Comment by lionkor
4 days ago
Acceleration is change in speed, so it is, by its very nature, relative just like speed is.
If I fall, I might accelerate at G meters per second, relative to the earth, but I don't absolutely accelerate. If the earth decelerates at the same time, I'm now both accelerating an decelerating. It's relative.
It’s absolute in the sense that you can determine your acceleration without any external reference. You feel a certain force (like what you feel in an elevator). That’s your acceleration. You don’t accelerate relative to Earth, or relative to anything else. You accelerate relative to when you wouldn’t be accelerating (your inertial rest frame, a state of free fall).
If you are in space accelerating and the Earth would decelerate (which is just an acceleration in the other direction), you would still feel exactly the same force (minus Earth’s gravity, to the small extent you’d still feel it), and people on the Earth would feel the Earth’s acceleration. (For them it would feel like “down” isn’t perpendicular to the Earth’s surface anymore, or as if the Earth’s surface was tilted.)
When you sit on a chair on Earth, the pressure you feel on your butt is your acceleration upwards. If there was no chair and no ground (and no air), so that you’d be in free fall, that’s when you’d have zero acceleration. Your inertial rest frame is the trajectory you’d take in free fall. When you’re sitting on a chair, or lying in bed, or standing on the ground, you’re accelerating upwards relative to that rest frame, and that’s the pressure you feel on your butt, or on your body, or under your feet.
I am in a gravitational field. I have no idea what my acceleration is, I just know that I feel 1G (I could be falling in a stronger gravity and only feel 1G, or I could be climbing in a weaker gravity and feel 1G). The only way of determining it is to see if I'm moving relative to the stuff around me. Even then, that's not definite - I could be in an elevator and everything around me is also accelerating.
I'm not disagreeing with you, I'm just pointing out that there are circumstances where "you can determine your acceleration without any external reference" isn't true. You might even say that this is relative to your circumstances ;)
If you measure acceleration in a single point, without other information you cannot know whether it is caused by gravitational attraction or by movement that is not rectilinear and uniform.
However, if you measure acceleration in many points, you typically can discriminate the 2 cases, because the spatial variation of the 2 kinds of acceleration fields is normally very different.
If you also move relatively to the local system of reference while measuring acceleration, you have additional distinguishing information from Coriolis forces.
So with enough measurements, gravitational forces and inertial forces can always be separated.
According to general relativity, you (and the ground) are accelerating at 1g, and feel weight because your inertia resists that acceleration. If you jump off a cliff, you'll stop accelerating for a bit, until the ground hits you.
Edit to reply:
> I am standing on the ground. I feel 1G acceleration. My speed is not changing. How much am I accelerating?
You are accelerating at 1g through curved spacetime. Newtonian "speed" behaves strangely in curved spacetime.
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You can always hold an accelerometer in your hand. If you did so now, assuming you're on Earth's surface, it'd register approximately 9.8m/s/s pointing in the upward direction.
You could also perform one of many historical experiments, such as dropping an object from an elevated height with careful timing, or rolling a round ball down a gently sloped track, and so on.
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You're conflating coordinate and proper acceleration.
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That is not correct. There is no upward acceleration causing the 1G felt in a chair on Earth.
There is in general relativity: https://en.wikipedia.org/wiki/Proper_acceleration
"Similarly, standing on a non-rotating planet (and on earth for practical purposes) observers experience an upward proper-acceleration due to the normal force exerted by the earth on the bottom of their shoes."
"You feel a certain force" is that true in zero-g?
Yes
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Think of it more as "speed is the indefinite integral of acceleration" with the extra constant denoting a choice of inertial reference frame.