# Symmetry and symmetry breaking

#### vikram_n

I am quite new to the branch of quantum physics and therefore am quite inexperienced with certain terminology and definitions. I have looked these topics up time and time again, but still cannot get a grasp on what they mean. Could someone please describe to me what the concept of "symmetry" in as simple as possible of a definition and also describe :symmetry breaking" also in a simple way. Just try to put it in words a novice would understand. Real examples would also be much appreciated. Thanks!

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#### tom.stoer

Let's taslk about rotational invariance and symmetry.

A sphere has rotational symmetry; you can rotate it as you like; it will always look the same. The same applies e.g. to the Newtonian potential of gravity; it ist V(r) ~ 1/r, therefore there is no dependence on the direction of the radius vector. It is direction independent. Now look at specific solution, a Kepler orbit i.e. ellipse: it has no rotational symmetry (!) b/c it lies in a specific plane defined be its normal vector and it has a second defining direction, namely the direction of its semi-major axis. But the symmetry is still there b/c when you rotate a specific Kepler orbit you get a different orbit, but this new orbit is again an allowed solution. The the symmetry is lost for each individual solution but is still exists 'on the set of all possible solutions'.

#### bhobba

Mentor
Tom is correct.

At rock bottom many things in QM, and indeed physics in general (eg Noethers Theroem) is based on symmetry. In fact guys like me tend to take it to a bit of extreme and think there is some startling symmetry waiting to be discovered that lies at the foundation of all physics, but that is another story. Basically when symmetry is involved any particular solution or specific value doesn't have a symmetry - its the laws governing such things that have it. Take the Principle Of Relativity for example. It really isn't a law as such - its a meta law ie a law about laws. Its the laws that have the symmetry ie are the same in any inertial reference frame - not the exact value of the stuff it describes like momentum or energy.

Thanks
Bill

#### M Quack

Breaking of symmetry is also often associated with phase transitions.

Gases or liquids, for example, are isotropic. They look exactly the same in all directions, so they have complete rotational symmetry, just like the perfect sphere.

When you freeze a liquid and form crystals, this is no longer the case. All crystals have a set of special directions. Complete rotational symmetry no longer exists, it is "broken".

#### Naty1

here is an understandable discussion relating symmetry and phase changes to the big bang:

This passage describes the change from a possible Planck scale like initial condition (very forthy, highly energetic environment where nothing appears as an individual entity..and space,time,energy,mass, all the forces are 'unified'...appear as one) environment to the one we see today where all those entities I named now appear an individual and distinct.
The 'opposite' seems to happen at the singularity of a black hole....once again mass, time energy and everything else we recognize disappears into a froth.

http://en.wikipedia.org/wiki/Big_Bang

...The earliest phases of the Big Bang are subject to much speculation. In the most common models the Universe was filled homogeneously and isotropically with an incredibly high energy density and huge temperatures and pressures and was very rapidly expanding and cooling. Approximately 10−37 seconds into the expansion, a phase transition caused a cosmic inflation, during which the Universe grew exponentially.[16] .....
The Universe continued to grow in size and fall in temperature, hence the typical energy of each particle was decreasing. Symmetry breaking phase transitions put the fundamental forces of physics and the parameters of elementary particles into their present form.[19] After about 10−11 seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle physics experiments.
Symmetry in all its forms, also called supersymmetry, is a theory not yet experimentally verified. Supersymmetry predicts a number of not yet observed particles, like the 'selectron' the superpartner of the electron.

"Symmetry and symmetry breaking"

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