You take two prisms, similar to those inside a pair of binoculars, glue them together, and then send a short laser pulse through the prism cube you've made, so that half of the light is reflected. Or you can use a half transparent mirror, separating the light pulse into two, one reflected back, its other part passing through. This down-convert the 'photon' into half its energy at the same time as it creates two particles from one, exactly the same but, as I understands it, now of oposite spin. There are also polarizing beam splitters that do the same using polarization instead. As I understands it a photons polarization is just another description of its spin, although I'm not a hundred percent sure on that one, it seems to differ in the amount of 'states' a photons spin can have (3) as compared to the polarizations (2)?

I believe that they are the same though, in that a photon only have two degrees of freedom in reality, disallowing one of the spins, whereas in theory particles of spin 1 should have three. the explanation to that is that even though 'point particles' have three states of freedom (dimensions), as the photon is massless it only have two states left. All Bosons, meaning particles without 'rest-mass' comes in whole integers, photons for example are of spin 1.

"Theory predicts the existence of two bosons whose s differs from 1. The force carrier for gravity is the hypothetical graviton; theory suggests that it has s=2. The Higgs mechanism predicts that elementary particles acquire nonzero rest mass by exchanging hypothetical Higgs bosons with an all-pervasive Higgs field. Theory predicts that the Higgs boson has s=0. If so, it would be the only elementary particle for which this is the case." And "QFT (Quantum field theory) defines the s_{z} = 0-state to corresponds to a non-physical degree of freedom. Such photons will exhibit a negative probability-distribution. The reason for these troubles are the fact that a photon has zero-restmass."

Now, all particles of matter, also called fermions, have a half-integer spin. All known elementary fermions have spin ½, including protons, neutrons, electrons, and quarks.

But it's confusing all the same.

I'm sure JP could answer that one though

(Phieww, had to rearrange it as my comments suddenly made very little sense, after me filling the material in, not that unusual even when such non-withstanding I have to admit:)

==Quote

The head-on collision of a quark (the red ball) from one proton (the orange ball) with a gluon (the green ball) from another proton with opposite spin; spin is represented by the blue arrows circling the protons and the quark. The blue question marks circling the gluon represent the question: Are gluons polarized? The particles ejected from the collision are a shower of quarks and one photon of light (the purple ball).

===End of quote.

Okay, with the risk to bore you physics savvy to death

Let's dive into what spin is, as I understands it

First of all you need to consider a vector, or a 'angular momentum'. All angular movements can be considered as being of two 'forces', working together on whatever there is, creating that 'invisible angle' of momentum/force. Like this. 2 forces shown | _ That then will produce a combined angular, 'invisible force', working inbetween those two. Can you see how I mean? Think of them as two leashes leading down to your dog. The dog (Sebastian) will feel it as one leash diagonally stretched between the two actual leashes if the same restraint is applied to both leashes.

(Da*n those two-legged bas*s he growls as he tries to get up to speed:)

Spin is a similar idea.

" Angular momentum is a vector quantity (something that has both a magnitude and a direction, just like a velocity) that can take on only certain values in quantum mechanics. Another thing we know about angular momentum is that, in quantum mechanics, it cannot take on just any old values, but only certain specific ones. If a particle has three units of total angular momentum, then its projection can be any of (-3, -2, -1, 0, 1, 2, 3) and that is it: projections must differ by an integer number of units.

Very weird, but quite a handy fact: if you know that a particle's angular momentum can take on only two different projection values, then you know its total angular momentum must be 1/2, and the projection values are (-1/2, 1/2). If you know there are three projection values, then you know the total angular momentum is 1, with projections (-1, 0, 1). Spin acts like this, so everything you've just learned about angular momentum is also true of spin."

And

"A particle with integral spin (0,1,2,...) is not in any way limited by other

particles of its own kind. At one location, you can have a huge number with

exactly the same energy, moving in exactly the same way. Photons of light,

neutrinos, and pions are such particles. These tend to be the communication

particles, the particles that spend most of their time passing between

things. These are called Bose-Einstein particles, or bosons for short.

A particle with half-integral spin (1/2,3/2,5/2,...) is very limited by

other particles of its own kind. If two such particles are at the same

location, something must be different about them. They may be "spinning" in

different directions. They may have different energies. They may be moving

in different directions. They cannot be identical in all ways. Protons,

neutrons and electrons are the most common such particles. These tend to be

the particles that build matter. These are called Fermi-Dirac particles, or

fermions for short"

"In 1924 Wolfgang Pauli introduced what he called a "two-valued quantum degree of freedom" associated with the electron in the outermost shell. This allowed him to formulate the Pauli exclusion principle, stating that no two electrons can share the same quantum state at the same time. The physical interpretation of Pauli's "degree of freedom" was initially unknown. Ralph Kronig, one of Landé's assistants, suggested in early 1925 that it was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. This would violate the theory of relativity."

"Inspired by the photon picture of light waves, Bose was interested deriving Planck's radiation formula, which Planck obtained largely by guessing. Using the particle picture of Einstein, Bose was able to derive the radiation formula by systematically developing a statistics of massless particles without the constraint of particle number conservation. He was quite successful, but was not able to publish his work, because no journals in Europe would accept his paper... in 1926, Einstein completed the Bose-Einstein statistics by extending Bose's work to the case of massive particles with particle-number conservation.

The Bose-Einstein statistics was not completely without troubles, because not all the particles obey this statistics. It was Paul A. M. Dirac who found out that the Bose-Einstein system particles are totally symmetric under permutation of particles. This observation of course led to the Fermi-Dirac statistics. It is interesting to note how intensely Dirac was interested in permutations from his book entitled "Principles of Quantum Mechanics."

Let us go back to the photon statistics formula derived by Bose. There is a factor "2" sitting on the numerator of this formula. The usual explanation is that it is because photons are massless particles. Then why not 1 or 3 ? Bose argued that the photon can have two degenerate states. This eventually led to the concept of photon spin parallel or anti-parallel to the momentum.

The question of why the photon spin should be only along the direction of momentum has a stormy history. Eugene Wigner (1939) showed that the internal space-time symmetry of massless particles is isomorphic to the symmetry of two-dimensional Euclidean space consisting of one rotation and two translational degrees of freedom. It is not difficult to associate the rotational degree with the photon spin either parallel or anti-parallel to the momentum, but what physics is associated with the translational degrees of freedom. These translational degrees were later identified as gauge transformations. This does not solve the whole problem because there is one gauge degree of freedom while there are two translational degrees of freedom. How do they collapse into the one gauge degree of freedom? This problem was not completely solved until 1990."

"If/when electrons decide to share a single orbital, we get pairs (as opposed to, say, triplets) because the electrons have total spin s=½ so there are two possible spin projections sz={−½ or +½}.

If electrons had total spin s=1 then there would be three possible spin projections sz={−1, 0, or +1} ... and you would find orbitals with three electrons in them. You can’t occupy a given orbital more times than are allowed by the spin multiplicity because of the (Pauli) exclusion principle.")

"In 1922 the Dutch physicists Otto Stern and Walther Gerlach made a discovery remarkably similar to that of Erasmus Bartholin, but instead of light rays their discovery involved the trajectories of elementary particles of matter. They passed a beam of particles (atoms of silver) through an oriented magnetic field, and found that the beam split into two beams, with about half the particles in each beam, one deflected up (relative to the direction of the magnetic field) and the other down."

And the reason they did so came to be known as their 'spin'." One outcome of quantum field theory was a quantization of the electromagnetic field, the necessity of which had been pointed out by Einstein as early as 1905. On an elementary level, Maxwell’s equations are inadequate to describe the phenomena of radiation. The quantum of electromagnetic radiation is called the photon, which behaves in some ways like an elementary particle, although it is massless, and therefore always propagates at the speed of light. Hence the "spin axis" of a photon is always parallel to its direction of motion, pointing either forward or backward"

Some from

here. but it's my own mix I'm afraid. Hope you could make some sense from it.