# Light gravity

Originally posted by marcus
Bravo!
Do you have a web reference to some sci.physics
conversation where a person who does not own
the parallel case?
No, all I could find were qualitative discussions of the subject. But if you look at the relativistically correct equation for mass:

m2 = E2 - p2 (c = 1)

You can see that a system of anti-parallel beams has a net momentum of zero so m = E. On the other hand a system of parallel beams of light has a momentum of p = E and therefore m = 0.

This isn’t Lightman or GR but it’s pretty convincing.

Um, photons have no mass, do they?

Forgive my ignorance, as this is all very new to me, but the definition of mass involves an object at rest, and photons are never at rest. Right? If we accept that, then must they also not have any gravitational attraction? I have the impression that objects with mass warp space, but objects without mass cannot...

John[?]

jcsd
Gold Member
They dopn't have invariant mass, but they do have a gravitational field.

Originally posted by LURCH
I believe that you are. If I understand Imagine's question correctly, he is asking if the two beams will exert gravitational attraction on one another.

BTW, the more I hear about it, the more convinced I become that light has no gravitational influence.

The short answer is that light itself does not emit gravitational waves because it does not occupy any space-time. You will see why this question is difficult to answer: the scenario simply cannot occur under any existing physical framework.

First, for clarification: Gravity does not bend light. Gravity bends space and light travels in a straight line through the curved space.

The problem with the original inquiry is that the universe is bounded by the material contained within. For only two light beams to exist in space, and nothing else, would mean that this universe is of zero dimensions. Two reasons: first, light is pure energy and massless, and therefore does not take up any space; and second, gravity, as the facilitator between the transfer and conversion of energy--and subsequently the observed change in systems (also known as time), would be nonexistent in a universe consisting of only light, hence the zero dimensions (a system in which change cannot be observed.)

On a mathematical note two parallel lines, no matter the mutual distance, intersect at infinity. Oddly enough, this perspective can apply to the original question and even hint to the answer. Assuming it was possible to create a universe of only two parallel light beams (where there is a distance greater than zero between the beams and time is constant everywhere), in order to increase the accuracy of our measurement, we need to increase our rate of travel. As our rate of travel increases, the observed distance between the two light beams decreases so that as we reach the speed of light the light beams would appear to intersect. Of course, our observation does not always reflect what is actually occurring. Our observations would be perturbed by our own gravity field, which gets stronger and stronger as we move faster and faster. If we were to somehow "shield" the oncoming space of our gravitational effects, either by ceasing to emit any waves ourselves or by making space itself immune to its effects, the light beams would be observed to run parallel forever.

It's quite clear that this question cannot be fully answered by the known laws of physics, quantum or otherwise.