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IANAP, but that argument strikes me as circular - you are presupposing that inertia works the way we are used to in order to figure out which astronaut is rotat

by danbruc 11y ago

IANAP, but that argument strikes me as circular - you are presupposing that inertia works the way we are used to in order to figure out which astronaut is rotating. But imagine two astronauts in empty space and let's turn one upside down stacking them head to head, or helmet to helmet. Now spin one of them around his vertical axis [1]. The situation looks completely symmetric to both of them. Why should the relative speed of rotation change if one of them extends or retracts his limbs but not if the other one does the same thing? What breaks the symmetry of the situation in absence of any other matter in the universe that could be used as a preferred frame of reference for defining spinning versus being at rest? [1] I am not sure if you could do that, but I tend to say no. One of the astronauts would have to try to spin the other one which should make himself spin in the opposite direction, conservation of angular momentum. Ad hoc it seems like you could establish a preferred frame of reference, a frame of zero angular momentum this way.

ISL 11y ago
As a thought experiment, you can certainly arrange whatever initial conditions you like. We already discarded the rest of the universe, after all. You're absolutely correct that I'm assuming the current understanding of how inertia works. It would be fascinating if we were to somehow perform the experiment and didn't get the usual result. Your symmetry argument is excellent and well-stated. I have no complete counter. To extend the argument: If just one astronaut is in an otherwise empty universe, can she tell whether or not she is spinning at 100 RPM by extending her arms to sense centrifugal force? The usual laws of physics would say that she can. A laser-gyro should work too. I think Mach would guess that she can't. Because I can't make an empty universe, I don't know how to do the experiment, but it's interesting to ponder.
tbabb 11y ago
One astronaut (the spinning one) will detect a centrifugal force, and the other will not. If the spinning astronaut took a yo-yo out of her pocket, she would observe it accelerates radially away from her. The stationary astronaut's yo-yo would drift freely with no acceleration. Edit: See: https://en.wikipedia.org/wiki/Bucket_argument https://en.wikipedia.org/wiki/Bucket_argument
- danbruc 11y ago
  The yo-yo is no different than extending and retracting limbs, it presupposes inertia as we know it. Why should the two yo-yos behave differently if the situation is totally symmetric?
  - tbabb 11y ago
    I am not sure what point you are trying to make or what you are asserting is being "presupposed". What is described above are the results of an experiment. That's the way physics works; that's what will happen if you do the experiment. No suppositions needed. The situation is not totally symmetric: The yo-yo behaves differently for the spinning astronaut than it does for the stationary one. That is why the article is wrong; the two situations are measurably different, not equivalent.
    - danbruc 11y ago
      You are missing the point. This is not an experimental fact because we have no empty universe at hand to do it. Two cylinders spinning relative to each other around a common axis in otherwise empty three-dimensional Euclidean space are totally symmetric. Or how would you tell which one is spinning? It is as meaningless to speak about the rotation of one of the cylinders as it is meaningless to speak about the velocity of a single object.
      - tbabb 11y ago
        Ah, I think I see what you are hung up on. In newtonian mechanics, the equivalence principle says that any two inertial coordinate frames look "the same". For example, if you have two spaceships heading toward each other, the picture looks "the same" as if you pretend that one spaceship is stationary and the other is moving twice as fast, or vice versa. This is not true only of geometric relationships, but also for the laws of physics: If you choose to view things in coordinate frame A, and apply the same laws of physics, you will still get the same predicted motion as if you had done the calculation in coordinate frame B. There is no experiment that can tell you which frame is "moving", because you always get the same answer. With your example of two rotating bodies, it is true that the picture looks geometrically "the same" if we pick a different rotating reference frame. The problem is that the laws of physics do not look "the same" under this transformation. If I choose a coordinate frame where the spinning astronaut is stationary, and I try to predict what will happen using the laws of physics of the original frame, I will get wrong results-- the motion of the yo-yo will look "unphysical" for a stationary system. So when you change between rotating and stationary coordinate frames, the laws of physics change too. That means I can tell whether I am in an "absolutely rotating" coordinate frame by doing tests to measure the laws of physics (i.e. are there coriolis and centrifugal forces acting on me?), without any reference to some other, external frame. So the fundamental question is under what circumstances the picture looks "the same". In both cases, geometric relationships are equivalent, but in only one of the cases are the laws of physics also equivalent. The original article lied by saying the laws of physics are the same in the rotating case, and that is simply not true. Does that make sense?

by danbruc 11y ago

ISL 11y ago

As a thought experiment, you can certainly arrange whatever initial conditions you like. We already discarded the rest of the universe, after all. You're absolutely correct that I'm assuming the current understanding of how inertia works. It would be fascinating if we were to somehow perform the experiment and didn't get the usual result. Your symmetry argument is excellent and well-stated. I have no complete counter. To extend the argument: If just one astronaut is in an otherwise empty universe, can she tell whether or not she is spinning at 100 RPM by extending her arms to sense centrifugal force? The usual laws of physics would say that she can. A laser-gyro should work too. I think Mach would guess that she can't. Because I can't make an empty universe, I don't know how to do the experiment, but it's interesting to ponder.

tbabb 11y ago

One astronaut (the spinning one) will detect a centrifugal force, and the other will not. If the spinning astronaut took a yo-yo out of her pocket, she would observe it accelerates radially away from her. The stationary astronaut's yo-yo would drift freely with no acceleration. Edit: See: https://en.wikipedia.org/wiki/Bucket_argument https://en.wikipedia.org/wiki/Bucket_argument

danbruc 11y ago
The yo-yo is no different than extending and retracting limbs, it presupposes inertia as we know it. Why should the two yo-yos behave differently if the situation is totally symmetric?
- tbabb 11y ago
  I am not sure what point you are trying to make or what you are asserting is being "presupposed". What is described above are the results of an experiment. That's the way physics works; that's what will happen if you do the experiment. No suppositions needed. The situation is not totally symmetric: The yo-yo behaves differently for the spinning astronaut than it does for the stationary one. That is why the article is wrong; the two situations are measurably different, not equivalent.
  - danbruc 11y ago
    You are missing the point. This is not an experimental fact because we have no empty universe at hand to do it. Two cylinders spinning relative to each other around a common axis in otherwise empty three-dimensional Euclidean space are totally symmetric. Or how would you tell which one is spinning? It is as meaningless to speak about the rotation of one of the cylinders as it is meaningless to speak about the velocity of a single object.
    - tbabb 11y ago
      Ah, I think I see what you are hung up on. In newtonian mechanics, the equivalence principle says that any two inertial coordinate frames look "the same". For example, if you have two spaceships heading toward each other, the picture looks "the same" as if you pretend that one spaceship is stationary and the other is moving twice as fast, or vice versa. This is not true only of geometric relationships, but also for the laws of physics: If you choose to view things in coordinate frame A, and apply the same laws of physics, you will still get the same predicted motion as if you had done the calculation in coordinate frame B. There is no experiment that can tell you which frame is "moving", because you always get the same answer. With your example of two rotating bodies, it is true that the picture looks geometrically "the same" if we pick a different rotating reference frame. The problem is that the laws of physics do not look "the same" under this transformation. If I choose a coordinate frame where the spinning astronaut is stationary, and I try to predict what will happen using the laws of physics of the original frame, I will get wrong results-- the motion of the yo-yo will look "unphysical" for a stationary system. So when you change between rotating and stationary coordinate frames, the laws of physics change too. That means I can tell whether I am in an "absolutely rotating" coordinate frame by doing tests to measure the laws of physics (i.e. are there coriolis and centrifugal forces acting on me?), without any reference to some other, external frame. So the fundamental question is under what circumstances the picture looks "the same". In both cases, geometric relationships are equivalent, but in only one of the cases are the laws of physics also equivalent. The original article lied by saying the laws of physics are the same in the rotating case, and that is simply not true. Does that make sense?