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Imagine two photons starting from origin and travelling in opposite directions. Can they redshift each other due to the gravitational potential between them?

Lets modify it even more to make the problem simple Two photon guns in different galaxies, light-years apart, fire photons toward a common origin, O, where an observer detects them at frequency F1 After crossing O, the photons continue in straight-line paths toward the opposite galaxy. One second later, if we "freeze" the system to include only O and the photons—excluding the galaxies—will the photons be redshifted due to gravitational attraction between them?

Vijay Adhithiyan
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The motivation behind this question seems to be that if the two photons are traveling away from each other at the speed of light, the gravitational effect of one cannot reach the other since changes in the gravitational field also propagate at the speed of light.

There are several problem however when trying to analyze this situation within general relativity:

First, photons (or massless particles in general) cannot be described by point-like objects: point particles have infinite energy density and are thus essentially black holes, but photons need to travel along light-like paths (while the worldline of black holes don't have a well defined spacetime interval since they are singular). So we need to consider classical electromagnetic waves instead.

Second, electromagnetic waves cannot be created from nothing, there would have to be some source of energy that is converted into the EM waves (for example, a massive particle decaying to photons). That source cannot be point-like either, because if it was it would be a black hole itself and the radiation would not be able to escape.

So we end up having to consider a non point-like source of energy that is converted into electromagnetic radiation. We can imagine for example a ball made of matter and anti-matter that at some instance in time annihilates into pure radiation. Now imagine a "photon" originating at the surface of this ball and traveling radially outwards: it cannot feel in any way what happened to he rest of the ball since he is outside its future light-cone, so it will continue to travel in the gravitational field of the original ball. This photon will thus be redshifted, not by the other photons but by the gravitational field of the original source! (which of course have the same total energy).

Of course more generally, photons (EM fields) contribute to the energy-momentum tensor and therefore have a gravitational effect on other photons. But the scenario described in the question, of only two photons originating from a single point, cannot be meaningfully realized in GR.

J. Delaney
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Suppose two photons are emitted at the same time and travel in the same direction. Your first thought might be to treat them like particles.

Suppose that photon B is directly behind photon A and they follow the same trajectory. Then, from the lab frame, A is in B's future light cone and B is in A's past light cone. So no mutual effects can exist. A might affect B by somehow leaving a wake of curved space time behind.

Suppose they are in parallel trajectories side by side. Then they are both elsewhere to each other. Neither affects the other.

The world line from A to B would have to be light like for one to directly affect the other, such as by A emitting a graviton that B absorbs.

If they are anti parallel, then they can have mutual effects.

But photons are not particles. They are sort of like particles and sort of like waves. Regardless, they do have wave functions that occupy extended regions of space. The regions can overlap. What then?

Photons do not interact with each other to any appreciable degree (except in extreme environments such as the interior of very massive stars.) That is, two beams of light do not affect each other when they cross. But do they interact gravitationally? We would need a theory of quantum gravity to say if there is a probability of exchanging gravitons.

But antiparallel beams of light attract each other, as described in the link provided by @meowdib Do two beams of light attract each other in general theory of relativity?. And beams are just so many photons that you can see the average effect of them all.

Given that, photons do have some sort of effect on the curvature of space time, and do respond to curvature. They must be able to interact with each other. We don't know how that interaction works on a photon by photon basis.

mmesser314
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