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Q & A: Special vs. General Relativity

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Most recent answer: 10/21/2011
Q:
This article is about Lorentz Symmetry Violation, I would like to have expert view: http://en.wikipedia.org/wiki/Shahdaei_Paradox
- Koorosh (age 47)
Gothenburg /Sweden
A:
There seems to be a serious problem with the discussion in that Wikipedia article. At several points, it refers to the inability of Special Relativity to deal with transformations to rotating frames, e.g. in the so-called Ehrenfest Paradox. Rotating frames have accelerations, and non-uniform accelerations at that. SR is not designed to handle such frames. General Relativity is required. the issues they discuss are all handled by the GR coordinate transforms.

Mike W.

(published on 10/13/2011)

Follow-Up #1: Is Lorentz symmetry broken ?

Q:
Originally my question was: Q: This article is about Lorentz Symmetry Violation, I would like to have expert view: http://en.wikipedia.org/wiki/Shahdaei_Paradox I received below answer which I was not able to respond (because of a tech problem), so I add a complementary comment please proceed to the end. A:There seems to be a serious problem with the discussion in that Wikipedia article. At several points, it refers to the inability of Special Relativity to deal with transformations to rotating frames, e.g. in the so-called Ehrenfest Paradox. Rotating frames have accelerations, and non-uniform accelerations at that. SR is not designed to handle such frames. General Relativity is required. the issues they discuss are all handled by the GR coordinate transforms. Mike W. Comment: I think the issue is more fundamental, and not related to inability of SR for handling rotation. What it brings up is: (non-tech speaking) for instance if a kid throw a ball up in a moving train he will only see a vertical movement of the ball i.e. up and down. But two guys standing on the platform; the one that standing still won't see the ball moving straight up and down (he will see a further path i.e. addition of the train movement), but the other guy on the platform that turns his eyes synchronized and aligned to the train's movement will also see the ball in almost the way the kid on the train sees it. (imagine in a special situation with a camera he might even not feel the movement of the train as in movies)
- Koorosh (age 47)
Gothenburg/Sweden
A:
The Lorentz symmetry only applies to transformations between coordinate systems moving at a fixed velocity with respect to each other. The sort of transformations you're discussing, to coordinates used by somebody rotating their axes, simply are not supposed to be described by Lorentz transformation.

Mike W.

(published on 10/13/2011)

Follow-Up #2: non-inertial frames

Q:
Follow-Up #1: Is Lorentz symmetry broken ? Q: Originally my question was: Q: This article is about Lorentz Symmetry Violation, I would like to have expert view: http://en.wikipedia.org/wiki/Shahdaei_Paradox I received last answer which I was not able to respond (because of technical issues)  A: The Lorentz symmetry only applies to transformations between coordinate systems moving at a fixed velocity with respect to each other. The sort of transformations you're discussing, to coordinates used by somebody rotating their axes, simply are not supposed to be described by Lorentz transformation. Mike W. Thank you for your feedback, Please reevaluate the article. The article is changed to include gauge transformation as well, but no matter approach, there exist a paradox (lorentz sym breaking)
- Koorosh (age 47)
Gothenburg/sweden
A:
The transformation to rotating frame is a completely standard exercise, not involving paradoxes. The time transformation, for example, involves an acceleration-dependent term which is just the square of the usual Lorentz gamma factor. As a result the rotating frame (we're assuming it's held in orbit by something other than gravity) sees the inertial one as running fast by exactly the same factor that the inertial one sees the rotating one as running slow. That acceleration-dependent factor is of course not part of the Lorentz transforms itself, since those transforms are only good between inertial frames with no gravity. If gravity is involved, in addition to the accelerations, one must use General Relativity. The lowest-order version of these calculations is so simple even I can do it. I just can't see what paradox is being discussed.

Mike W.

(published on 10/21/2011)

Follow-up on this answer.