3 ms·

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 m

by 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.
  - danbruc 11y ago
    Right now I am again convinced that there is no problem, but I have gone back and forth between it makes sense and it makes no sense a couple of times. I probably never looked at it with enough rigour and got things overlooked or confused. But thanks for your effort and I will also read through "Mach's principle and a relativistic theory of gravitation" which I came across yesterday during this discussion, maybe I will finally reach a state of lasting non-confusion.

by tbabb 11y ago

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.
- danbruc 11y ago
  Right now I am again convinced that there is no problem, but I have gone back and forth between it makes sense and it makes no sense a couple of times. I probably never looked at it with enough rigour and got things overlooked or confused. But thanks for your effort and I will also read through "Mach's principle and a relativistic theory of gravitation" which I came across yesterday during this discussion, maybe I will finally reach a state of lasting non-confusion.