Gravity and Inertia: Similar but not Equivalent

[Ontophobe]

I just heard something that made me realize I was taking the equivalence principle way too literally. If I were in a windowless room, and was standing on its floor, then there is, in principle, a performable experiment by which I could determine whether I was moving upward at 1 g of acceleration, or whether I was standing on a massive body generating 1 g of gravity. I always thought such an experiment was impossible, but gravity causes tidal forces while acceleration doesn't. Or does it? Are they equivalent or not?

 

[David Lewis]

It depends on how big your room is, and how long the experiment is carried out (for a given level of precision of the measuring instruments).

Lines of gravitational force are not parallel, and gravitational field strength drops off as altitude increases.

 

[Dale]

gravity causes tidal forces while acceleration doesn't

This is one place where the difference between pop-sci sources and professional sources becomes important. Any professional source would specify that the region of space and time covered by the room and its experiments must be small enough that tidal gravity is undetectable. Pop-sci sources usually neglect that detail in order to get to the splashy stuff.

 

[PeterDonis]

I just heard something

Where?

If I were in a windowless room, and was standing on its floor, then there is, in principle, a performable experiment by which I could determine whether I was moving upward at 1 g of acceleration, or whether I was standing on a massive body generating 1 g of gravity.

What experiment?

 

[A.T.]

gravity causes tidal forces while acceleration doesn't.

Non-uniform gravity does. The equivalence applies to uniform gravity.

 

[haushofer]

The keyword here is 'local'. Locally in spacetime a gravitational field can be described by an observer as if he/she is accelerating.

 

[stevendaryl]

I just heard something that made me realize I was taking the equivalence principle way too literally. If I were in a windowless room, and was standing on its floor, then there is, in principle, a performable experiment by which I could determine whether I was moving upward at 1 g of acceleration, or whether I was standing on a massive body generating 1 g of gravity. I always thought such an experiment was impossible, but gravity causes tidal forces while acceleration doesn't. Or does it? Are they equivalent or not?

Well, if you're standing on a planet, there are two relevant properties of the gravitational field: (1) The acceleration due to gravity at your location, and (2) how the acceleration due to gravity changes with location. Sufficiently precise measurements can you tell you both properties, but the most immediately striking effects of gravity only involve (1). You drop something, it accelerates to the floor. You shoot a light beam straight up, and it undergoes gravitational redshift. You move a clock to the top of a mountain, and it undergoes gravitational time dilation. These effects don't depend on (2). Any effect that only depends on the strength of gravity at a point, as opposed to its variation with location, can't distinguish the gravity of a planet and the "pseudo-gravity" of an accelerating rocket. Measurements of the variation of gravity with location can indeed distinguish these cases (because precise measurements of the variation with location tells you the spacetime curvature, which in turn tells you about the presence of gravitating matter).

 

[David Lewis]

Also (in the case of a rocket ship whose mass is not enormous compared to yours) every time you jump up and down in the ship, the force on test objects will be momentarily reduced.

 

[Janus]

I just heard something that made me realize I was taking the equivalence principle way too literally. If I were in a windowless room, and was standing on its floor, then there is, in principle, a performable experiment by which I could determine whether I was moving upward at 1 g of acceleration, or whether I was standing on a massive body generating 1 g of gravity. I always thought such an experiment was impossible, but gravity causes tidal forces while acceleration doesn't. Or does it? Are they equivalent or not?

Look at it this way. You are in such a room and do an experiment to test for tidal force between floor and ceiling and come up with a null result. Can you now definitely say that you are accelerating?. What if you are just on a very massive body with a radius that gives it a 1g surface gravity, one so huge, that the gravity difference is between floor and ceiling is too small for you to measure? Even if you increase the sensitivity of your experiment, all you are doing is setting a lower limit to the mass of the body and your distance from the center. No matter how accurately you can measure the tidal force across the room, you can never totally eliminate the possibility that you are simply at rest with respect to a very massive and very distant mass.