What happens to gravity when light travels at the speed of light?

[Dmitry67]

(Offtopic from another thread)

So I have a super-duper laser which can emit a very short but extremely powerful pulse in some direction. This pulse is so powerful that the energy of light is say 1Kg * c**2, or the relativistic mass of light is 1Kg.

What is a gravity from that light according to GR?

I was thinking about it and it looks weird. So, this 'body' is moving at speed of light, so the gravity can not 'outrun' it, contrary to any other moving bodies.

So if we have a test body close to the path of the beam. Until the beam arrives, the test body does not move, because gravity does not arrive yet. Gravity hits the test body at the same time the light passes by. After it is passed, test body is attracted into the direction where the beam is gone.

So contrary to the flyby of any other body, this process is assymetric (!). The test body is pulled into the direction where the beam is gone, getting some of the momentum of the pulse. Hence, light in the beam loses energy and momentum and becomes redder.

Finally, everything which is applicable to the powerful pulse is also applicable to the normal pulse or light from distant stars. They also can become redder.

Do you see anything wrong so far?

 

[Jonathan Scott]

(Offtopic from another thread)

So I have a super-duper laser which can emit a very short but extremely powerful pulse in some direction. This pulse is so powerful that the energy of light is say 1Kg * c**2, or the relativistic mass of light is 1Kg.

What is a gravity from that light according to GR?

I was thinking about it and it looks weird. So, this 'body' is moving at speed of light, so the gravity can not 'outrun' it, contrary to any other moving bodies.

So if we have a test body close to the path of the beam. Until the beam arrives, the test body does not move, because gravity does not arrive yet. Gravity hits the test body at the same time the light passes by. After it is passed, test body is attracted into the direction where the beam is gone.

So contrary to the flyby of any other body, this process is assymetric (!). The test body is pulled into the direction where the beam is gone, getting some of the momentum of the pulse. Hence, light in the beam loses energy and momentum and becomes redder.

Finally, everything which is applicable to the powerful pulse is also applicable to the normal pulse or light from distant stars. They also can become redder.

Do you see anything wrong so far?

It's not as asymmetric as you are suggesting. The light beam sees the existing field of the test body pulling it forwards and sideways until it passes the test body then pulling it back and sideways after it has passed it. From the point of view of the test body, the field from the earlier position of the arriving light pulse reaches it first, just as the pulse passes it, then the field arrives in rapid succession from each point of the passing pulse. I'm not sure exactly what happens; the analogy with the Lienard-Wiechert potentials in electromagnetism gets a bit messed up at light speed, and there's also gravitomagnetism involved. However, I think that the overall effect would only be that the test body would be pulled sideways towards the path of the pulse.

 

[Dmitry67]

Yes, good point but I am still confused how this symmetry works if pulse is much heavier then a test body

 

[Jonathan Scott]

Yes, good point but I am still confused how this symmetry works if pulse is much heavier then a test body

The interaction time will be very short, so the effect wouldn't be much in any case.

Basically, the test body will experience the field due to each point on the path of the pulse, but the effect from the points along the arriving path is all bunched up together and intensified like a shock wave and the effect from the points along the departing path is all spaced out and weakened. My guess is that the net result is simply a sideways force.

The gravity of continuous photon beams has some interesting features. From special relativity considerations, if you consider two parallel beams of light as the limiting case of two streams of massive particles traveling in the same direction (as you increase the velocity but modify the rest mass and/or separation so that the energy flow remains constant), I think you find that the gravitational force between them seems to be time-dilated to zero, and I believe that the same result has been obtained using General Relativity. However, two non-parallel beams of light do interact gravitationally.

 

[Dmitry67]

Hm, I believe 2 parralel beams would attract, because each curves the spacetime independently, and light follows the geodesics.

Well, the question is - do we have a thaory to CALCULATE it, not to SPECULATE about it? :) Sorry, I am an amateur...

 

[thenewmans]

(I must be reading this wrong.) Are you saying that light puts out a gravitational force? Wouldn't it have to have mass? I thought light has no mass.

 

[Dmitry67]

Oh, not again.
Light has 0 invariant mass, but it has a non-zero relativistic mass

In another thread I gave an example. Inside an ideal reflecting sphere I have 1kg of matter and 1kg of antimatter. There is a test body orbiting a sphere. Reflecting sphere is very thin so its mass is approx. 0.

Then matter and antimatter anihilate and only light is left, reflecting over and over inside the sphere. The relativistic mass of light is still 2Kg and test body outside is still rotating on the same orbit.

 

[thenewmans]

Well I appologize for my ignorance. Can you point me to that thread?

 

[Dmitry67]

https://www.physicsforums.com/showthread.php?t=284089
it is somewhere in the middle

 

[Dale]

Again, the source of gravity in GR is the stress-energy tensor. It doesn't matter if you are talking about rest mass or relativistic mass, mass is a scalar and cannot be identified with a tensor.

When you are talking about a planet in its rest frame the energy component dominates the tensor, and the mass dominates the energy. Neither is true for a beam of light.

 

[Dmitry67]

I agree, but... Tensor is not an observable, let's talk in terms of observables, in terms of outcomes of experiments.

annihilation inside the reflecting sphere - do you agree that small planet will continue orbiting a sphere?

2 parralel light beams to infinity - do you think that they would attract to each other?

light pulse - reaction of the test body?

 

[Mentz114]

annihilation inside the reflecting sphere - do you agree that small planet will continue orbiting a sphere?

Yes, I agree, provided it's not too close.

If we had a spherically symmetric arrangement of matter and anti-matter, say a sphere of matter surrounded by a shell of equal mass of antimatter ( but not touching the inner sphere) we can assume a Schwarzschild metric for the space around the spheres. If spherical symmetry is lost when the matter is annihilated, the gravitational field will change although maybe not by much.

This assumes two things -1) matter and antimatter gravitate the same, 2) no energy is carried away by a gravitational wave while the field fluctuates. If 2) is not true, the final field will be weaker than the original one.

 

[Dale]

I agree, but... Tensor is not an observable,

Huh? The components of the stress energy tensor are energy, momentum, pressure, and stress. How is that not observable?

annihilation inside the reflecting sphere - do you agree that small planet will continue orbiting a sphere?

I believe the tensor is the same, energy is energy regardless if it is in the form of matter or EM.

2 parralel light beams to infinity - do you think that they would attract to each other?

light pulse - reaction of the test body?

I don't know. All I know is that the momentum terms of the tensor are significant now and you cannot just say "relativistic mass" and ignore those terms.

 

[Naty1]

2 parralel light beams to infinity - do you think that they would attract to each other?

yes. Anything with energy undergoes gravitational attraction.

One such view: from Peter Bergmann, a student of Einsteins, THE RIDDLE OF GRAVITATION,1992, Page 64/65:

Light carries energy; hence it posses mass. In the presence of gravitation it must undergo acceleration.

(Note his terminology is a bit different from that preferred by some on this forum..but the point is clear.)

 

[Jonathan Scott]

yes. Anything with energy undergoes gravitational attraction.

One such view: from Peter Bergmann, a student of Einsteins, THE RIDDLE OF GRAVITATION,1992, Page 64/65:
(Note his terminology is a bit different from that preferred by some on this forum..but the point is clear.)

Beams of electromagnetic radiation have gravitational fields, but I've definitely heard that exactly parallel light beams do NOT attract one another in GR, and long ago I remember working out that Special Relativity seems to imply the same. I think that if you consider two streams of matter with a Newtonian acceleration towards one another in their rest frame, then transform to another frame where their speeds are nearly c, then adjust the mass density in the stream so that the energy flow matches the light beam and let the speed tend to c, the acceleration towards each other becomes time dilated out of existence.

 

[xantox]

So I have a super-duper laser which can emit a very short but extremely powerful pulse in some direction. This pulse is so powerful that the energy of light is say 1Kg * c**2, or the relativistic mass of light is 1Kg. [..] So if we have a test body close to the path of the beam [..]

If the body is exactly half-way over the pulse emission/absorption path, it will only accelerate perpendicularly toward the pulse pathway. If it is not half-way, then it will also accelerate toward the longest side.

 

[Phrak]

So contrary to the flyby of any other body, this process is assymetric (!). The test body is pulled into the direction where the beam is gone, getting some of the momentum of the pulse. Hence, light in the beam loses energy and momentum and becomes redder.

Whatever the answer is, the time-reversed experiment must also make sense. For a body traveling slowly by, having a velociy component from left to right, a light pulse coming from the right would be required to bring it to rest, in our frame, given the full set of initial conditions.

 

[Phrak]

In another thread I gave an example. Inside an ideal reflecting sphere I have 1kg of matter and 1kg of antimatter. There is a test body orbiting a sphere. Reflecting sphere is very thin so its mass is approx. 0.

(On an aside. Realistically, the box alone must have a mass equal to, or greater than the mass of the contained light, or it will obtain less than zero mass when subjected to the light pressure from within... https://www.physicsforums.com/showthread.php?t=116769")