General Relativity tells us that the paths of parallel photons propagating in free space should be unaffected by each other, while the paths of anti-parallel photons should bend towards each other. I'm using an already answered question as a reference:

Do two beams of light attract each other in general theory of relativity?

I would like to extend this question to further consider the spin angular momentum of a system of two photons.

Consider the following two scenarios for anti-parallel (moving towards each other) propagating photons $A$ and $B$.

  1. The photon spins are parallel (e.g. helicity of $A$ is 1, helicity of $B$ is -1).

  2. The photon spins are anti-parallel (e.g. helicity of $A$ is 1, helicity of $B$ is also 1).

My question is: Since general relativity and QFT don't predict a difference in the paths taken by the pair between 1 and 2, how do candidate theories for quantum gravity approach this? Do they produce specific predictions for the paths of the photons accounting for their spin alignment?


1 Answer 1


I think general relativity is a distraction here, because the spin-exchange interaction in electromagnetism is local.

The photon interacts with electric charges and magnetic dipole moments, but the photon itself has neither of these properties. This lack of self-interaction is why electromagnetic fields and waves in classical EM obey superposition: the photons which make up the fields pass through each other without interacting.

The first-order mechanism for photon-photon scattering is via the polarization of the vacuum, where each photon spends part of its time as an electron-positron pair, and the other photon can scatter from those virtual charges. Photon-photon scattering has only recently been observed, and even then in a resonant cavity where the density of "target" photons can be made very high. One way to think about the length scale is to imagine the virtual particles "tunneling" between the two photons; remember that the probability of tunneling decreases exponentially with distance.

Note that your linked question and its literature references discuss the interactions between beams of light, for which the stress-energy tensor is well-behaved in classical electromagnetism and in the continuum theory that is general relativity. I'm not sure whether extrapolating the beam-beam interaction down to a photon-photon interaction, as you do in the premise of your question, is quite so straightforward as just invoking the correspondence principle.

  • $\begingroup$ Thanks for this answer. Is the stress energy tensor known/theorised to be symmetric under the reversal of circular polarization of one of the beams? $\endgroup$
    – Jamie S
    Jan 6 at 14:17
  • $\begingroup$ The homework-assignment answer to that question is to write down the $E$ and $B$ fields for circularly polarized light, and then to compute the tensor yourself. I actually don’t know the answer (yet). $\endgroup$
    – rob
    Jan 6 at 16:17

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