Parallel light beams converge?

[johne1618]

Would General Relativity predict that two initially parallel light beams will converge due to their energy curving space-time?

John

 

[Naty1]

I think you got it right.

Light has energy and momentum and so the beams are ever so slightly attracted to each other...as if they had mass. They will ever so slightly curve space.

I assume you are thinking about a flat universe, one without mass or energy, to obstruct the
attraction beteen your two test beams. In other words, before you fire the two test beams, everything is flat.

 

[Naty1]

here's an interesting related discussion, to about post #9:
https://www.physicsforums.com/showthread.php?t=442266&highlight=light+beams+converge

And note Ben Crowell's post #4

 

[johne1618]

Thanks for the link to previous posts on this subject. Yes I was thinking of a flat universe.

In terms of a simple space-time diagram two parallel beams of light are represented by two parallel diagonal lines at 45 degrees to the horizontal space axis. No signal carrying an influence (at the speed of light) from the first beam could reach the second beam because it would just travel along the same path as the emitter.

Don't know if this would stop linearly propagating light beams interacting.

A diagram would help me get this point across I think!

Regarding Ben Crowell's post#4, I presume that conditions would be energetic enough in the early universe that photons could spontaneously decay into matter and antimatter that definitely is a source of gravity as it has rest mass.

 

[Dmitry67]

This is correct, light beams create gravity.

However, when it was discussed here about 1 or 2 y ago, I remember that someone (with much deeper knowledge of GR - I am just a layman) told me that:

2 parallel light beams going in the same direction do not attract (even they attract the surrounding objects)
2 parallel light beams going in opposite directions do attract.

The first fact might be clear if we look at 2 massive objects, separated by some distance, flying in the same direction. In their inertial system they collide, say, in 1s. For an external observer, this process would take longer because of the time dilation. The faster 2 objects are flying the longer it takes. You can think about the case N1 as a limit where v --> c (it takes forever)

P.S.
Interesting problem: what is Jean's mass for the light itself? :)

 

[johne1618]

This is correct, light beams create gravity.

However, when it was discussed here about 1 or 2 y ago, I remember that someone (with much deeper knowledge of GR - I am just a layman) told me that:

2 parallel light beams going in the same direction do not attract (even they attract the surrounding objects)
2 parallel light beams going in opposite directions do attract.

The first fact might be clear if we look at 2 massive objects, separated by some distance, flying in the same direction. In their inertial system they collide, say, in 1s. For an external observer, this process would take longer because of the time dilation. The faster 2 objects are flying the longer it takes. You can think about the case N1 as a limit where v --> c (it takes forever)

P.S.
Interesting problem: what is Jean's mass for the light itself? :)

Thanks very much for the reply. I like your thought experiment.

As far as I can see if a pulse of light is traveling towards a massive object then no gravitational influence from the pulse can reach it before the light itself. The light can deliver mass/energy to the object which then acts as a gravitational source but the light itself can't act as a source.

I'm only a layman so the above is just a guess.