## Thursday, July 24, 2008

### Spontaneous symmetry breaking & society

Sean Carroll is promoting a new analogy between the concept of spontaneous symmetry breaking in physics and various phenomena in the society.

I think that the analogy sounds silly but it is actually much better than he realizes, as long as you concentrate. We will look at it somewhat carefully and I will argue that the paradigm of spontaneous symmetry breaking shows why most left-wing people and social engineers, including Carroll himself, completely misunderstand what the rule of law in a democratic country means and what it doesn't mean.

Let me say in advance that the basic principle of spontaneous symmetry breaking, namely that
the symmetry is broken at long distances but restored at short distances,
is turned upside down by Carroll. This principle is very important both in physics and in the democratic society. Carroll is like a student who could memorize the term "spontaneous symmetry breaking" but he hasn't learned or understood its basic properties. F.

Physics: unification at short distances

Let me start with physics. Neutrinos and electrons look very different in our everyday world. Electrons are heavy and interact electromagnetically; neutrinos are light and their interactions are negligible.

However, it turns out that when you increase the energy of all particles to hundreds of GeV per particle or higher or - equivalently - if you study experiments to reveal the architecture of matter at distances comparable to 10^{-18} meters or shorter, you will discover something called the electroweak unification.

The properties of (left-handed) electrons and (left-handed) neutrinos will become indistinguishable. All of their interactions with the rest of the world will have the same probabilities, assuming that you replace the other particles in every process by their electroweak partners, too.

In the world of short-distance phenomena, the symmetry holds. But the Higgs boson in the Mexican hat potential makes the symmetry disappear in the long-distance phenomena. That's why photons are massless but W,Z bosons are not. That's why the electrons interact differently than the neutrinos.

Another example is the chiral symmetry breaking. At short distances, the left-handed and right-handed portions of the quarks carry two independent (approximate but almost exact) color symmetries. But at distances longer than the proton radius (QCD scale), the left-handed and right-handed components must combine into a Dirac spinor and only the "overall" SU(3) symmetry rotating them simultaneously survives.

There may exist many similar symmetries that are broken at long distances but they haven't been empirically established so far. Supersymmetry might be restored at distances shorter than something like 10^{-19} meters or less while a grand unified symmetry, extending the democracy between electrons and neutrinos to the quarks (and generalizing the SU(3) symmetry between colors of quarks from the previous paragraph that is never broken in our world), might take over at distances shorter than 10^{-32} meters.

But there also exist simpler examples outside high-energy physics. For example, materials can be found in different states of matter. H₂O can be a gas (vapor), liquid (water), or solid (ice). At very short distances, you may find out that all these seemingly different materials are made out of the same H₂O molecules: that's why you can easily change ice into water or vapor and vice versa.

When you focus on the state of matter that corresponds to low temperatures - which are also related to low energies and long distances - it is nothing else than the ice. Ice is a crystalline solid. Liquids or gases are invariant under rotations: for example, a symmetric glass of water doesn't change if you rotate it by a nonzero angle.

However, this rotational symmetry is broken by crystalline solids such as ice that pick preferred directions in space. This symmetry breaking only occurs at long distances - when you can actually see sufficiently many molecules to figure out that they like to organize themselves into a crystalline structure. But you couldn't determine that the symmetry is going to be broken by looking at a few molecules in your microscope only.

Society: equal rights of individuals

What does Sean Carroll mean by the symmetry breaking in the society? Well, he proposes that the blacks should have human rights that other groups don't have. For example, the blacks should be allowed to say "nig*er" while the whites shouldn't. But he would clearly like to extend his "symmetry breaking" to many other situations in our lives, too. One of his other proposals is that quality control shouldn't quite apply to women in science. He justifies this unusually unequal treatment of the individuals by his desire to equally treat the groups overall.

The examples from physics that we mentioned above should make it instantly obvious that this is exactly how symmetry breaking in physics doesn't work. Carroll's policies are also profoundly incompatible with the very basic rule of law in a democratic society.

In a democratic society, it is the individuals who are guaranteed equal rights and equal opportunities, if you wish. This rule is directly analogous to the restoration of symmetries at very short distances. The national and even international laws treat them - or should treat them - equally. But what these individuals do with these rights depends on where they live, whom they interact with, what they are able to do, what they like to do, and what they decide to be. The outcomes will inevitably be different.

In the example involving the states of matter, every H₂O molecule had the same "rights": it had to follow the same local laws of physics. Nevertheless, the macroscopic conglomerates of these molecules sometimes looked like a liquid and sometimes they became a crystalline solid. That's quite normal. That's how the symmetry breaking always works in physics.

Analogously, every democratic country guarantees the same rights to all individuals but they may lead to very different outcomes for different groups. It is quite normal - and, in fact, essential for a working society - that different groups end up using their rights and lives differently, depending on their traditions, abilities, and other innate properties.

Sean Carroll's idea about symmetry breaking is very different. He postulates that all the matter in the world should look like a uniform material of a constant density in a particular state of matter - I guess it is some kind of a liquid, but surely not a drinkable one. But because it doesn't seem that this is what the molecules always wanted to do, he requires that the mass, size, and interactions of every molecule must be changed in such a way that his dream about the universal water - a material containing hydrogen atoms, nitrogen, argon, iron, gold, and strangelets living in peace with each other - is respected at long distances.

So the big government has to be given the tools to control the life of every individual atom and change his or her mass, size, and interactions with his or her family and neighbors as required for the society to look like Sean's universal water at long distances.

Sorry, Sean (and social engineers of all countries), but it is both non-democratic as well as impossible to create this universal water out of gold and nitrogen. Both at the level of the materials and the societies, this is not how the world works and any kind of a society that tries to do something crazy of this sort is guaranteed to end up as a totalitarian system that is fortunately going to collapse soon or later.

It's time for the far-left people to notice that there is something absolutely fundamental and critical about the society in particular - and the world in general - that they misunderstand or deliberately pretend to misunderstand.

And that's the memo.