

the environment goes down, eventually they split, and become distinguishable. The symmetry breaks, and we get different forces.

The Nobel prize in physics this year was given to three physicists. One, Yoichiro Nambu, worked out the mechanism for spontaneous symmetry breaking in subatomic physics. The other two, Makoto Kobayashi and Toshihide Maskawa, worked out the origin of the broken symmetry. (Don’t ask me the difference between the mechanism and the origin in this case; that’s well beyond my understanding of how symmetry-breaking applies to physics. I’m just paraphrasing the press release.)

John ArmstrongThe canonical example to define symmetry-breaking is a bunch of people seated around circular table. Each place setting has a plate, and there’s a cup set between each pair of plates. The situation has a rotational symmetry (turn by one setting) and a reflection symmetry (draw a line across the center of the table, through a pair of plates).

But is the cup on your right side or your left side part of your setting? When everyone sits down, it doesn’t matter, since everything is symmetric. But if I grab the cup on my right, the woman sitting there has to grab the cup on her right, and the man on the other side has to grab the cup on

hisright, and so on all round until we get to the woman on my left who grabs the cup on her right — my left.Now the reflection symmetry has been broken, but the rotational symmetry remains.

Mark C. Chu-CarrollJohn:

That is a *beautiful* example. Thanks!

John ArmstrongIt strikes me I should say something about

spontaneoussymmetry-breaking.The canonical example here is to consider a punted wine bottle. That is, the bottom isn’t flat, but is domed up in the middle. It’s rotationally symmetric. If you place a marble on the punt in the

exactcenter, it will balance and the situation is still symmetric.But that situation isn’t stable. The

slightestnudge will push the marble off the center (just like one person grabbing the left or the right cup). Then it will roll off in that directly until it comes to rest in the groove at the base of the punt. Now the rotational symmetry has been broken, since one direction from the center has been identified as different.The important thing is that nobody made a “choice” here. Energetically, the non-symmetric configurations are all just as good as each other, but they’re all

betterthan the symmetric position. So the tendency of the universe to minimize energy is what “spontanously” breaks the symmetry without having to “intentionally” break it by making a choice to pick out one direction over the others.greggreat explanations mark and john.

BTW, it is “Masukawa”. i have seen it written several places without the “u”, but the correct transliteration includes a the “u” in the spelling.

greggreat explanations mark and john.

BTW, it is “Masukawa”. i have seen it written several places without the “u”, but the correct transliteration includes a the “u” in the spelling.

PatrickThanks, I’ve been looking for an simple example of what this means all day. The physics blogs have all been rather silent, or at least the ones I follow.

Thanks Mark + John.

AmbitwistorAnother canonical example is ferromagnetism.

At high temperatures (above the Curie temperature), a magnet is composed of little magnetic domains that are disordered. There is no preferred direction, so the system is symmetric, and there is no net magnetism.

As you lower the temperature, the domains don’t jiggle around as much. Eventually, by random chance, they will be pointing more in one direction than another. This preference gets “locked in” as you continue to cool, and eventually they’re all pointing in the same direction. The system is asymmetric (has a preferred direction), and there is net magnetism.

At high energiese, the system melts into a symmetric state, but at low energies, it freezes into a spontaneously chosen asymmetric state. This is analogous to how, in particle physics, forces can “melt together” and unify in particle physics at high energies, but at the ordinary low energies we experience, they “freeze out” into separate, specific forces with different behaviors.

Uncle AlThe weaker the force the more it displays chiral symmetry breaking, 1957 Yang and Lee through Nambu, Kobayashi, and Masukawa. Gravitation is the weakest force, 10^(-25) of the Weak interaction, and should display the greatest chiral symmetry breaking.

alpha-Quartz in enantiomorphic space groups P3(1)21 (right-handed) and P3(2)21 (left-handed) provides opposite parity (chirality in all driections) atomic mass distributions. Do left and right shoes vacuum free fall identically? A parity Eötvös experiment is the relevant observation. Look for gravitational symmetry breaking.

Model it! Point group

I(notIh ) giant fullerene (charge neutral). Point groupT(notTd orTh) tiny rigid carbon atom skeleton (charge neutral). Stick a left-handed or right-handed probe inside or outside a fullerene of constant handedness. High rotation symmetry but zero mirror symmetry. Minimize system energy with HyperChem. Do left and right shoes give identical non-contact results at equilibrium? Look for gravitational symmetry breaking.http://www.mazepath.com/uncleal/chivac2.png

inside ~3.6 A gap, outside ~3.1 A gap at minimum energy

http://www.mazepath.com/uncleal/980out.png

http://www.mazepath.com/uncleal/980in.png

Porges@Greg

I guess it is a transcription rather than a transliteration; his name is given as Maskawa on his ‘most famous’ paper.

greg@Porges

interesting. could you post a link to his paper? i have read the abstract in japanese, but cannot find an abstract in english.

cheers

daithiI’d seen the wine bottle analogy before but that didn’t make sense to me. I could understand the marble rolling off in a random direction, but then how does this correlate to more matter than anti-matter? It always seemed to me that for each individual particle becoming matter or anti-matter that it would be random and we should end up with a 50-50 mix. I viewed each symmetry break as autonomous.

John Armstrong’s analogy on the other hand made things click for me. If a single symmetry break can influence other results then now I can see how a single symmetry break (a random event that no one chooses) can result in the creation of more matter than anti-matter.

John Armstrongdaithi, if you’re really mentally limbered up, try this:

There’s something like the bottom of a wine bottle at

every point in space. And they’re connected in such a way that if two nearby points break the symmetry in different ways, there’s a huge energy penalty. So once one marble rolls one way at one point, nearby marbles are pulled down in the exact same directions.But why should faraway points know about each other? One marble rolls in one direction here, but another marble rolls in a different direction over there. Expanding “shock waves” of symmetry breaking expand out through space, until every point has broken the symmetry in some way or another. At the interfaces between these “cells” of broken symmetry, there should be some way of noticing the difference, but those cells might be extremely large.

As I understand it, the current theory is that we’re all contained in one of these cells that happens to have broken towards “more matter”. Other cells have broken towards “equal amounts” or “more (of what we call) antimatter”. “Matter”, then, is just whichever side is preferred in our little 15-billion-light-year-wide neighborhood.

SteveMIt always seemed to me that for each individual particle becoming matter or anti-matter that it would be random and we should end up with a 50-50 mix. I viewed each symmetry break as autonomous.

Even with each particle “choosing” to be matter or anti-matter with perfect 0.5 probability, it is actually not all that probable to end up with a perfect 50/50 mixture for a large number of events. You are very likely to have some imbalance. Imagine tossing a perfectly fair coin and for every head add 1 and for every tail subtract 1 and plot the sum as you repeatedly toss the coin, the longer you toss the less likely you are to end up at exactly zero.

Michael OrlitzkyI’d go with n=1 for the number of tosses that’s least likely to sum to zero!

Johan F PrinsSymmetry breaking occurs when the entropy decreases. The Cosmoligists want to tell me that we have had symmetry-breaking while the entropy of our universe increases. Does this make any sense? Please enlighten me!

AntonioEntropy may decrease locally, but if you look at the Universe it increases globally