Do all observers agree on gravitational mass?

[nickyrtr]

If I understand right, GR says that internal motions in an object add to its gravitational mass, because there is associated kinetic energy. My question is, do all observers agree on the quantity of gravitational mass?

To an observer far away from the object, the object's internal motions would appear slower due to gravitational time dilation, so wouldn't the distant observer assign the object a lower internal kinetic energy than another observer deep in its gravity well? If so, do the two observers each measure a different gravitational mass, or does some other effect cancel out the apparent difference in kinetic energy?

 

[Dale]

do all observers agree on the quantity of gravitational mass?

What is gravitational mass? In relativity mass does not gravitate by itself, the whole stress-energy tensor is what causes gravity.

Mass (or energy) is only one component of the stress energy tensor. And no, a single component of a tensor is not invariant.

 

[nickyrtr]

What is gravitational mass? In relativity mass does not gravitate by itself, the whole stress-energy tensor is what causes gravity.

Mass (or energy) is only one component of the stress energy tensor. And no, a single component of a tensor is not invariant.

Thanks for your answer, that is what I am asking. What is the invariant quantity then, is it the trace of the stress energy tensor maybe? or something else?

 

[atyy]

Thanks for your answer, that is what I am asking. What is the invariant quantity then, is it the trace of the stress energy tensor maybe? or something else?

The whole tensor. An observer with 4-velocity v, will see an energy density of T(v,v).

It is possible to make a relativistic theory of gravity in which the trace of the stress-energy tensor is the source of gravity. In such a theory, electromagnetic fields will not generate spacetime curvature, since their stress-energy tensors are traceless. See eg. Nordstrom's second theory. This theory, although mathematically consistent and relativistic, is ruled out by observation.

 

[Passionflower]

This theory, although mathematically consistent and relativistic, is ruled out by observation.

Could you give a reference to one single observation or experiment that indicates that spacetime is curved by an electromagnetic field?

 

[Antiphon]

I donk know if this fits your request but the bending of starlight together with the conservation of momentum implies that starlight pulls on stars via gravity.

 

[Dale]

Thanks for your answer, that is what I am asking. What is the invariant quantity then, is it the trace of the stress energy tensor maybe? or something else?

Yes, the trace of the stress-energy tensor is an invariant scalar, but I don't know if it has a nice convenient interpretation.

 

[JustinLevy]

Could you give a reference to one single observation or experiment that indicates that spacetime is curved by an electromagnetic field?

Based on the previous sentences, I can see how you interpreted it that way, but Atyy was merely saying that the theory while relativistic and mathematically consistent, was ruled out experimentally.

One such example is that the theory predicts an incorrect orbit for Mercury (while GR predicts the correct one).

And as Antiphon argued (at least in the Newtonian limit), it indeed turns out that the theory doesn't have gravity bend starlight either; which goes against experimental evidence.

 

[Ich]

Yes, the trace of the stress-energy tensor is an invariant scalar, but I don't know if it has a nice convenient interpretation.

There's a good paper by http://math.ucr.edu/home/baez/einstein/" . It's the Newton-like source term for gravitation of perfect fluids like dust. Very helpful to understand cosmology.

 

[Passionflower]

I don't know if this fits your request but the bending of starlight together with the conservation of momentum implies that starlight pulls on stars via gravity.

Obviously not.

It is true that starlight is defined as an electromagnetic phenomenon. We can also validly interpret that spacetime must be bent around the Sun based on observation. However based on these observations one can not directly conclude, and those who disagree please correct me with a valid counterargument, that an electromagnetic field bends spacetime.

If one interprets the phenomenon as curved spacetime, then the starlight basically follows a geodesic in that curved spacetime but in no way does it indicate that the starlight 'pulls' as you incorrectly suggest. Starlight 'pulling' in some kind of way is completely incompatible with both a Newtonian or general relativity interpretation.

Based on the previous sentences, I can see how you interpreted it that way, but Atyy was merely saying that the theory while relativistic and mathematically consistent, was ruled out experimentally.

One such example is that the theory predicts an incorrect orbit for Mercury (while GR predicts the correct one).

And as Antiphon argued (at least in the Newtonian limit), it indeed turns out that the theory doesn't have gravity bend starlight either; which goes against experimental evidence.

I am not a word twister and like to get things straight. Hopefully general relativity, which is merely a theory, is not treated here as some kind of a global warming dogma.

Bottom line: Is there one single shred of evidence that electromagnetic fields curve spacetime? If the answer is no, then clearly the poster's statement is incorrect. If you think the answer is yes, then back it up with observation or experiment. That is how science works!

Don't write that something is empirically verified if it is not!

 

[nickyrtr]

The whole tensor. An observer with 4-velocity v, will see an energy density of T(v,v)...

What about the integral of energy density over volume? T_00 changes with observer velocity, but does the measure of the integral (dV) also change (inversely) so that the total mass-energy is invariant?

 

[Dale]

What about the integral of energy density over volume? T_00 changes with observer velocity, but does the measure of the integral (dV) also change (inversely) so that the total mass-energy is invariant?

Energy is not invariant. Even in Newtonian mechanics you find that energy is frame variant.

 

[JustinLevy]

Starlight 'pulling' in some kind of way is completely incompatible with both a Newtonian or general relativity interpretation.

I'm not sure where that comment is coming from. Let us hopefully agree at least on the predictions of GR, which as mentioned earlier is that EM energy can curve spacetime according to GR. So this isn't "completely incompatible" with GR; actually it is more than compatible with GR, as GR actually require it.

If the only contribution to the stress-energy tensor was from energy in electromagnetic fields, then the trace would be zero and hence the Ricci curvature scalar would be zero. But the Ricci curvature tensor would be non-zero (and would actually be directly proportional to the stress-energy tensor in this case).

Bottom line: Is there one single shred of evidence that electromagnetic fields curve spacetime?

I would argue yes. But I'm not sure if you'd consider the evidence direct enough. The Cavendish experiment has been performed with many different kinds of materials. They all gave consistent results. Considering the electromagnetic energy contribution to the mass of a proton or nuclei in general is non-negligible on at least the part per thousand level, all one needs to do is compare the results from using a neutron rich material to proton rich material of the same weight. Such precision has only been recently available. The Eot-Wash group has done many precision torsion balance experiments, and have even explicitly chosen materials to get a range of N/Z ratios.

The force of gravity from even a 1kg chunk of material is hard to measure. I, as I'm sure many other people here, had to reproduce the Cavendish experiment at one point for school. It is very tedious. It really made me appreciate how weak gravity is. So hopefully such torsion balance experiments are direct enough for you, because I'm not aware of any other means of measurement of a chosen object in the lab "sourcing" gravity.

If there is a nicer way of using experimental evidence to constrain this, I'd love to hear it. The weak-equivalence principle has be _very_ stringently verified (something like parts per trillion). So using that in conjunction with other experiments may yield the desired example. I'd have to think about it some more though, as nothing pops to mind right now.

 

[Passionflower]

Let us hopefully agree at least on the predictions of GR, which as mentioned earlier is that EM energy can curve spacetime according to GR.

We agree on that. GR indeed predicts that. But obviously that does not make it automatically true, only the observation and experiment can verify that, after all there is a distinct difference between a scientific theory and a religious dogma.

I would argue yes. But I'm not sure if you'd consider the evidence direct enough. The Cavendish experiment has been performed with many different kinds of materials. They all gave consistent results. Considering the electromagnetic energy contribution to the mass of a proton or nuclei in general is non-negligible on at least the part per thousand level, all one needs to do is compare the results from using a neutron rich material to proton rich material of the same weight. Such precision has only been recently available. The Eot-Wash group has done many precision torsion balance experiments, and have even explicitly chosen materials to get a range of N/Z ratios.

The force of gravity from even a 1kg chunk of material is hard to measure. I, as I'm sure many other people here, had to reproduce the Cavendish experiment at one point for school. It is very tedious. It really made me appreciate how weak gravity is. So hopefully such torsion balance experiments are direct enough for you, because I'm not aware of any other means of measurement of a chosen object in the lab "sourcing" gravity.

If there is a nicer way of using experimental evidence to constrain this, I'd love to hear it. The weak-equivalence principle has be _very_ stringently verified (something like parts per trillion). So using that in conjunction with other experiments may yield the desired example. I'd have to think about it some more though, as nothing pops to mind right now.

I hope you are not mixing up relativistic mass with rest mass here.

If I understand right, GR says that internal motions in an object add to its gravitational mass, because there is associated kinetic energy. My question is, do all observers agree on the quantity of gravitational mass?

What else is increased mass due to internal motions than increased relativistic mass?

 

[atyy]

What about the integral of energy density over volume? T_00 changes with observer velocity, but does the measure of the integral (dV) also change (inversely) so that the total mass-energy is invariant?

Ouside a spherically symmetric mass, the metric is vacuum Schwarzschild with mass parameter M. By matching boundary conditions inside and outside the mass, M is an integral over "stuff" inside the mass. However, as Schutz (chapter 10) says, this analogy to Newtonian gravity is somewhat deceptive, since the volume element in the integral is anot an element of proper volume. http://books.google.com/books?id=qhDFuWbLlgQC&dq=schutz+relativity&source=gbs_navlinks_s

In the 3+1 formulation of GR, there is a mass called the ADM mass, but that includes the mass of gravity, not just of matter. A couple of interesting references about "mass" in GR:
http://arxiv.org/abs/1001.5429
http://arxiv.org/abs/0912.4001