If photons had mass they would attract each other as well.
Gravitational lensing is pretty strong proof that photons follow the curvature of space affected by a gravitional field. If photons had mass themselves they would not follow straight lines in free space but they'd clump together over astronomical distances and long periods of travel. Though there is a way to get them to act in unison which gives some pretty odd effects:
Photons do interact with each other gravitationally. It's not as simple as just attracting each other - the Newtonian limit doesn't work here - but parallel photon beams going in opposite directions, for instance, will be deflected towards each other.
But photons traveling in (almost...) the same direction (such as the photons that arrive at some destination after gravitational lensing do not gravitationally attract.
I thought photons also contributed to the curvature of spacetime because they have momentum (and thus energy). I would expect it to be a pretty miniscule contribution, though.
Hm... just an interested layperson here but would that not require some kind of mechanism by which the photon sheds some of that momentum? Which would seem to be pretty hard if it really is an 'elementary' particle. Unless 'photon === graviton' and you find photons shedding other photons!
I'm a layman as well, but I think photons can effectively lose energy in various ways, one of them being the well-known redshift effect. And one of the main causes of redshifting is photons climbing out of a gravitational well (this is called a gravitational redshift).
However, whether that translates to a loss in momentum is a bit more fuzzy and I really can't tell whether it does or doesn't. Although I'm far from being a physicist, so hopefully someone more knowledgeable chimes in to enlighten us...
But I'm curious: what is your reasoning for asking whether photons have a mechanism to lose momentum as a consequence of them affecting the curvature of spacetime? It's not at all obvious to me the relationship between these two concepts.
> However, whether that translates to a loss in momentum is a bit more fuzzy and I really can't tell whether it does or doesn't.
Yes, redshifted photons lose momentum. Momentum (really the stress-energy tensor) is conserved locally, and along trajectories that preserve the metric, but global momentum conservation in GR isn't even well-defined.
If they don't lose momentum then there is no interaction (in order for any kind of interaction you need to lose some energy). Momentum is pretty much all a photon has and it could conceivably toss off much lower energy photons to shed that momentum.
