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Photons don't directly interact with each other, but if one photon pair produced an e+/e- then the second photon could interact with that pair. The interaction has to conserve the energy of the two photons and conserve their momentum as well of course. But yes they could (and most probably depending on their energy) just pass right "through" each other.


Usually absolutely nothing. Electromagnetism is linear, which means that the result of doing something with two photons is the superposition of the results of doing something with each one individually. By that reasoning, since one photon by itself just goes on its own merry way, then two photons, even if they go near each other, just go along on their ...


To leading order, nothing happens in any photon "collision". To higher order there are light-light interactions that involve particle loops, but they don't (can't) depend on the geometry because we can always boost to a frame in which the pair has zero net momentum (even though you can't boost to the frame where a single photon has zero momentum).


Andromeda and the Milky Way belong to a group of galaxies called the Local Group. The two galaxies are the largest galaxies in the group, so to a pretty good approximation their interaction can be treated as a two body problem, with the other galaxies in the group producing only minor perturbations to their motion. So as you suspected, it isn't the case ...


Suppose someone suggests that following a perfectly elastic collision, two billiard balls are each traveling twice as fast as they were before (and opposite to their original directions). You can't prove him wrong using conservation of momentum, but you can prove him wrong using conservation of energy. Therefore conservation of energy has implications that ...

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