Symmetry and Unification


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Symmetry and Unification

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Editado: Mar 7, 2010, 12:26 pm

Symmetry is the vehicle towards understanding the unification of forces. High energies are needed to see the underlying symmetry that is hidden when energy levels are low enough that particle mass significantly impacts exchange.

My question is why symmetry is thought to be the underlying hidden state, when it requires such high energy levels.

Symmetry is seen as being spontaneously broken when energy levels drop.

It seems to me the reverse, that adding energy would impose a symmetry that otherwise does not exist.

Maybe this is just semantics, the same path different directions.

Does symmetry underlie particle interactions and has been broken by energy level drops? Or does a lack of symmetry underlie particle interactions and high energy imposes an otherwise non existent symmetry?

Which is more ordered - symmetry or non symmetry? It seems to me that if direction matters, then order is increased when symmetry is decreased?

These may be dumb layman questions, if so I apologize - I'm a dumb layman.

Mar 7, 2010, 10:05 pm

There is an issue of semantics: the "gauge" symmetry that describes the electroweak interaction is not actually "broken", even though this terminology is almost universally used. Similarly for any other proposed spontaneously broken gauge symmetry. It would be more accurate to say that these symmetries are "hidden", "not manifest", or "non-linearly realized" instead of "broken": they are always present. This is my attempt to explain this to liberal arts college physics majors.

As for order, you are correct to note that order can increase when symmetry decreases. A ferromagnet is a simple physical example: in the symmetric phase, there is no distinction between directions, and any spin in the ferromagnet can point in any direction. This (non-gauge) symmetry is (really) broken when an external magnetic field is applied and all the spins line up, very orderly.

Chris Quigg (one of the few researchers I know who makes an effort to talk about "symmetry hiding" as opposed to "symmetry breaking") tells me that this point of view (relating symmetry to disorder) is more common in Asia than in Europe or the Americas (where "symmetry" tends to be associated with regularity and patterns).

Mar 7, 2010, 10:25 pm


Thanks so much for the response, and - wow - thanks so much for the power point. I will study it this week.

I think my question is less about whether symmetry is broken or hidden, an more if symmetry can be considered as the underlying state. With as much as 10E14 GeV needed to impose symmetry I would think that viewing symmetry as underlying the visible non symmetry would be backwards. Almost as if infinite energy levels are the base state of matter.

The Western view of symmetry as a pattern is also my tendency - from the Greek perhaps? It was only realizing that symmetry means there is no significance to direction that a lack of symmetry seemed to mean order.

And I am still fighting gravity as a force. If a gravitron has spin 2, then can it be unified with spin 1 bosons?

After looking into symmetry some, it is obvious that I need some work in group theory.

Anyway, no need to respond. I am excited to look over the power point.

Thanks again.

Editado: Abr 8, 2010, 6:16 pm

The important point is that you don't need high energies to "impose" the symmetry; the symmetry is always present. You may need high energies to test some of the predictions of theories based on such symmetries, but that's a separate issue.

As an aside, it might be best to avoid Wikipedia on this question. Last I checked (actually when preparing those slides I linked to above), there was a lot of confusion.

When you start talking about "unifying" particles with different intrinsic spins, you have entered the land of supersymmetry, where I'm not an expert. I initially wrote something completely wrong here, which I have edited this post to remove; it does not seem to be possible to get spin-2 gravitons and spin-1 gauge bosons in the same supersymmetric multiplet (what I would consider "unifying" them to mean).

PS. It's actually LaTeX, not power point.

Mar 8, 2010, 3:42 pm

Again thanks.

But do not worry about me and Wikipedia. The write ups for math and science in wikipedia is generally tough reading at least for me. Past the first paragraph I am generally lost.

Pointing to supersymmetry helps.

BTW, I saw a book today titled Quantum Gravity. Did not purchase it, but I will probably take a look at it sometime later.

And thanks for taking time to find tune my thinking about imposing symmetry. Your leading sentence in #4 helps me frame things a little better.