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.
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.
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, the solutions fit data perfectly. 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.
Edit after comment:
The original energy that set the universe in motion, created the particles and induced rotations is described currently by the Big Bang model, at the origin of our universe billions of years ago, starting with quantum mechanical fluctuations.
The origin of spin can be traced in two fundamental physical postulates:
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 Poincaré group, therefore the laws of physics are covariant under the Poincaré 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 Poincaré group, we obtain that elementary particles carry irreducible unitary representations of the Poincaré 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.
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.
Why planets, stars and other extended masses have rotation.
Firstly, a few points:
To move any body, you have to give it a momentum.
The momentum need not be oriented in any particular direction and need not be transferred at any particular point.
Let us take a rod that is situated in free space as our body. This rod may be bombarded with all sorts of objects that transfer momentum to it. If momentum is transferred to the body at any point other than the com, rotation takes place. If we want pure translation, we'll have to strike the rod at exactly the center of mass. Since transferring momentum at exactly the center of mass is impossible (since there will always be an error in measuring where the center of mass is), there will always and inevitably be rotation of the body when an impulse is given to it. Therefore, most extended masses in the universe such as planets and stars have some amount of rotation. The earth, for example, collided with another planet long ago, due to which it rotates about its own axis even today.
Why galaxies and solar systems have rotation.
The fundamental principle that gives them rotation goes something like this:
Say you have two masses moving in opposite directions but not head-on. You know that gravity acts between them. As they move closer, they will curve in towards each other due to gravity. This curving-in causes a centrifugal force to act on either of them. For some configuration of this two-mass system (i.e the seperations between them and the velocities), the centrifugal forces due to this curving in manage to balance gravity such that the masses settle into orbit.
In galaxies, the same thing happens. Initially, as the galaxy forms, many gas molecules start to rotate in the same way as above. This initial angular momentum is conserved as more and more gas molecules accumulate in this galaxy, and thus it retains this rotation. The solar system also forms the same way, and the matter forms clumps and coalesce to form planets and so on.
See: How galaxies form
I'm not exactly sure whether this applies for the angular momentum but I know it is true for the spin.. When things condense they begin to rotate or their existing rotation is accelerated. This can easily be seen in the form of neutron stars, and as an example from here on earth, a tornado. In the case of the neutron star, it spins rapidly, but before its collapse, it was slowly rotating. This is because, as the collapse happens the particles inside of the star condense and therefore the whole star condenses, resulting in accelerated rotation.
I'm not exactly certain but I believe that the angular momentum is a result of the spin and the effect it has on the surrounding matter.
Planets spin when it moves about a central mass. This is because spin and orbital angular momentum are related. S=m/M L. Hence, any orbiting planet must spin in order to be in equilibrium and stay in its stable orbit. This relation is shown in a paper published in Astrophysics and Space Science, V.348, 57 (2013) by Arbab A. I. et al.
