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If two bosons (or photons) posess energy and momentum, then they will interact gravitationally. If they approach each other to within a distance r, and r is small compared to their positional uncertainty then they can be considered to partially overlap. The gravitational interaction should then be estimated by the average over all relative distances and will certainly contain infinities due to the (1/r) nature of the gravitational potential. How are such infinities dealt with? Or did I get their occurence all wrong?

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In the case of photons, you will just add up the energies to obtain the total energy. This total energy will curve space according to Einstein's general relativity theory.

In the case of bosons, the gravitational energy scale is much smaller than the energy scale of the electro-magnetic and the strong force. Hence, your consideration becomes purely hypothetical and nobody will be able to answer that.

QM does not incorporate gravity. Hence, you can't just apply concepts from quantum mechanics to calculate gravitational potentials. You must dig deeper using theories which combine these two worlds. Good luck!

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