I think symmetries are in nature because a symmetry requires less information than nonsymmetry

Dear Kharpko,

Thank you very much.

If lowering information is a principle that nature follows as your reply seems to suggest then, whence comes non-symmetry and why?

Regards,

Rajat

non-symmetry comes from an imperfection of nature. Symmetry is broken spontaneously

Dear Khrapko,

Please visit the thread that was started by me on the issue of SSB a few months back. Spontaneity must have some deeper underlying reason which we are yet to uncover.

Regards,

Rajat

It should be realized that laws governing behaviour of matter have more symmetries than observed in the various states of matter. The structures we see around us are all consequences of cascades of spontaneous symmetry breakings. Spontaneous symmetry breaking brings about rigidity (generalized rigidity) which accounts for stable vacua. If we restrict ourselves to low-energy physics and view matter as a collection of atoms, each consisting of a nucleus and some electrons, then we encounter matter in three main classes of solids, liquids and gases, which can be understood by the principle that any collection of atoms chooses a configuration that minimises its free energy. By manipulating temperature, pressure and volume (i.e. the external thermodynamic variables), we can turn gasses into liquids and to solids, or, in the reverse order, from solids into liquids and gases. The existence of these phases (and within each, in particular in the condensed phase, a multitude of other phases), all can be understood in terms of the minimization of free energy.

Dear Farid,

It seems that symmetries( like records and laws and relationships !) are meant to be broken, whether spontaneously or otherwise. When we fail to assign a deeper reason we take shelter under the cover of spontaneity and terms like that. Right?

Regards,

Rajat

Dear Rajat, symmetry breaking is a serious matter and by no means a convenient scape route. You can clearly see that at work in the transition between a liquid and a regular solid; the regular solid has clearly a lower symmetry than a liquid (the former is characterized by a discrete translation group, and the latter by a continuous one; the former is characterized by a discrete rotation group, or point group, and the latter by a continuous one --- if the solid phase is not a regular one, one considers a variety of correlation functions, and the behaviours of these are markedly different from the behaviours of the same functions in the liquid phase). It is important to realize that in effecting a phase transition from the liquid to a solid phase (varying the external thermodynamic parameters, T, V and P, available to us), we do not change the constituent atoms of our system, neither do we change the type of potential that governs the interaction between the constituent atoms (at a deeper level, we do not change the Coulomb potential with which charged particles, electrons and protons, interact). What we do, is creating the conditions by which the free energy of the assembly of atoms is minimized by acquiring a lower symmetry (or higher symmetry when we deal with the solid-liquid, instead of the liquid-solid, transition). We have also gauge symmetry that can break, like the continuous U(1) gauge symmetry whose spontaneous breaking characterizes the transition from the normal state of an assembly of electrons to the superconducting state (Meisner effect is a direct manifestation of this symmetry breaking). We have also topological phase transitions to deal with (as in the Kosterlitz-Thouless phase transition).

I should very warmly recommend the very inspiring book 'Basic Notions of Condensed Matter Physics', by P.W. Anderson (Benjamin-Cummings, London, 1984). For now, going very briefly through the following article provides a glimpse of the manifold of the symmetry-breaking events that took place subsequent to the moment of the Big Bang:

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

Dear Farid,

Thank you very much for your very lucid explanation and references. All this is standard stuff. The question that bothers me is whether there is a deeeeper principle at work which first of all generates symmetries and then breaks them !

Regards,

Rajat

Dear Rajat, you are welcome. I am not aware of any other principles at work. There are of course some who discuss certain issues in terms of things taking place on the Planck scale (I heard one such thing some 20 years ago from Roger Penrose), but I am professionally not competent enough to opine on them. Perhaps you wish to read the following article by P.W. Anderson (More Is Different, Science, Vol. 177, pp. 393-396), which is one my all-time favourites:

http://www.ph.utexas.edu/~wktse/Welcome_files/More_Is_Different_Phil_Anderson.pdf

Thank you very much Farid for the reference.

Regards,

Rajat

You are welcome Rajat.

Dear Farid and others

I think, at a much deeper level symmetries are related to two definite aspects of the human mind.

(1) The analytical mind finds the TRUTH of conservation laws in symmetries.

(2) The aesthetic mind finds the BEAUTY of creation/nature through symmetries.

Regards,

Rajat

Dear Rajat, there are two aspects to symmetry, one mathematical and the other psychological. Many have expanded on these and the relationship between the two, notably Heramnn Weyl in his highly-recommendable 1952 book Symmetry (Princeton University Press). I strongly believe that the two must not be intermixed. Of course, sciences, in particular mathematics, being creations of human mind, there must be certain reasons why human mind has been attracted to study symmetry in nature and systematize the notion of symmetry in the mathematical framework of groups (in doing so, going to such extent as to study the so-called Monster Group, a finite group that has of the order of 10^54 elements). However, whatever the psychological connection between aspects of symmetry and the symmetry as described by (or inherent to) mathematical formulations of the laws of physics, this connection is in a sense irrelevant. Physical theories are accepted or rejected by the very strict criterion that their predictions be verifiable by observations, whether we like the observations (that is, whether these observations appeal to our aesthetic sense) or not.

In addition to the above-mentioned book by Hermann Weyl, you may wish to study the following paper by Professor Chris McManus of University College London:

Symmetry and asymmetry in aesthetics and the arts

http://www.acadeuro.org/fileadmin/user_upload/publications/ER_Symmetry_supplement/McManus.pdf

Thank you very much Farid for the references.

The irrelevancy of the human mind to the issues of recognition, classification and study of symmetry in Physics and mathematics that you point out is okay from a very limited scientific standpoint that is currently accepted. But a true unification should also take that into account. How long will we continue to confine ourselves to study of objectivity only, leaving aside the vast arena of subjectivity that in fact is unavoidably present at the very basis of science as well as the scientist, be (S)he a theorist or an experimenter.

And coming to aesthetics in science, please do not forget Dirac, Feynman and Einstein and also Chandrasekhar and many others who recognized the beauty in equations in particular, and in physics in general.

Regards,

Rajat

As for the references, you are welcome Rajat. I think you have misunderstood my previous comment (please re-read it). I did not make any value judgement about issues, and certainly did not deny the importance of everything else at the expense of scientific objectivity, whatever that may be. I just mentioned that ultimately the judgement about the validity of a scientific theory (that is the theory that is relied upon within the scientific discipline) is not made on the basis of our aesthetic notions, but on the basis of impartial and reproducible observations. Without any doubt, being humans we are guided by many things at our disposal that make us human beings. Doing science involves a great deal of routine work, but with routine work alone one does not get very far; from time to time intuition, and many other objective issues, will have to help us in climbing very steep intellectual slopes, or we will get stuck in going round and round without really arriving at any new heights -- i.e. achieving things that are both new and profound.

Oh, Thank you very much Farid. I didn't misunderstand your thoroughly scientific stance on the matter.

Best Ragards,

Rajat

You are welcome Rajat, and my thanks to you.

Rajat,

there are no symmetries (ideal) in nature (observations). All observed symmetries are approximate. Are they (symmetries) at all and where are they is another question. See Derek Abbot.

Regards,

Eugene.

Dear Eugene,

This is  a very good point that you have raised. The real symmetries in nature are truly approximate. We idealize them for purposes of convenience in dealing with a problem.

Thanks and regards,

Rajat