B Gravity between light beams

1. Jan 25, 2017

calinvass

In the experiment using pencils of light by Tolman, is has been shown that two parallel light beams do not attract but anti parallel beams do.
What happens if we use different wavelengths for the light beams. Will the higher frequency beam be less deflected ?

2. Jan 25, 2017

Staff: Mentor

Energy density is the relevant parameter (technically energy and momentum density, but for light they have a fixed relation). Wavelength alone doesn't tell you what will happen.

3. Jan 25, 2017

PAllen

Just a nit pick - Tolman's work, and other similar work on this phenomenon are all theoretical. The deflections are many orders of magnitude too small to observe.

4. Jan 26, 2017

calinvass

But isn't energy density proportional to wavelength for a stream of photons ?

5. Jan 26, 2017

Ibix

Energy per photon depends on wavelength, yes. The energy of a beam depends on the number of photons, too. And remember that GR is a classical theory. It can deal with a light beam as a source of gravity, but not a quantum particle. That's why @mfb is talking about the energy density (of a classical beam).

6. Jan 26, 2017

Staff: Mentor

And the gravitational force on Earth is proportional to the mass of Earth. That doesn't mean lifting a truck is as easy as lifting a grain of sand, even though the mass of the Earth is the same in both cases. The other mass matters as well, and only their product is relevant for the force.

Wavelength alone doesn't tell you anything, You need the energy density, the product of photon density and energy per photon.

7. Jan 26, 2017

pervect

Staff Emeritus
For the parallel beams, there isn't any deflection, so it won't matter. For the anti-parallel beams, one would need to work it out in more detail. It's probably coordinate dependent, if we imagine two almost-parallel light beams of the same frequency and energy density in a rest frame, by going to a moving frame we can make the energy densities and frequencies unequal.

8. Jan 27, 2017

calinvass

Ok, but, when I said a stream of photons I meant a constant homogeneous stream, because that is what a laser approximately does.
The energy per photon is hν.

The problem is, I understand, a photon can only be described as a quantum object, and GR doesn't deal with them.

Last edited: Jan 27, 2017
9. Jan 27, 2017

Staff: Mentor

That is not the "problem". Even with classical particles you would need the density. The energy per particle is not sufficient to determine what happens.

10. Jan 27, 2017

calinvass

Thanks, yes, the density of particles over a volume of space makes sense. This I suppose corresponds to the intensity of the beam.

11. Jan 28, 2017

Staff: Mentor

The numerical values of energy and momentum density are. But the fact that anti-parallel light beams attract is not.

Yes, but that also makes the momentum densities and pressures unequal in the same way, and the action of the beams as a source of gravity depends on all of those things. The actual source of gravity is the stress-energy tensor of the light beam, whose components include all of those things and co-vary appropriately when you change frames.

12. Jan 28, 2017

calinvass

I'm not sure of this, but an observer sees these light beams curving space around them , therefore, why doesn't see them moving towards each other. Usually intuition doesn't work very well in relativity. Is it possible that as the beams curve spacetime around them, they also move further and the spacetime curvature manifests like gravitational waves always behind the light beams. However, if we use continuous beam (not short pulses) this explanation doesn't work anymore.

13. Jan 28, 2017

PAllen

Two anti parallel beams do move towards each other, while parallel beams do not. You don't notice this only because the amount of deflection is too small.

14. Jan 28, 2017

calinvass

Yes, I know. Is there any contradiction to what I said?
If the curved spacetime is always behind the pulses of light, the beams don't get attracted. But this explanation doesn't work when we use continuous beams.

When antiparallel, the spacetime curvature clearly affects both pulses but after they pass by.

15. Jan 28, 2017

Staff: Mentor

Light beams moving in opposite directions attract each other, a bit like massive objects moving in opposite directions would do. If we increase the intensity of light beam A, the deflection of light beam B increases. If we increase the intensity of light beam B, the deflection of light beam A increases.

16. Jan 28, 2017

Staff: Mentor

Yes. That means you should not be trying to use intuition to analyze this problem, as you are doing. You need to actually look at the math.

17. Jan 28, 2017

PAllen

Yes, it directly contradicts what you seem to be saying. You say the beams don't get attracted. I say they do, and (given ridiculous precision), you would measure this. Light in oppositely moving light pulses would also mutually deflect each other (again, by an amount too small to be observed with current technology).

18. Jan 28, 2017

calinvass

Sometimes I do that but usually, as Feynman says, I guess it, then I compute the consequences. Unfortunately for this case, it is harder to guess.

19. Jan 28, 2017

calinvass

But on post #13 you said parallel beams do not attract.
Ps
Oh, I understand now, you said they don't but in fact it is only that we can't measure this.

I still don't understand what is the solution given by GR.

Last edited: Jan 28, 2017
20. Jan 28, 2017

PAllen

Maybe I am misunderstanding you.

Anti-parallel beams attract and deflect. Parallel beams do not. Anti-parallel pulses defect each other. For parallel pulses I have never actually studied or performed a calculation. My guess is they don't deflect, but I would not have much confidence in this guess without further analysis. Even with some experience, intuition is unreliable in GR.

As for your attempts at intuitive explanations in terms of curvature, I don't think these are useful.