[Kryptid (OP)]

By "spin", I mean the quantum mechanical concept. Spin does not seem to be conserved in a straightforward sense, as an electron and positron (each with spin 1/2) can annihilate to produce two photons (each with spin 1). Are there rules as to what kind of changes can and cannot occur to spin in particle interactions?

[chiralSPO]

As far as I understand it, angular momentum is conserved.

Spin is a type of angular momentum, but does not necessarily have to be conserved (although it's generally a pretty good rule of thumb), so long as there is some other part of the system that can change so that overall angular momentum is conserved (for instance, typically "spin-forbidden" electronic transitions, which involve the change of the spin state of an atom or molecule, can happen in conjunction with a change in the orbital angular momentum (spin-orbit coupling)--this is how many phosphorescent materials work).

[evan_au]

My simplistic reading of the situation is that antiparticles have opposite signs for their quantum numbers.

In pair annihilation (or the inverse, pair production), the quantum numbers of the incoming antiparticles sum to 0, as do the quantum numbers of the outgoing particles (photons are their own antiparticles).

So when you include the sign of the spin:
Electron Spin 0.5 - 0.5 = 0
Photon Spin 1 - 1 = 0

You can also get pair annihilation producing 3 gamma rays. I read this as:
Electron Spin 0.5 + 0.5 = 1
Photon Spin 1 + 1 - 1 = 1
See: https://en.m.wikipedia.org/wiki/Electron%E2%80%93positron_annihilation

Please correct where I got this wrong!

[Janus]

By "spin", I mean the quantum mechanical concept. Spin does not seem to be conserved in a straightforward sense, as an electron and positron (each with spin 1/2) can annihilate to produce two photons (each with spin 1). Are there rules as to what kind of changes can and cannot occur to spin in particle interactions?

You seem to be treating quantum spin as being analogous to angular velocity, it is not.
Quantum spin is analogous to Classical angular momentum, and is conserved in the same manner.   
If you combine two objects with equal angular momentum, the resulting combination may or may not end up with the same angular velocity( depending on exactly how they combine), but will have a total angular momentum equal to twice that of either of the two original components.   The final angular momentum will be equal to the sum of the individual angular momentum values.
This is conservation of angular momentum 
Quantum spin is conserved the same way, the final spin is the sum of the spin of the individual components
1/2+1/2 =1 signifies the conservation of spin.

[jeffreyH]

Once you start looking at the commutation relations of rotation and displacement you start to see the connections with group theory. Then on to symmetries and conservation laws. That then connects to Noether's theorem.

[Kryptid (OP)]

My simplistic reading of the situation is that antiparticles have opposite signs for their quantum numbers.

In pair annihilation (or the inverse, pair production), the quantum numbers of the incoming antiparticles sum to 0, as do the quantum numbers of the outgoing particles (photons are their own antiparticles).

So when you include the sign of the spin:
Electron Spin 0.5 - 0.5 = 0
Photon Spin 1 - 1 = 0

You can also get pair annihilation producing 3 gamma rays. I read this as:
Electron Spin 0.5 + 0.5 = 1
Photon Spin 1 + 1 - 1 = 1
See: https://en.m.wikipedia.org/wiki/Electron%E2%80%93positron_annihilation

Please correct where I got this wrong!

If this is the case, then would it be possible to get a graviton, with spin 2, from the interaction of two photons with aligned spin 1? I realize there might be some issues with conservation of momentum here, so how about four photons interacting to form a pair of gravitons? Or could you get a Higgs boson (spin 0) from two high-energy photons with opposite spins interacting?

[jeffreyH]

Gravitons? No. Experiments using light have shown promise in finding the axion (possible cold dark matter component).

https://en.wikipedia.org/wiki/Two-photon_physics

https://en.wikipedia.org/wiki/Axion

[Kryptid (OP)]

Gravitons? No.

What prevents this from occurring? Does conservation of spin prevent this or is something else at work?

[jeffreyH]

If you have two highly energetic photons, with short wavelengths, how can you transform this into a low energy graviton? The ranges of wavelengths do not significantly overlap. Where is the conservation of energy and momentum? It would be like stating that you could amplify the gravitational field by colliding photons.

[Kryptid (OP)]

If you have two highly energetic photons, with short wavelengths, how can you transform this into a low energy graviton?

When I said "high-energy photons", I was referring to the formation of a Higgs boson, not a graviton (since the Higgs boson has a  high rest mass, the photons would have to have sufficient combined energy to at least equal this).

The ranges of wavelengths do not significantly overlap. Where is the conservation of energy and momentum?

Really? Photons don't seem to have any strong constraints on what their wavelengths can be. They can be much smaller than an atomic nucleus or many times wider than the Earth. Why would the same not be true for gravitons? Take note that I am not talking about what wavelengths are often produced by naturally-occurring sources, but rather as to what the laws of physics actually allow in principle. Is there something constraining possible graviton wavelengths?
 

It would be like stating that you could amplify the gravitational field by colliding photons.

Not exactly, given that gravitational waves aren't exactly the same thing as a static gravitational field, but that's kind of beside the point. If it's not possible to get a graviton out of photon interactions, I'd like to know why it is not possible. What conservation laws would prevent it?

EDIT: I found an explanation saying that photon-graviton conversion is possible, but extremely unlikely due to the enormous disparity between the relative strengths of the gravitational and electromagnetic fields: https://www.quora.com/Is-it-possible-to-transform-a-photon-into-a-graviton

[jeffreyH]

Therefore the energy differences mean the wavelengths don't match. This is what I said originally. If you wish to blue shift gravitational waves you would need to accelerate a mass to almost the speed of light. To be able to detect this would require a celestial object such as a planet or star to be accelerated to such a speed. Then you are likely to get a high energy, detectable source of gravitons. Some collision products are extremely likely while others are very rare. So yes it may be possible. How to you prove it does happen?

[jeffreyH]

At this point in this thread it is useful to learn what sigma is and why it is important. The details are on the following page.
http://news.mit.edu/2012/explained-sigma-0209