If you’re young (or if you’re old but your mind remains flexible) i urge you to think hard about this problem.. i do and i will! my mind is already quite inflexible so i’m not going say anything definite about this question out of fear of saying something dumb/misleading. Your q hides monsters ready to snipe any serious mind of the planet!

That said, an easier question to ponder (and many have tried) might be:

  Do photons self-interact? With each other? In free space?

After thinking thru this question yourself, you might be more prepared to consider gravitons (=“spin-2 massless bosons”) ditto for me!