Can Two Photons Co-Orbit Stably Through Mutual Energy Attraction?

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Loren Booda
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Is it possible for two photons to co-orbit stably, solely by attraction between their mutual energies?
 
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Photons barely get deviated by stellar scale masses, so I would imagine the size of mass to induce one into some kind of orbit would be simply huge, much bigger than the mass of the sun could provide, let alone another photon.
 
I remember that there was a proposal for "two-photon bound state" using nonlinear media. Basically one would have two photons behaving like two orbiting solitons:

http://prola.aps.org/abstract/PRL/v67/i11/p1399_1