# Polarization of gravitational waves VS polarization of photons

This might be a stupid question, but I think i am mixing important concepts.

It is well-known that gravitational waves (GWs) come in two polarizations or two states of helicity: the so called "+" and "×" polarizations, related by a 45° rotation. I've also read that this is the reason why the gravitons (the quantum excitations of GWs) are expected to have spin 2.

On the other hand, photons also have two polarizations (the only difference is that they are related by 90° rotation): the left and right circular polarizations. According to the logic applied to GWs, then photons should have spin 2 as well. However, they have spin 1.

Where does my reasoning fails? Thanks in advance.

Note: In addition, I know that the spin 2 of the graviton can be explained by the fact that gravity is represented by a tensor $$h_{\mu \nu}$$, whereas the spin 1 of the photon is explained by the fact that electromagnetism is represented by a vector potential $$A^{\mu}$$. However, this does not give me any physical intuition about the polarization states.

• Why do you think that the number of polarizations matters for determining the spin but their rotation and vector/tensor nature doesn’t? – G. Smith Sep 21 at 22:03
• I am not saying that the rotation or tensor/vector nature does not matter for determining the spin, I know it does. I am just saying that I don't quite understand the connection between the number of possible polarizations and the spin. – Guillermo Franco Abellán Sep 22 at 0:50
• I think for massless particles and nonzero spin, the number of polarizations is 2 regardless of the spin... basically either positive or negative helicity. From my point of view the thing determining the spin is whether the field is scalar, spinor, vector, tensor, etc. – G. Smith Sep 22 at 4:06
• Ok, then I need to grasp some concepts regarding polarization. Thanks! :) – Guillermo Franco Abellán Sep 22 at 14:46