Practical limit of equivalence principle

Question

The equivalence principle says, for a small elevator, it is not possible to distinguish between a closed elevator moving at a constant acceleration, and the same amount of gravitational acceleration caused by a massive planet.

If an observer is standing on a planet, the g will be constant. But for an elevator, a constant force is needed to maintain a constant acceleration.

That constant force has to be imparted by some kind of practical mechanism.

Suppose the observer puts a weight on a sensitive scale on the floor of the accelerating elevator, and jumps on the floor. Wouldn't the acceleration momentarily change due to reaction, and weight on the scale would fluctuate.

In order for the weight to not fluctuate, the force has to instantaneously adjust to the reaction, and back, when the observer lands back on the floor.

I am not sure if there is any practical mechanism of constant force that would shield this observation?

I guess only practical way, is that the elevator is very very heavy (same mass as the planet in ideal case). In that case, it will cause its own gravity anyway.

So, is the equivalence principle really practical? Say, for human sized elevator, with simple equipment like a scale? Because the observer can cause the weight to fluctuate inside an elevator, but not (equally) on a planet.

I know, by jumping, the original requisite of the equivalence principle is changed. That is why the question is about practicality.

Answer 1

The equivalence principle is a principle that applies over "small" regions of space and time, and it really isn't especially important whether it is practically possible to build an elevator that can provide uniform acceleration (it isn't). There are always going to be ways that you can distinguish between acceleration and a gravitational fields in realistic situations like this - not least when the lift reaches its destination; no need to jump up and down.

If you are interested in how the equivalence principle is tested (not in a lift) then you could look up torsion balances or the more recently proposed space-based missions to test the equivalence principle.(https://en.m.wikipedia.org/wiki/STEP_(satellite). The idea here is to have a satellite with an outer shell and an inner enclosure containing a free-falling test mass. The mass should follow a geodesic, affected only by gravity. The outer shell may (will) experience non-gravitational forces, but these can be corrected by thrusters attached only to the outer shell, in such a manner to keep the shell centred on the inner mass.

I suppose there are still practical problems here. The process of measuring where the test mass is with respect to the shell must be done so that no (net) force is exerted on the mass. Even if you could do this perfectly, the finite size of the equipment means that the gravitational field is not perfectly uniform across it.

Answer 2

Make the elevator bigger and taller than you, and put you in the middle, not touching it. Not touching the walls or the floor.

• It could be sitting on the earth with you falling.
• Or else it could be in space with some rockets on the back end firing away.

How would you tell? That's what the equivalence principle is all about. (Except it's a thought experiment so to make the elevator small you have to imagine making you small, and it also only holds for small amounts of time.)

You wouldn't be able to tell because the general in general relativity says that inertial frames don't have to be global frames, that having global inertial frames just a special case, that only happens sometimes, if ever.

So the inertial frames are the (possibly local) frames that you'd call freely falling. Really they are the frame that aren't accelerating upwards.

You accelerate upwards merely because the pressure on your feet pushes you upwards.