what can snowflakes teach us about the UNIVERSE?

[krstlmthd]

okay before i say anything else first let me apologize. my last posts were not well received because i do not know the language of science. so i am going to try VERY HARD here to keep my enquirey scientific in nature. i do not know science but have read about science ideas so please bare with me

 

the idea i want to know about is SYMMETRY. as i understand SYMMETRY is a burning hot topic in science right now. physicsts think the entire universe can be described through symmetry.

 

i think this too. physics is very important to symmetry.

 

now i read about SPONTANEOUSLY BROKEN symmetry. if i understand it right, this is why there are no two snowflakes that are exactly the same. they always CRYSTALIZE differently. what you end up with is a unique shape which is still perfectly symmetrical.

 

so what i guess i'm really asking is about what happened after the big bang. can it be described like a snowflake. did the universe crystalize out of the big bang through spontaneously broken symmetry, just like a snowflake?

 

thank you for taking the time to read this. and please don't laugh at me, i'm just trying to learn

[Cap'n Refsmmat]

The universe became the way it is because the atoms move randomly, and so it was not perfectly symetrical. Expansion made those anomolies larger.

[Norman Albers]

You are asking excellent questions. I am on the far end of this spectrum with detailed electromagnetic model of an electron (http://laps.noaa.gov/albers/physics/na). I am describing a frozen state of light as literal as ice, but in this case, each one seems to be simply identical. Same problem, though. Phase change. Then again, there is no far and near. Physics of the nature of electrons and hadrons (nuclear stuff) all is critical where I am trying to get discussion over on 'plasma recombination'.

[Severian]

now i read about SPONTANEOUSLY BROKEN symmetry. if i understand it right' date=' this is why there are no two snowflakes that are exactly the same. they always CRYSTALIZE differently. what you end up with is a unique shape which is still perfectly symmetrical.

[/quote']

 

That is an example of symmetry breaking but not in the way you mean.

 

The the laws of physics are rotationally invariant, so if we neglect gravity for the snowflake (it is in freefall), it has not way of telling which way is up and which way is down.

 

Now, lets for the sake of argument say a snowflake forms in the shape of a star. If the laws of physics are rotaionally invariant, how does the snowflake choose the direction that the points of the star are pointing? Should one of the points be pointing straight up? No, because the snowflake doesn't know which way up is!

 

The answer is that they form randomly. Even though the laws are rotationally invariant, the snowflake is not (rotate the snowflake by a small angle and it looks different).

 

There is still a residual symmetry in the snowflake - I can rotate the star by the angle between the points and it will look the same. The shows another interesting principle - the rotation symmetry we started with has been broken down into a smaller symmetry group.

[Norman Albers]

The universe became the way it is because the atoms move randomly, and so it was not perfectly symetrical. Expansion made those anomolies larger.

Didn't there have to be variations before there were atoms? I have been trying to get at processes coming down through energy levels of temperature where protons and neutrons are first stable, then again around 1MEV where electrons can stabilize. Can we look at these things as phase changes? Each electron sucks up half an MEV as "heat of fusion", no longer available in kinetics.

[Igor Suman]

[Norman Albers]

HOLY GOD, m = 13!!! You must give me some time. I was going to start on m=3.

[the tree]

what can snowflakes teach us about the UNIVERSE?

That uppercase is only apropriate for the first letter of a word at most?

[Norman Albers]

I have just found a statement near the end on VOL.I, Feynman lectures, about symmetries where I have been working: "The conservation law which is connected to the quantum mechanical phase seems to be that of conservation of electric charge". This is exciting to me, because, electrodynamically, I found the only possible model of the type I have done involves zero azimuthal variation: cylindrical symmetry of current and spherical symmetry of charge. I got there by investigating the realm of zero frequency, omega=0. If you do this in the current equation, you produce a term which looks like you declared <m=1>, but in fact you have not!

[Severian]

Electromagnetism is based on a U(1) symmetry. So the wavefunction can be shifted by an arbitrary phase

[math]\psi \to e^{i\theta}\psi[/math]

leaving the physics unchanged. What Feynman is refering to, is that this is exactly the symmetry we see when converting wavefunctions into probability distributions,ie.

[math]P = |\psi^* \psi| \to |\psi^* e^{-i\theta} e^{i\theta} \psi | = |\psi^* \psi |[/math]

[Norman Albers]

How does this relate to conservation of charge? Conservation of the probability: is this how you say "the same physics of experiencing" whatever? I was appreciating the fact that the electron field must be featureless with the agreed symmetries. I have not yet connnected my electromagnetic visions with the Schroedinger eq., but I am working on this. They are clearly not the same statements but somehow they spring from the same Hamiltonian roots. I firmly believe there is more to be learned here. . . . . Specifically, in a spherical system the quantum phase in a superconducting loop must change by integrals of 2pi so the wave function 'catches its tail'. I realize that the 'theta' is usually a generalized function of position but once you declare geometric symmetry it becomes more specific. I do not intend to confuse the two ways of doing mechanics. QM assumes states of mass, charge, angular momentum, etc., and characterizes interaction probabilities. Inhomogeneous electrodynamics allows vacuum polarization to flesh out some details of local field densities.

[Severian]

How does this relate to conservation of charge?

 

It is the requirement that the symmetry should be local (i.e. that [math]\theta[/math] can depend on position) which gives charge conservation.