Talk:Symmetry breaking

Contradiction

The first paragraph discusses symmetry breaking as a small change to a disordered system which brings about a fixed state, then later says disordered states are more symmetric because small changes don't vary them much. — Preceding unsigned comment added by 117.120.18.134 (talk) 00:23, 30 December 2011 (UTC)[reply]

I believe this part has since been removed, but I believe the original authors were referring to the fact that a small change in the system does not effect the Hamiltonian, it is invariant to these symmetries. However, when there are many possible, equally likely, states for the atoms to be in, an infinitesimally small perturbation to the system can transform it to just one of the many possible states. This is like in the bifurcation illustration shown in the article. The particle at the top of the hill is equally likely to fall down either side, so an outside perturbation must force it to go one way or the other. Footlessmouse (talk) 05:18, 8 August 2020 (UTC)[reply]

Symmetry breaking vs. Wavefunction collapse

Any similarity? I found reading these 2 subjects separately confusing. — Preceding unsigned comment added by Mastertek (talk • contribs) 08:40, 20 October 2011 (UTC)[reply]

NO! Sorry I'm late to answer, but might as well leave an answer in case someone sees this in the future. Explicit symmetry breaking is nothing fancy, it occurs because a term in the Hamiltonian or Lagrangian of the system explicitly break a symmetry, and therefore the equations of motion will break that symmetry. This can be anything, and so is only useful to discuss when the symmetry that is missing is important in some respect. The vast majority of the time when discussing symmetry breaking, it is spontaneous symmetry breaking. Spontaneous symmetry breaking occurs when the system is represented by a Hamiltonian or Lagrangian that observes some symmetry, yet the system itself does not. The symmetry is broken by infinitesimal perturbations to the system leading to finite results, due to the fact that there are many possible states that produce the same equations of motion. In condensed matter, for instance, a crystal can be thought of as a state of spontaneously broken symmetry. That is, the Hamiltonian of the crystal system will be invariant under translations, rotations, and point inversions, to name a few. This ultimately means that there are many different arrangements of the atoms that would lead to the exact same Hamiltonian. As all these states are equally likely, there is no good reason for the system to choose any of the states, yet it does.

Wave-function collapse is just the name of the phenomenon attached to the measurement problem. A quantum state may be of the form C = (A +/- B) / sqrt(2) (using the matrix mechanics equivalence of the wave-function). Where we know the system is in state C because of previous interactions, but C is a superposition of states A and B. We don't know which of the states it is in until we try to measure in the basis of A and B. At which time, the wave-function of the state "collapses" from being a combination of the states A and B, to a single state A or B. This is gross simplification, but I hope it resolves any confusion with symmetry breaking. To understand what I mean by these states, chech out the Stern-Gerlach experiment.Footlessmouse (talk) 05:12, 8 August 2020 (UTC)[reply]

Symmetry breaking in computer science

This article seems to discuss symmetry breaking from the perspective of physics. I wonder where we could discuss computer science aspects of the concept? Among others, symmetry breaking is one of the central hurdles in the design of distributed algorithms; see, e.g., leader election, deadlock, Cole–Vishkin algorithm; see also [1]. Should we expand this page to cover computer science aspects? Or create something like Symmetry breaking (computer science) and add a hatnote here? — Miym (talk) 23:58, 28 November 2009 (UTC)[reply]

Better make another page for the computer science concept. Cogiati (talk) 04:55, 22 August 2011 (UTC)[reply]

Earnshaw's Theorem

Is Earnshaw's Theorem, which says that you can't passively balance a magnet in mid-air between two other magnets, related to the concept of symmetry breaking? — Preceding unsigned comment added by 99.118.9.181 (talk) 18:23, 6 August 2012 (UTC)[reply]

Symmetry Restoration?

Is there any notion of symmetry restoration, that is, moving from an ordered state to a less ordered state that results in additional symmetry? — Preceding unsigned comment added by 70.247.168.8 (talk) 17:36, 9 August 2016 (UTC)[reply]

There is such a notion of emergent symmetries, but they are not so helpful. There is not even a wikipedia page for them. To understand why, you have to realize that everything in physics is based on mathematical models of the world. We use the mathematical models to make predictions that drive experiments that improve the models. Emergent symmetries are emergent, by definition, because they are not present in the mathematical description of the system, and therefore only exist as "coincidences" usually due to fine-tuning of model parameters. If the symmetries are not present or predicted by the models, they may not be generalization and may only be due, for instance, to the limited range of input the models are subjected to. Thus it seems unlikely that we could use emergent symmetries for anything substantial. Their use would seem to be limited to computational shortcuts in fields where the limitations of the symmetry are well documented.Footlessmouse (talk) 05:11, 8 August 2020 (UTC)[reply]

Level of discourse

I'm not a scientist but I am a science writer. This article throws a lot of jargon at me without explaining any of it. A science article should first define what a concept is in language any educated person can understand and then proceed to nuances like which paper developed the concept, what the different variations of the concept are. There's so much terminology here in such rapid succession that I can't make heads or tails of it. Please don't throw reductionism in the mix and the various types of symmetry breaking (which seem not relevant to an initial definition) in the top section! Honestly, most science articles on Wikipedia feel like a jargon-fest and I suspect few were written by people who actually understand the concepts they are explaining, but this one has no plain English to buffer the effect. If there are any subject editors out there who actually see the potential for Wikipedia to bolster our collective science literacy, hear my plea and bring in people to write who can explain and not just string jargon together! — Preceding unsigned comment added by 2601:643:8000:A550:A8E0:E9F:46C4:E63 (talk) 02:13, 17 March 2022 (UTC)[reply]

Hello,

I have tried to fix this issue recently (it's still very far from perfect - the ESB & Example sections remain untouched.) Do you mind looking over again? I did quite a few revisions, but I fear that if I do many more I'll just be re-stirring the same information in my head without any outside perspective. I need to sit on this article for a moment, and I think your background as a science writer may help with some of the flow that I have been struggling with.

If you do help out, thanks in advance :-) Tea-caff (talk) 07:31, 1 March 2023 (UTC)[reply]