cmb said:
if you hold your arm out above the floor and let go of an apple, the ground accelerates up to hit it
In a suitable frame, yes.
cmb said:
What is causing the ground to move
"Move" is relative. In a frame in which the apple is at rest, the ground is moving upward. But in a frame in which the ground is at rest, the apple is moving downward. Neither frame has any privileged position; GR says they are both valid. So asking what is causing the ground to move is mistaken, because something that can be made to go away just by changing frames is not something "real" that requires a cause.
The cause of the ground's
proper acceleration (i.e., the fact that standing on the ground feels weight, while the falling apple doesn't) is the fact that the Earth is a solid object with internal pressure, which creates a force that pushes upward on the standing person. There is nothing exerting a force on the apple, so it falls.
cmb said:
if not the rest of the universe underneath the ground is expanding and pushing the floor up?
This is obviously wrong since the force pushing the floor up is not in the same direction across the entire Earth; it's always away from the Earth's center, so if anything were expanding to make the force it would have to be the Earth. If the force were due to the universe expanding, it would be in the same direction across the entire Earth, but it isn't. And the Earth is not expanding, so "expansion" can't be the cause of the force the floor exerts on you when you stand on it.
cmb said:
my understanding is that it is not possible to tell the difference between gravity and an acceleration
More precisely, it is not possible to tell the difference between
being at rest in a gravitational field and
being at rest inside an accelerating rocket in the absence of gravity (or some other source of acceleration). That means that, if you were inside a rocket far out in empty space accelerating at 1 g (i.e., feeling the same weight that you do standing on Earth), and you released an apple, you would not be able to tell from the apple's trajectory (or from the weight you felt) that the rocket was in fact far out in empty space accelerating at 1 g, instead of just sitting at rest on the surface of the Earth.
cmb said:
when all acceleration in the universe reverses, then you would be able to tell the difference
The universe contracting instead of expanding does not mean "all acceleration in the universe reverses". The
acceleration is the same in a contracting universe as in an expanding one. The difference is the
velocity, more precisely the
direction of the velocity.
Basically, a model of a universe that expands, then reaches maximum expansion and starts contracting again, is no different from a ball thrown up from the surface of the Earth at less than escape velocity. The ball rises for a while (corresponding to the expanding phase of the universe), then reaches maximum altitude (corresponding to the universe at maximum expansion), then starts falling (corresponding to the contracting phase of the universe). But the
acceleration of the ball (more precisely, the ball's
coordinate acceleration in a frame in which the Earth is at rest) is the same all the time--towards the Earth.
Note, btw, that I said
coordinate acceleration just now. The ball is in free fall, so it has zero
proper acceleration--it doesn't feel any weight. In GR, the concept of proper acceleration is considered much more useful (because it's an invariant, unlike coordinate acceleration which can be made to go away by changing coordinates). But in any case, since the term "acceleration" can have two possible meanings, it's important to be clear about which one you're talking about.
Note also that the model of a universe that I described above does not apply to our universe according to our best current knowledge; our universe will never stop expanding and start contracting. It will keep expanding forever.
