B What is the distinction between the Weak and Strong Equivalence Principles?

[Shirish]

I'm reading Carroll's GR book. I'm able to follow the introduction so far, but a couple of paragraphs are a bit hard to decipher:

According to the WEP, the gravitational mass of the hydrogen atom is therefore less than the sum of the masses of its constituents; the gravitational field couples to electromagnetism (which holds the atom together) in exactly the right way to make the gravitational mass come out right.

What exactly does "couples to" mean? Right now that's just a vague phrase to me that implies gravitational field has something to do with EM - but what's the precise notion behind it?

Sometimes a distinction is drawn between "gravitational laws of physics" and "nongravitational laws of physics," and the EEP is defined to apply only to the latter. Then the Strong Equivalence Principle (SEP) is defined to include all of the laws of physics, gravitational and otherwise. A theory that violated the SEP but not the EEP would be one in which the gravitational binding energy did not contribute equally to the inertial and gravitational mass of a body; thus, for example, test particles with appreciable self-gravity (to the extent that such a concept makes sense) could fall along different trajectories than lighter particles.

I have no idea what the statement in bold means at all. Could anyone please explain this so that a layman like me could understand?

 

[Ibix]

What exactly does "couples to" mean?

That the fields interact. If EM did not couple to gravity then light would travel in straight lines and energy stored in EM fields would not be a source of gravity. For any theory of gravity respecting the equivalence principle this cannot happen because you would be able to tell whether you were accelerating in a lift or at rest on a planet by whether light rays curved or not.

I have no idea what the statement in bold means at all. Could anyone please explain this so that a layman like me could understand?

This is easiest to explain in semi-Newtonian terms. The equivalence principle says that the $m$ in $F=ma$ and the one in $F=GMm/r^2$ are the same, because if they weren't you could find a pair of objects which accelerate differently in a gravitational field and drop them to detect the difference between a lift accelerating in space and sitting on a planet.

The Einstein equivalence principle says that EM, strong force and weak force energy contributions to both $m$s are the same. The strong equivalence principle says that all those contributions plus that of gravitational potential contribute the same. So if you believe the EEP and not the SEP you could consider a theory of gravity where a massive object (one with a measurable escape velocity, and hence one with a large amount of gravitational potential change involved in creating it so a large gravitational contribution to one of its $m$) falls on a different trajectory from a light one.

 

[vanhees71]

Well, the Einstein equivalence principle also includes the strong interaction, from which about 98% of the mass of the matter surrounding us is generated.