> It is the surface of the earth that is experiencing acceleration towards you.
This is failing to click with me. If me and my buddy on the opposite side of the world jump out of a plane at the same time the situation doesn't make sense if you say we aren't experiencing acceleration, the surface is accelerating towards us. That'd have it accelerating in two different directions.
On the other hand saying we are each accelerating towards the earth makes perfect sense with our two vectors converging on the same point.
Sorry, I was completely wrong in my explanation, and in what I thought was happening. You are completely right that the Earth of course can't simultaneously be accelerating towards both people.
The correct explanation is that there is no acceleration happening at all. The increase in speed through space is compensated by a decrease in speed through time. It can be looked at as Earth's mass bending spacetime such that "the future" for any nearby object points towards the center of the Earth. You are moving along at constant speed in a straight line towards the future, as you always do when you are not otherwise accelerated in some other direction, but because of the curvature of spacetime around the mass of the Earth, that "straight line" is pointed towards the center of the Earth (it's only a slight curvature: you're still moving much, much faster towards the future than towards the Earth).
Equivalently, we could say that there is no change in velocity: the speed increase is compensated by time dilation. The closer you are to the center of the Earth, the slower your clock ticks; if your speed is constant as measured with a clock high above the earth, it will appear to increase as your clock gets slower. Say you are moving at 1m/s as measured from outside the gravity well. Say that at some altitude inside the gravity well, when your clock shows 1 second has passed, 2 seconds passed according to the original clock. Since your speed is constant, you will have moved 2 meters in the 2 seconss, but you will experience this as moving 2m in one second. When you go deeper down, say your clock now shows one second has passed for every 3s in the original clock: now you moved 3m in 1 of your seconds, even though you're still moving at 1m/s with the original seconds. So you will think your speed is increasing, when in fact it's just your clock getting slower.
Of course, this second explanation doesn't help explain why you're moving towards the center of the Earth and not standing still relative to the earth or some other direction, so the first explanation is still better.
This is failing to click with me. If me and my buddy on the opposite side of the world jump out of a plane at the same time the situation doesn't make sense if you say we aren't experiencing acceleration, the surface is accelerating towards us. That'd have it accelerating in two different directions.
On the other hand saying we are each accelerating towards the earth makes perfect sense with our two vectors converging on the same point.