How Does Energy Source Curvature? Exploring the EEP

[Frank Castle]

TL;DR Why does the Einstein equivalence principle imply that all forms of (non-gravitational) energy source curvature?

Now, as understand it, the Einstein equivalence principle (EEP) implies (or at least suggests) that gravity is the manifestation of spacetime curvature, the reason being that it is impossible to locally distinguish, through conducting any non-gravitational experiment, between inertial acceleration and acceleration due to the presence of a gravitational field. As a consequence, all non-gravitational forms of energy will fall at the same rate in a gravitational field. This observation suggests that the curved trajectories of energy in a gravitational field is due to geometric nature of spacetime itself, and not due to a force, i.e. spacetime is curved.

We know from Newtonian gravity that mass sources gravity and thus, if gravity is the manifestation of spacetime curvature, the presence of mass must curve spacetime.

I’ve read that the EEP implies that all forms of non-gravitational energy source curvature, but I don’t understand why this is so?

I thought that it was simply due to the consequence of mass-energy equivalence from special relativity that energy sources curvature?!

Is the point that the weak equivalence principle neglects other contributions to mass energy (e.g. electromagnetic binding energy) and so in principle it could be that mass sources curvature, but that the electromagnetic binding energies etc. do not, and so would respond differently in a gravitational field. However, the EEP claims that all forms of energy couple to gravity in the same way and so they must also be considered sources of curvature?!

 

[PeterDonis]

I’ve read that the EEP implies that all forms of non-gravitational energy source curvature

Where did you read this? Please give a reference. (And if the reference is not a textbook or peer-reviewed paper, please be ready to be told that it's not a valid reference and you should go read a textbook or peer-reviewed paper.)

 

[Frank Castle]

Where did you read this? Please give a reference. (And if the reference is not a textbook or peer-reviewed paper, please be ready to be told that it's not a valid reference and you should go read a textbook or peer-reviewed paper.)

Sorry for the delayed response. I’ve been reading these notes on the cosmological constant problem: https://arxiv.org/pdf/1502.05296.pdf

“However, when (classical) gravity is switched on the equivalence principle tells us that all forms of energy curve spacetime[...]”

It’s just a short sentence at the bottom of page 3, but it has left me confused.

 

[SiennaTheGr8]

I thought that it was simply due to the consequence of mass-energy equivalence from special relativity that energy sources curvature?!

Careful here. The equivalence you speak of is between mass and rest energy.

 

[Frank Castle]

Careful here. The equivalence you speak of is between mass and rest energy.

Good point.

So what is the motivation for why all forms of (non-gravitational) energy source curvature? Is it simply that we know from Newtonian gravity that mass sources the gravitational field. If gravity is simply the manifestation of spacetime curvature, then mass must source curvature (locally). Then by the EEP we know that all forms of (non-gravitational) energy must couple to gravity identically (otherwise we would be able to detect whether we are in local uniform acceleration, or in a gravitational field simply by carrying out experiments involving different non-gravitational phenomena), and so these must also source local spacetime curvature?