> It will go upwards, yes, but only because of an upwards velocity.

In this picture, what imparted the upwards velocity to it, given its starting point on the ground?

>> a falling ball [...] in reverse

> it will still be accelerating downward.

It seems strange to ask this of someone with your choice of username, but for the sake of anyone else who is reading along in this thread :

Which way does a freely-falling accelerometer point? [1]

(Ignoring the atmosphere.)

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(But if we don't ignore the atmosphere, in the limit where a smartwatch inside a dropped wall reaches terminal velocity, which way does the accelerometer point? If the smartwatch can move freely within the ball, where does one expect it at terminal velocity, and where does one expect it far from terminal velocity? cf. "vomit comet" [5]).

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[Now make the ball transparent to a broadcast of the accelerometer's reading. Who is "more right" about the interpretation broadcasted value: you standing below and observing it moving ever faster towards terminal velocity, or a skydiver who manages to tuck into a shape that allows her to remain alongside the ball-and-accelerometer for some time at the start of their descent? What do they make of your on-the-ground accelerometer as they are (a) far from terminal velocity, (b) as aerodynamics separates one from the other?]

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I agree that the value of the accelerometer on the ground with you does not change if we run a film of this experiment backwards; it's the only one that should remain effectively constant throughout.

As we take the anti-falling ball from resting on the ground -- can we agree its accelerometer will be at the ground-facing end of the ball, and that it will have the same reading as your always-on-the-ground accelerometer? -- to a drop balloon hovering kilometres overhead, what do you expect the direction of the accelerometer to be? How does the magnitude evolve, approximately? (In the human-time direction, experimenter lifts the ball off the floor of the gondola of the balloon, carries it to the door, extends her arm, and drops the ball. The ball falls and eventually crashes onto the ground right beside you. Let's pretend we absorb bounces and avoid bursts and breaks of the ball resp. accelerometer inside the ball.)

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> It is velocity that switches signs

(with the caveat that we are supposing that we are working with a family of systems of coordinates, and coordinate velocity, and a way for all parties to measure that; or that everything is moving slowly with respect to light and aren't aiming for maximal precision, so don't engage Pound-Rebka and similar results if we want to measure spectroscopically rather than kinematically (or astrometrically, per IAU [2]) [3]. More generally, velocity can get really complicated especially when we are dealing with a system in which matter's coupling to gravitation is what's under study.)

Taking a different view, Baez says, "In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime."[4] and I find it hard to disagree.

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[1] If you have an iPhone or iPad, I highly recommend https://phyphox.org/ and a case like https://griffintechnology.com/survivor and a visit to a grassy or snowy park where you can give your device a good hard throw (or e.g. climb a tall tree or form a human pyramid and drop it). Don't rely solely on gedanken experiments or search-engine results. Go measure! What a pity Einstein didn't have these tools for his jumping-off-a-roof, and that Newton didn't for his apple tree.

You'll want to consider https://phyphox.org/experiment/acceleration-with-g/#more-680

[2] Soffel et al. The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement. Astron. J. 126(2003), 2687–2706 ( https://arxiv.org/abs/astro-ph/0303376 ).

[3] Lindegren, Dravins. The fundamental definition of ‘radial velocity’. Astron. Astrophys. 401(2003), 1185–1202 ( https://arxiv.org/abs/astro-ph/0302522 ).

[4] http://math.ucr.edu/home/baez/einstein/node2.html

[5] For example https://www.youtube.com/watch?v=i2KrEH-8lJw https://www.youtube.com/watch?v=O9XtK6R1QAk