Does energy alone contribute to spacetime curvature?

[e2m2a]

Do Einstein's field equations explicitly show that energy alone can curve the metric of spacetime? True, energy is included in the stress-energy tensor, but is it assumed that energy in of itself curves spacetime? Or, is it possible that only energy "embedded" in mass contributes to curvature? The tensor also includes stress and pressure, but could we imagine stress or pressure without a mass to contain it? I think that would be impossible. Could we assert then that stress or pressure alone curves spacetime? I think it must be assumed that stress or pressure must manifest within existing mass in order for stress or pressure to contribute to curvature. So, is it possible that the same restriction applies to energy?

 

[bcrowell]

Or, is it possible that only energy "embedded" in mass contributes to curvature?

This isn't what the Einstein field equations say. If you wanted to construct an alternate theory with such a requirement, you would have to define your terms rigorously and translate them into mathematics. You would also have to avoid contradicting all the previous experimental tests of general relativity.

The tensor also includes stress and pressure, but could we imagine stress or pressure without a mass to contain it? I think that would be impossible.

An electromagnetic wave is a counterexample that shows that it is possible.

 

[Antiphon]

All three bend spacetime; mass, energy, pressure (aka stress aka force per unit area.). As noted elsewhere a hot rock creates more gravity than a cold rock. A wound spring is heavier than (the same) loose spring.

A more interesting question is this: two negative charges are pushed very close together and held there by a special "bracket.". There is a stress in the bracket and equal stress in:
a) the field between the charges
b) the field immediately surrounding each charge
c) the stress is concentrated over the volume of the charge only

 

[e2m2a]

This isn't what the Einstein field equations say. If you wanted to construct an alternate theory with such a requirement, you would have to define your terms rigorously and translate them into mathematics. You would also have to avoid contradicting all the previous experimental tests of general relativity.


An electromagnetic wave is a counterexample that shows that it is possible.

Mmm. I know there is a controversy over the magnitude of the vacuum energy. Some critics of the zpe say it would be impossible according to some estimates of its magnitude because that amount of energy according to GR would collapse spacetime into a little ball. Is it possible that given: the vacuum does contain an enormous energy density and the fact that spacetime has not collapsed, that this is an indication that the energy in the Stress-Energy tensor cannot be applied alone to deterimine curvature?

 

[JesseM]

Mmm. I know there is a controversy over the magnitude of the vacuum energy. Some critics of the zpe say it would be impossible according to some estimates of its magnitude because that amount of energy according to GR would collapse spacetime into a little ball. Is it possible that given: the vacuum does contain an enormous energy density and the fact that spacetime has not collapsed, that this is an indication that the energy in the Stress-Energy tensor cannot be applied alone to deterimine curvature?

There's apparently no reliable way to do a theoretical calculation of the magnitude of the vacuum energy (as opposed to 'measuring' it using the assumption that it's the same as the 'dark energy' causing the expansion of the universe to accelerate) without having a theory of quantum gravity--see here for a discussion.

 

[e2m2a]

There's apparently no reliable way to do a theoretical calculation of the magnitude of the vacuum energy (as opposed to 'measuring' it using the assumption that it's the same as the 'dark energy' causing the expansion of the universe to accelerate) without having a theory of quantum gravity--see here for a discussion.

Thank you for the reference. It was an interesting article. I see there really isn't a definite answer to any of this. One of the great mysteries of the cosmos. It may never be answered conclusively because of the rift between general relativity and quantum field theory.
But I have a grand unified theory. Here it is:

Laws of the universe = (a x general relativity) + (b x quantum mechanics)

where:
for very big things, a = 1 and b = 0;
for very small things, a = 0 and b = 1;

Seriously, maybe general relativity and quantum physics will never be unified because of philosophical reasons. General relativity is a deterministic theory. Quantum physics is a probabilistic theory. Not only are the scales of the domains of study on opposite ends, but the philosophical approach are at extreme ends. Could we have a determinism based on probability or probability based on determinism? I think not. Maybe reality has not only a wave-particle duality, but also a deterministic-probability causality duality-- simultaneously. That was a mouthful.