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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.

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    $\begingroup$ " However, I can't imagine a bound state. " Neither can I. General relativity says two photons should attract via gravity, but the attraction is so weak I can't imagine a quantum bound state would result. Since photons are quantum objects by nature, there would be no classical bound states either. Can the photons at least bend each other's trajectories? Yes, according to GR but I can't imagine one could ever detect this experimentally. $\endgroup$ – Lewis Miller Mar 5 '16 at 16:52
  • $\begingroup$ Think about the Hanbury Brown and Twiss effect. From Wikipedia: "In 1956, Robert Hanbury Brown and Richard Q. Twiss published A test of a new type of stellar interferometer on Sirius, in which two photomultiplier tubes (PMTs), separated by about 6 meters, were aimed at the star Sirius. Light was collected into the PMTs using mirrors from searchlights. An interference effect was observed between the two intensities, revealing a positive correlation between the two signals,..." $\endgroup$ – HolgerFiedler Mar 6 '16 at 14:06
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    $\begingroup$ Possible duplicate of Are there bound states from light-light or gravity-gravity scattering in general relativity? $\endgroup$ – Bzazz Sep 19 '18 at 20:32
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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,

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  • $\begingroup$ Entanglement is not relevant for the question, but thanks for mentioning it. You're saying that the bounding distance would be bigger than the size of the universe and at the same time that there is no bound. $\endgroup$ – Bzazz Mar 5 '16 at 17:14
  • $\begingroup$ Yes. That's true. If something is bigger than the size of Visible Universe, gravitational binding will have no physical meaning. This is under the assumption that we live in a Universe rather than a Multiverse. Thanks, $\endgroup$ – Benjamin Mar 5 '16 at 18:11
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    $\begingroup$ And for those users who give negative energy as they would like to grade the arguments being made: If there is an accompanying correction to the mistaken statements, there will be a healthier environment. Simply liking to disliking an idea is not constructive so long as it is devoid of criticism and argument. We are in stackexchange to learn and teach from each other not in facebook to like or dislike each other. In summary, if you don't have positive energy to give away, don't give negative energy unless you have the correct answer which we are not aware of. Thanks, $\endgroup$ – Benjamin Mar 5 '16 at 18:29
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    $\begingroup$ Quantum mechanics isn't defined by some size of length scale. $\endgroup$ – Timaeus Mar 6 '16 at 22:19

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