Varying Intensity of Gravitational Field and Equivalence

[Charlie G]

Hi all, I was just looking for some assistance in reconciling the equivalence principle and the varying intensity of the gravitational field. (I'm in high school so go easy on me, I'm just studying Einstein's Relativity for the general reader).

For convenience let's keep with Einstein's example of the man in an intergalactic elevator. When the elevator accelerates with respect to some inertial frame, the man and the other contents are given the same downward acceleration.

Now, for all practical purposes the man is, as Einstein noted, in a gravitational field. But the field of force the man finds is entirely uniform, imbuing objects with the same acceleration throughout the elevator. But in an elevator at rest on the Earth, one could, in principle, measure the differing intensity of the gravitational field at varying points inside the elevator; the intensity of the field being greater at the bottom than at the top for instance.

I understand that at those points, the equivalence principle holds, but because the man can do an experiment (or so I think) to distinguish a field of force produced by a nearby body of mass and a uniform force which occurs when accelerating with respect to inertial frames, how can the two be held as equivalent??

I suppose if we allow Mach's principle to be true, this difficulty disappears, but let's keep to GR for now.

 

[A.T.]

The equivalence principle is about the equivalence between a uniform gravitational field and an uniformlly accelerated frame, not between any field or any acceleration.

 

[Bill_K]

Charlie G, You're right, the elevator in the thought experiment is assumed to be so small that variations in the gravitational field within the elevator are negligible. Otherwise you can say that the equivalence between gravity and acceleration is just at a single point.

 

[Charlie G]

Alright, thanks for clearing that up guys; couldn't read ahead until I understood lol.