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The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons.

Where has all the angular momentum come from? Why is it so natural?

I was also thinking do photons spin? we always think of the wave as a standard 2d sin wave but could this rotate in 3d? What implications would this have?

And what about spacetime how does all the spinning effect?

This has always been avoided in all lectures and classes I ever went to.

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Re: waves, see en.wikipedia.org/wiki/Circular_polarization –  Willie Wong Jul 11 '11 at 0:07
    
    
Your question is not entirely "true"! Elliptic galaxies do not spin. Same is for the central bulge of spirals galaxies afaik. –  Georg Jul 11 '11 at 12:50
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4 Answers

In elementary particles all particles that have spin different than 0, spin, i.e. have angular momentum, so photons are spinning too, they have spin 1. There exist particles and systems with spin 0 (pions as an example), those do not spin :) .

Since physics started from macroscopic studies one has to look at the equations that describe motion classically, very successfully. These equations, obey "Noether's theorem" that shows there are conserved quantities in the dynamics of motion coming from the symmetries of the system. Energy, momentum and angular momentum are conserved.

This means that once a path or a system rotation is established by some interaction, for example by a grazing impact of two asteroids, if there are no further interactions the asteroids will keep on spinning because the angular momentum they gave each other will be conserved individually.

So the answer to your question

Where has all the angular momentum come from? Why is it so natural?

is : from conservation laws. It is natural because equations of motion and conservation laws are a description of the mechanics of nature, and that is the way nature works.

Now space time and angular momentum are another story in General Relativity, where, because a rotating object has acceleration in the radial direction it distorts space time around it. For a simplified view see this experiment.

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Sticking strictly to classical mechanics, things in space are all moving, in different directions. They are not standing still. You could ask why are they not standing still, but I guess that's cosmology.

Suppose two cars pass in opposite directions on a road. When they pass, there is a certain distance between them. So if you draw a dotted line around the pair of them, that pair has angular momentum, which is just momentum at a distance. They don't have to be spinning around a center to have angular momentum. They only have to be traveling past each other.

If one of the cars threw out a magnet on a rope and captured the other, now they would start spinning like a bolas. That's what happens when things moving past each other are pulled together. Whether or not they're pulled together, they still have angular momentum. It's just another way of saying they're moving past each other.

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I think that the simplest way to answer this question is to state the apposite. when you put, launch or deliver something in space it is nearly impossible for it not to spin. To have no angular momentum in 0g is nearly impossible. Besides vacuum random spin is the most difficult problem in space.

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Spin in space is a problem because there is a lack of things to impact. i.e. on the Earth you will only spin so long before air resistance or the ground dissipates it. This is not a direct consequence of zero-gravity. This is implied by your answer, but perhaps not intentionally. Can you clarify it please? –  qubyte Nov 25 '11 at 17:34
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The origin of spin can be traced in two fundamental physical postulates:

  1. Einstein's (general) relativity postulate
  2. Wigner's principle stating that elementary particles carry irreducible unitary representations of the symmetries of nature

According to the first principle, every local reference frame of space-time is Minkowskian and the laws of physics are the same in all local reference frames. Now, the automorphism group of a Minkowski space is the Poincare group, therefore the laws of physics are convariant under the Poincare group.

The second principle allows us to actually identify between elementary particles and irreducible representations of the symmetry groups of nature. Applying this principle to the Poincare group, we obtain that elementary particles carry irreducible unitary representations of the Poincare group, and by consequence irreducible unitary representations of its subroups, in particular, the rotation group. Now, since elementary representations of the rotation group are classified by the spin, then elementary particles carry spin.

There is a subtlety in this description, in that the representations of the rotation group correspond only to integer spin and as we know half integer spin exists in nature also. This issue was also addressed by Wigner, who generalized the correspondence between elementary particles and representations to projective representations as well (see for example Wigner's collected works). The projective representations of the rotation group correspond to half integer as well as integer spin.

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