3 ms·

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

by 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?

danbruc 11y ago
We are getting closer. You are essentially saying that we can have geometrically indistinguishable states that are physically different. We can have an astronaut with a yo-yo hanging down and one with a yo-yo extending straight away while the world otherwise looks exactly the same to both of them. Both astronauts have to go through the same change in angular velocity just in opposite directions to get to the same state as the other one but one would see the yo-yo dropping down while the other one will see it rising. How does that make sense? What is so special about the one coordinate frame without centrifugal forces? With respect to what is the astronaut not rotating? Note that nothing looks unphysical here, just different but without any obvious thing that justifies the difference. And I am definitely not trying to say I am right and you are wrong, it just doesn't look consistent to me to have centrifugal forces in an empty universe.
- tbabb 11y ago
  The short answer (i.e. without teaching all of Phys 101 in this comment) is that physics treats linear motion differently from curved motion. Objects that are moving in a straight line will continue moving in a straight line unless acted upon by a force. An inertial coordinate frame is by definition one where this holds true. We can define "absolute rotation" as rotation relative to that coordinate frame. We will not have any trouble agreeing on who is rotating and who is not, because only one coordinate frame will observe perfectly inertial movement, and all the others will measure some coriolis and centrifugal forces. See this video for better intuition: https://www.youtube.com/watch?v=_36MiCUS1ro https://www.youtube.com/watch?v=_36MiCUS1ro
  - danbruc 11y ago
    Introducing a probe body does not really solve the problem, it still does not explain what picks one frame of reference over the other. Why does the force free motion of the probe body appear straight for on astronaut but not the other one? I am pretty sure this entire topic is not nearly as straightforward as you suggest, otherwise there would be no debate about Machian views and so on. I will have a look at the papers referenced here [1], they seem to touch a couple of interesting and related points. [1] http://physics.stackexchange.com/questions/1048/what-if-the-universe-is-rotating-as-a-whole http://physics.stackexchange.com/questions/1048/what-if-the-...
    - tbabb 11y ago
      I do not really see what the "problem" is. One can easily define a unique (up to translation) "rotation-free" coordinate system that all observers will agree on, without any reference to "fixed stars" or the rest of the universe. Centrifugal force in a rotating frame is an inevitable consequence of a universe in which conservation of momentum exists. Conservation of momentum is an inevitable consequence (by Noether's theorem) of a universe in which translational symmetry exists (i.e. the laws of motion are not different at some displacement dx). By all observations, all three of those properties hold for appropriate choices of frame. You cannot suppose a universe with both translational symmetry and symmetry under rotational movement; the two are in conflict. If conservation of momentum holds in some coordinate frame, then it will not hold in coordinate frames that are rotating relatively to it. If you suppose a universe where a "rotating" reference frame is the one where conservation of momentum holds, then I would be forced to ask "rotating relative to what, if not an inertial frame?" And the inhabitants of such a universe would still certainly find it meaningful to label that frame as "inertial" and define rotation as relative to it. If you are asking how we tell rotating and non-rotating reference frames apart, the answer is trivial-- non-rotating reference frames obey inertia and rotating frames do not; and there is no ambiguity or disagreement between observers. If you are asking why there exists an inertial reference frame at all, the answer is that this arises from translational symmetry. If you are asking why the universe has chosen a particular coordinate frame to be "non-rotating" over any other, the question seems rather meaningless, because it does not make sense to define rotation except with respect to an inertial frame.

by tbabb 11y ago

danbruc 11y ago

We are getting closer. You are essentially saying that we can have geometrically indistinguishable states that are physically different. We can have an astronaut with a yo-yo hanging down and one with a yo-yo extending straight away while the world otherwise looks exactly the same to both of them. Both astronauts have to go through the same change in angular velocity just in opposite directions to get to the same state as the other one but one would see the yo-yo dropping down while the other one will see it rising. How does that make sense? What is so special about the one coordinate frame without centrifugal forces? With respect to what is the astronaut not rotating? Note that nothing looks unphysical here, just different but without any obvious thing that justifies the difference. And I am definitely not trying to say I am right and you are wrong, it just doesn't look consistent to me to have centrifugal forces in an empty universe.

tbabb 11y ago
The short answer (i.e. without teaching all of Phys 101 in this comment) is that physics treats linear motion differently from curved motion. Objects that are moving in a straight line will continue moving in a straight line unless acted upon by a force. An inertial coordinate frame is by definition one where this holds true. We can define "absolute rotation" as rotation relative to that coordinate frame. We will not have any trouble agreeing on who is rotating and who is not, because only one coordinate frame will observe perfectly inertial movement, and all the others will measure some coriolis and centrifugal forces. See this video for better intuition: https://www.youtube.com/watch?v=_36MiCUS1ro https://www.youtube.com/watch?v=_36MiCUS1ro
- danbruc 11y ago
  Introducing a probe body does not really solve the problem, it still does not explain what picks one frame of reference over the other. Why does the force free motion of the probe body appear straight for on astronaut but not the other one? I am pretty sure this entire topic is not nearly as straightforward as you suggest, otherwise there would be no debate about Machian views and so on. I will have a look at the papers referenced here [1], they seem to touch a couple of interesting and related points. [1] http://physics.stackexchange.com/questions/1048/what-if-the-universe-is-rotating-as-a-whole http://physics.stackexchange.com/questions/1048/what-if-the-...
  - tbabb 11y ago
    I do not really see what the "problem" is. One can easily define a unique (up to translation) "rotation-free" coordinate system that all observers will agree on, without any reference to "fixed stars" or the rest of the universe. Centrifugal force in a rotating frame is an inevitable consequence of a universe in which conservation of momentum exists. Conservation of momentum is an inevitable consequence (by Noether's theorem) of a universe in which translational symmetry exists (i.e. the laws of motion are not different at some displacement dx). By all observations, all three of those properties hold for appropriate choices of frame. You cannot suppose a universe with both translational symmetry and symmetry under rotational movement; the two are in conflict. If conservation of momentum holds in some coordinate frame, then it will not hold in coordinate frames that are rotating relatively to it. If you suppose a universe where a "rotating" reference frame is the one where conservation of momentum holds, then I would be forced to ask "rotating relative to what, if not an inertial frame?" And the inhabitants of such a universe would still certainly find it meaningful to label that frame as "inertial" and define rotation as relative to it. If you are asking how we tell rotating and non-rotating reference frames apart, the answer is trivial-- non-rotating reference frames obey inertia and rotating frames do not; and there is no ambiguity or disagreement between observers. If you are asking why there exists an inertial reference frame at all, the answer is that this arises from translational symmetry. If you are asking why the universe has chosen a particular coordinate frame to be "non-rotating" over any other, the question seems rather meaningless, because it does not make sense to define rotation except with respect to an inertial frame.