When did objects stop falling down from gravity? Or is this some hairsplitting about how gravity takes effect by pulling instead of pushing?
But the difference is important: when you are falling down, you are in freefall, you don't experience any acceleration in spacetime. 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.
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.
What if we replace the Earth in that scenario with another person? Alice and Bob are in empty space both in free fall. They each measure the relative velocity of the other and find that it is zero.
Sometime later they again measure relative velocity and now it is non-zero. Each sees that the other is now moving toward them.
Sometime later they measure again, and see that other is moving toward them even faster.
Since they are both in free fall, by your argument neither is experiencing any acceleration. But if no one is experiencing acceleration where do the velocity changes come from?
The proper "a" here in F=ma is the time derivative of four-velocity or spacetime velocity, and that is constant. It's c (the speed of light). Its time derivative is zero; hence no force and no acceleration.
Yes, this gets tricky because you have to care about "the speed of time through time." Welcome to general relativity.
The answer here goes into more detail:
https://physics.stackexchange.com/questions/102910/why-would...
When the two people are far away from each other, they are both moving along through space time, having a speed that is, say, 1m/s through space, each towards the other, and (c-1) m/s in the time direction, both oriented towards the future. As they get close enough to each other, spacetime gets curved by their mass-energy, such that the direction of "the future" now points towards their shared center of mass. If we project this curvature back onto the flat plain in which they were originally moving, it will look as if their direction of movement has changed and their speed through space has increased, while their speed through time has decreased.
Gravity is the curvature of Space Time. From that perspective, objects under gravity are traveling in a straight line.
Fun Veritasium video on the topic: https://www.youtube.com/watch?v=p1W0dpunOaM
By contrast, if you strap a rocket to the box, it's quite easy to measure the acceleration from within the box.
To argue that the acceleration exists because the position changes is to assume that the observer's reference frame is somehow the correct one, and Einstein has showed us that that's a problematic assumption.