Does Spontaneous Symmetry Breaking Contradict Symmetry?

[askalot]

Hello, I was thinking about, how symmetry can be realized, when there is SSB occurring! Dont these terms contradict?

 

[ohad]

They do not contradict.
the system has symmetry, but the ground state breaks it. you can check the following example:
ferromagnetic Iron, you heat it up and there is no magnetic field. Than you start to cool it down, the system has rorational symmetry so the magnetic pole can be in any direction, however due to infitesimal fields the field of the Iron settles somewhere. This is example of SSB when you have symmetry.

 

[askalot]

Sorry but why is "Symmetry" needed when we only have SB in nature?
As you said, there are always variations that produce SSB: the "infitesimal fields" as you mentioned!
Symmetry, sounds like an "Unreachable Ideal", when there is only SB. You could argue that the entire Theoretical Physics, is an ideal too, but there is no "Theoretical Physics Breaking" (TPB). We are assuming that there is always going to be a hope for Theoretical Physics to explain everything.

 

[Vanadium 50]

What is your level of physics understanding? By making this an A thread you are saying that it's at the level of a graduate student, but what you wrote clearly indicates that's not the case.

 

[askalot]

I will only keep the following text:

Sorry but why is "Symmetry" needed when we only have SB in nature?
As you said, there are always some kind of variations, that produce SSB: the "infitesimal fields" in your example.
Symmetry, sounds like an "Unreachable Ideal", when there is only SB.

 

[mfb]

Sorry but why is "Symmetry" needed when we only have SB in nature?

It is not "needed", it is observed. The laws of physics don't prefer a given value (e.g. for the direction of magnetic field in a magnet), but magnets will still have such a direction.

Laws of physics which would prefer a given direction for the magnetic field would have to look completely different.

 

[askalot]

..but magnets will still have such a direction.

Laws of physics which would prefer a given direction for the magnetic field would have to look completely different.

mfb: Do you imply that laws of physics are defined in such a way that they don't reflect, the observed, reality?

 

[mfb]

mfb: Do you imply that laws of physics are defined in such a way that they don't reflect, the observed, reality?

No, and I don't see how you got that impression.

 

[askalot]

First of all I want to apologize for labeling this thread with an "A". I didn't know what it was actually meant by labeling.

however due to infinitesimal fields the field of the Iron settles somewhere

ohad, you mentioned "infinitesimal fields". But what are the laws governing these fields? Shouldn't we consider Symmetry valid globally (still ruling the set of the infinitesimal fields)?

 

[my2cts]

Askalot, you should read something about group theory and representations of symmetry groups.
The totally symmetric representation is not the only possibility that is consistent with a certain symmetry.

 

[lychette]

What is your level of physics understanding? By making this an A thread you are saying that it's at the level of a graduate student, but what you wrote clearly indicates that's not the case.

What is it about the question that makes you think that this 'clearly' not the level of a grad student Vanadium.

 

[Vanadium 50]

The messages that the OP posted - and now that he understands what the A is, it's evident I was right.

 

[lychette]

The messages that the OP posted - and now that he understands what the A is, it's evident I was right.

I see from post 9 that you are, indeed, correct. Thankyou

 

[askalot]

Askalot, you should read something about group theory and representations of symmetry groups.
The totally symmetric representation is not the only possibility that is consistent with a certain symmetry.

I understand, now, that SSB is allowed and does not conflict "Total" symmetry, however I would like to ask, how and why SSB is justified. Which are the physical laws that determine and explain this phenomenon? Where should I look for these answers?

Thank you for your time,
Askalot.

 

[mfb]

What do you mean by "justified"? There are observations that fit to models with SSB, and some of them do not have any other plausible explanation. In macroscopic systems we can observe SSB directly.

 

[Stephen Tashi]

It would help to interpret "symmetry" and "spontaneous symmetry breaking" as specific statements. A single phrase (like "global warming" or "corporate greed") can stimulate many different emotional responses.

The most general interpretation of the question that I can make is that there are physical theories that assert that mutually exclusive alternatives exist that are "possible" (not necessarily "equally probable"). In physical reality, we apparently see only one of the alternatives existing at a time. So are such physical theories an incomplete description of reality ? ( Of course, I'm making a thinly veiled analogy to the arguments about whether QM is a complete description of reality.)

If we have a physical theory which deals with probabilities, I don't see that SSB (meaning the realization of one alternative out of many equally possible alternatives) is any more of a conceptual problem that the concept of probability itself. There's no greater mystery in a fair coin actually landing "heads" in a particular case than an unfair coin actually landing "heads" in a particular case.

If we have a physical theory that does not admit the notion of probability then how can SSB be formulated? Postulating that there "infinitesimal deterministic effects" let's us claim that the theory is complete, but it forces us to admit that we have an incomplete description of the situation we're applying it to.