Why the photon have one spin?

Answer 1

From the original best answer:

From Wikipedia: "In the modern Standard Model of particle physics, photons are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of photons, such as charge, mass and spin, are determined by the properties of this gauge symmetry."

From what little I understand, it seems this is some fairly advanced math; you would have to read the article in Wikipedia and follow some links - and perhaps do some serious study in advanced math topics, and other advanced science topics, to understand the "why".

Added:

This math is indeed advanced. I have studied quantum mechanics for a while and it isn't always easy. I will try to answer this without getting to mathematical.

Short answer: The spin of a photon is 1 due to the spin-statistics theorem.

Longer answer:

(1) Quantum mechanics to explain it simply, uses wave functions to describe the particles to be modeled, much like bare-bones sine or cosine wave functions. These functions have symmetries. When some operators are used on some functions (think of addition or multiplication), they change the function from positive to negative, others keep their sign no matter what.

(2) A photon is a boson. A boson is a particle that can occupy the same quantum state (i.e. position) as other bosons, including if they have the same energy the same space. This makes them perfect for being "force carriers".

(3) A photon is the force carrier for the electromagnetic field. Any time there is an energy exchange, for example in an atom, where an electron goes into a "higher" orbit or a lower orbit a photon must be absorbed or emitted (Note: Not any old "jump" is allowed).

(4) Electrons as fermions cannot have the same quantum state at the same time (See the Pauli exclusion principle).

(5) Spin itself, is the angular momentum of the particle, which is not due to the orbital angular momentum of the particle. All particles either have a whole spin or half a spin.

With this knowledge we can press on. The wave function of a boson (like our friend the photon) does not change under a swap of position with another same boson particle, thus the wave function is symmetrical.

As for fermions, the wave function changes under a position exchange, which gives us antisymmetry.

One could say that because you are allowed to "stack" photons together in the same state (position), they have a whole spin, where as electrons are halved because they need to be "separated" from one another by their quantum numbers (momentum, energy, etc).

(Note: This is my personal and very simplified interpretation of the answer)

Finally: Please remember, what we are talking about here are things so tiny they have no smell, color, or taste. They are not waves nor particles. They are something we cannot see and could never imagine. When I say particle, I don't mean an actual particle. They are mathematically treated that way in some ways, the calculations of where they will end up and many other things are handled as probabilities, wave-like probabilities using wave functions. In that sense they are waves, their movement as well as other factors are handled as "probability waves". Furthermore, The theories behind what we cannot see are built so highly on experimental evidence that some of them have an accuracy of the highest order of any mathematical theory ever obtained. The math works and is able to probe where our visual imagination breaks down. Only the indirect effects of this tiny world can be seen by us, but they are seen every day.

I hope this was helpful.

-Bartmoss