4 ms·

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 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 ;)

qubitcoder 7mo ago
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.
- marcus_holmes 7mo ago
  Yes, because there is no way of differentiating between acceleration and gravity. Which was my point.
p1mrx 7mo ago
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.
- marcus_holmes 7mo ago
  I am standing on the ground. I feel 1G acceleration. My speed is not changing. How much am I accelerating?
  - hcs 7mo ago
    You are more quickly being carried by the ground further from where you would otherwise be. Hope that clears it up.
    - marcus_holmes 7mo ago
      Not really, no. The ground isn't moving. I'm not moving. I get that if the ground wasn't there, I would be moving, but that's not the same thing, I think? Like I said in another response, I have always been told that acceleration is change in velocity over time. If my velocity is not changing, I don't understand how I'm accelerating? I do understand that gravity exerts a force that is indistinguishable from acceleration, which was my original point. But that doesn't mean it is acceleration.
  - brabel 7mo ago
    You say later that you think gravity and acceleration look the same but cannot be the same , which is funny since that’s exactly what relativity says: if two things are indistinguishable from each other even in principle, then they must be the same. Which is what led Einstein to realize that gravity really is just a curvature in space time. Hard to wrap your head around that! But if you study relativity, you eventually understand what being relative actually means.
  - tsimionescu 7mo ago
    You need to take into account your entire 4-vector for speed. You don't just have a speed in the 3 spatial coordinates, you're also moving thorough the "time" coordinate, and that is happening at a slower pace near a large mass like the Earth than it would of you were far away from here.
  - layer8 7mo ago
    Your speed relative to what? There is no absolute speed. Relative to an inertial rest frame, you're accelerating upwards at 1G, which is what you are feeling and what an accelerometer is measuring. Of course, relative to the non-inertial reference frame of the ground, your speed doesn't change.
- JumpCrisscross 7mo ago
  > According to general relativity, you (and the ground) are accelerating at 1g I don't believe this is correct. If I lock two rockets in opposition to each other, they aren't accelerating. They're pushing at each other. And their propellant is accelarating away. But their displacement and orientation are unchanging, which means their velocity is zero which means acceleration isn't happening. Similarly, the normal force resists your gravitational force to produce zero net acceleration. (An object at rest in a gravity well is its own local frame.) > If you jump off a cliff, you'll stop accelerating for a bit, until the ground hits you I don't believe this is correct. In GR, free fall is still inertial motion. You're just free of fictitious forces and thus following the curvature of spacetime.
  - tsimionescu 7mo ago
    It is correct, and you're also right that two rockets tethered to each other would not feel acceleration. The acceleration we feel in Earth's gravitational field is affecting our speed, though - it's slowing down the speed at which we move towards the future.
    - JumpCrisscross 7mo ago
      > you're also right that two rockets tethered to each other would not feel acceleration I just realized that the energy of the exhaust would warp local spacetime. So one might feel acceleration depending on how that geometry settles.
  - ben_w 7mo ago
    As I understand it, in GR acceleration is indistinguishable* from gravity, so while you're on the ground feeling 1 gee, you're being accelerated up at 1 gee, and so is the ground. When you're in free-fall, that's when you're in a non-accelerating frame, even though a non-relativistic description** would say that you are, in fact, accelerating. Caveat: I only do physics as a hobby, neither academically nor professionally, so take with appropriate degree of doubt. * for point-like observers at least ** ignoring rotation and curved orbits
BDPW 7mo ago
You're conflating coordinate and proper acceleration.
- marcus_holmes 7mo ago
  I don't think I understand the difference. I have always been told that acceleration is change in velocity over time. Is that wrong? Are there other types of acceleration?
  - magicalhippo 7mo ago
    > I have always been told that acceleration is change in velocity over time. Is that wrong? Not per se, but it's more complicated when relativity gets involved. Wikipedia has some decent starting points: https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_acceleration https://en.wikipedia.org/wiki/Proper_acceleration https://en.wikipedia.org/wiki/Four-acceleration https://en.wikipedia.org/wiki/Four-acceleration
adrian_b 7mo ago
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.

qubitcoder 7mo ago

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.

marcus_holmes 7mo ago
Yes, because there is no way of differentiating between acceleration and gravity. Which was my point.

p1mrx 7mo ago

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.

marcus_holmes 7mo ago
I am standing on the ground. I feel 1G acceleration. My speed is not changing. How much am I accelerating?
- hcs 7mo ago
  You are more quickly being carried by the ground further from where you would otherwise be. Hope that clears it up.
  - marcus_holmes 7mo ago
    Not really, no. The ground isn't moving. I'm not moving. I get that if the ground wasn't there, I would be moving, but that's not the same thing, I think? Like I said in another response, I have always been told that acceleration is change in velocity over time. If my velocity is not changing, I don't understand how I'm accelerating? I do understand that gravity exerts a force that is indistinguishable from acceleration, which was my original point. But that doesn't mean it is acceleration.
- brabel 7mo ago
  You say later that you think gravity and acceleration look the same but cannot be the same , which is funny since that’s exactly what relativity says: if two things are indistinguishable from each other even in principle, then they must be the same. Which is what led Einstein to realize that gravity really is just a curvature in space time. Hard to wrap your head around that! But if you study relativity, you eventually understand what being relative actually means.
- tsimionescu 7mo ago
  You need to take into account your entire 4-vector for speed. You don't just have a speed in the 3 spatial coordinates, you're also moving thorough the "time" coordinate, and that is happening at a slower pace near a large mass like the Earth than it would of you were far away from here.
- layer8 7mo ago
  Your speed relative to what? There is no absolute speed. Relative to an inertial rest frame, you're accelerating upwards at 1G, which is what you are feeling and what an accelerometer is measuring. Of course, relative to the non-inertial reference frame of the ground, your speed doesn't change.
JumpCrisscross 7mo ago
> According to general relativity, you (and the ground) are accelerating at 1g I don't believe this is correct. If I lock two rockets in opposition to each other, they aren't accelerating. They're pushing at each other. And their propellant is accelarating away. But their displacement and orientation are unchanging, which means their velocity is zero which means acceleration isn't happening. Similarly, the normal force resists your gravitational force to produce zero net acceleration. (An object at rest in a gravity well is its own local frame.) > If you jump off a cliff, you'll stop accelerating for a bit, until the ground hits you I don't believe this is correct. In GR, free fall is still inertial motion. You're just free of fictitious forces and thus following the curvature of spacetime.
- tsimionescu 7mo ago
  It is correct, and you're also right that two rockets tethered to each other would not feel acceleration. The acceleration we feel in Earth's gravitational field is affecting our speed, though - it's slowing down the speed at which we move towards the future.
  - JumpCrisscross 7mo ago
    > you're also right that two rockets tethered to each other would not feel acceleration I just realized that the energy of the exhaust would warp local spacetime. So one might feel acceleration depending on how that geometry settles.
- ben_w 7mo ago
  As I understand it, in GR acceleration is indistinguishable* from gravity, so while you're on the ground feeling 1 gee, you're being accelerated up at 1 gee, and so is the ground. When you're in free-fall, that's when you're in a non-accelerating frame, even though a non-relativistic description** would say that you are, in fact, accelerating. Caveat: I only do physics as a hobby, neither academically nor professionally, so take with appropriate degree of doubt. * for point-like observers at least ** ignoring rotation and curved orbits

BDPW 7mo ago

You're conflating coordinate and proper acceleration.

marcus_holmes 7mo ago
I don't think I understand the difference. I have always been told that acceleration is change in velocity over time. Is that wrong? Are there other types of acceleration?
- magicalhippo 7mo ago
  > I have always been told that acceleration is change in velocity over time. Is that wrong? Not per se, but it's more complicated when relativity gets involved. Wikipedia has some decent starting points: https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_acceleration https://en.wikipedia.org/wiki/Proper_acceleration https://en.wikipedia.org/wiki/Four-acceleration https://en.wikipedia.org/wiki/Four-acceleration

adrian_b 7mo ago

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.