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I've always wondered if it's possible to bind two photons, in particular by gravitational interaction. Photons don't have a rest mass, but do nevertheless have a gravitational mass, by which they can attract each other. However, I can't imagine a bound state. My intuition of special relativity goes against it. Is it possible at all? Can photons at least bend each other's trajectories?

Interactions of other kinds (non gravitational) are also an acceptable answer, but I'm not interested in (if they exist) effective interactions in matter.

Martino
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I agree with Lewis Miller that they cannot form a bound states if the binding is thought to be of gravity essence. By definition, a quantum state is understood only in small scales which is way too smaller than the bounding distance between two photons; it will be bigger than the size of Visible Universe. However, I would like to add to it the possibility that two photons can be entangled so that they feel each other's presence even in cosmological distances given the fact they are originated from a common source, e.g. annihilation of e+ and e- resulting into two back-to-back photons. These produced photons would then be entangled and you can prove it experimentally. But, binding is different than entanglement. Thanks,

Benjamin
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