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

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SUMMARY

The discussion centers on the feasibility of two photons co-orbiting stably through mutual energy attraction. It is established that photons are minimally affected by massive bodies, indicating that the mass required for stable orbit would need to be extraordinarily large, far exceeding that of the Sun. A proposal for a "two-photon bound state" utilizing nonlinear media was referenced, suggesting that under specific conditions, two photons could behave similarly to orbiting solitons.

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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
 

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