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Thread: Michelson-Morley explained in uniformly rotating frames

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    Michelson-Morley explained in uniformly rotating frames

    All sources I have had the chance of consulting explain the null result of the Michelson-Morley experiment from the perspective of frames in linear uniform motion. But the experiment is conducted in a lab attached to the Earth, i.e. in a frame rotating with constant angular speed. Is there any source that explains the null result in the rotating frame of the lab? A few references would be great. Thank you.

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    Lightbulb Michelson-Morely in accelerated reference frame

    See The Michelson-Morley experiment in an accelerated reference frame (Dennis Crossley; preprint submitted to Foundations of Physics, arXiv December 2010). Conclusion: "We conclude that it is possible in principle (though exceedingly difficult in practice) for an observer to measure his speed relative to the absolute reference frame by performing the Michelson-Morley experiment in an accelerated reference frame."

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    Quote Originally Posted by Tim Thompson View Post
    See The Michelson-Morley experiment in an accelerated reference frame (Dennis Crossley; preprint submitted to Foundations of Physics, arXiv December 2010). Conclusion: "We conclude that it is possible in principle (though exceedingly difficult in practice) for an observer to measure his speed relative to the absolute reference frame by performing the Michelson-Morley experiment in an accelerated reference frame."
    Thank you, this is a very "interesting" reference. I was looking for the theory of uniformly rotating frames while this paper deals with accelerated frames. The claims are definitely fringe:

    "This suggests that we should go beyond the large class of experiments that have been
    considered in inertial frames (which all fail to detect absolute motion) and reconsider
    performing them in accelerated reference frames. If we are clever enough, perhaps
    we can find one with enough sensitivity to measure our absolute velocity."

    I wonder if Foundations of Physics accepted the paper. After all, the journal has a long history of publishing fringe material of this ilk, see:

    R. Klauber., “New Perspectives on the Relativistically Rotating Disk and Non-time-orthogonal Reference Frames” Found. Phys. Lett., 11(5) (1998)

    F. Selleri, “Noninvariant One Way Speed of Light and Locally Equivalent Reference Frames”, Found. Phys. Lett., 10, (1997)

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    A uniformly rotating frame is an accelerated frame.
    Velocity is a vector, not a scalar.

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    Quote Originally Posted by caveman1917 View Post
    A uniformly rotating frame is an accelerated frame.
    Velocity is a vector, not a scalar.
    I have a sneaky feeling that this is not news to @macaw

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    Quote Originally Posted by Perikles View Post
    I have a sneaky feeling that this is not news to @macaw
    I know, it was time for my pedantry hour around the board

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    In any case, isn't a null in MM expected since the paths encompass zero area?
    You can rotate it as fast as you want, the difference in path-length between the two legs will remain zero.
    You need a ring setup for a sagnac correction.

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    Quote Originally Posted by caveman1917 View Post
    In any case, isn't a null in MM expected since the paths encompass zero area?
    You can rotate it as fast as you want, the difference in path-length between the two legs will remain zero.
    You need a ring setup for a sagnac correction.
    Interesting approach but incorrect, there is ample proof (both theoretical and experimental) that Sagnac experiments executed with devices of zero area give non-null results. The correct explanation of the Sagnac effect shows that the effect is proportional with the perimeter of the enclosing loop, the fact that it is proportional to the enclosed area is incidental. Very few books (if any) mention this fact. This might be surprising but it is perfectly correct. So, you cannot use the argument that "MMX is a Sagnac experiment of zero area , therefore it should give a null result".
    On the other hand, the proof that MMX executed in rotating frames gives null results is VERY complicated, it requires profound knowledge of SR in rotating frames. The theory is backed up by numerous experiments using rotating resonating cavities.

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    Quote Originally Posted by Perikles View Post
    I have a sneaky feeling that this is not news to @macaw
    Yep :-). I am still searching for some good references for the theoretical explanation of the null result in uniformly rotating frames, I can't find any.

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    Seeing as the experiment was usually spun, I dont know what the question is. The MMX is designed to detect the Earth's linear motion with respect to the ether. The experiment was spun to detect the effective path length difference using an interferometer. Seeing as the transit time for light was nanoseconds, and the Earth's rotation is in microradians per second, the experiment was pretty close to a non-rotating frame. Still not all that relevant tho, seeing as the experiment was rotated and that the Earth's rotation and revolution were taken into account in the experiment from the beginning.

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    Quote Originally Posted by korjik View Post
    Seeing as the experiment was usually spun, I dont know what the question is. The MMX is designed to detect the Earth's linear motion with respect to the ether. The experiment was spun to detect the effective path length difference using an interferometer. Seeing as the transit time for light was nanoseconds, and the Earth's rotation is in microradians per second, the experiment was pretty close to a non-rotating frame. Still not all that relevant tho, seeing as the experiment was rotated and that the Earth's rotation and revolution were taken into account in the experiment from the beginning.
    The standard textbook explanation uses linear motion, I am looking for a reference that uses the realistic, rotating motion even if the approximation by a linear motion is "pretty close". I am looking for the exact treatment, if it exists. I couldn't find it, I am asking for help.

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    Quote Originally Posted by macaw View Post
    Interesting approach but incorrect, there is ample proof (both theoretical and experimental) that Sagnac experiments executed with devices of zero area give non-null results.
    Does that matter?
    Even in the more correct interpretation that it is proportional to the projection of a path segment on the direction of velocity of that path segment, it would still give a null result.

    Alternatively, since the coordinate speed of light in the rotating frame depends on the angular velocity of the light wrt inertial coordinates, and seeing that we have perfect symmetry for both arms of the experiment as far as this is concerned, we can conclude that there would not be a different travel time for both arms in the rotating frame of reference.

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    Quote Originally Posted by caveman1917 View Post
    Does that matter?
    Even in the more correct interpretation that it is proportional to the projection of a path segment on the direction of velocity of that path segment, it would still give a null result.
    No, that's just as false as before. I think I can trace your error to attempting to apply the calculations of Kennedy-Thorndike (done for frames in linear motion) to rotating frames. To convince yourself, consider a loop made of fiberoptic cable going over two spindles of very, very small diameters. The area of the loop (or, in your parlay, the projection of the path segment) is zero. Nevertheless, the device would exhibit a very strong phase shift between two counterpropagating light waves if the spindles go really fast.

    Alternatively, since the coordinate speed of light in the rotating frame depends on the angular velocity of the light wrt inertial coordinates,
    It doesn't, it is invariant wrt the angular velocity. Nikolic proved that it doesn't in this paper:

    H.Nikolic, “Relativistic contraction and related effects in non-inertial frames”, Phys.Rev. A, 61, (2000)

    I can reproduce the proof in one page of calculations. Perhaps you are thinking about the closing speed , ?



    and seeing that we have perfect symmetry for both arms of the experiment as far as this is concerned, we can conclude that there would not be a different travel time for both arms in the rotating frame of reference.
    No, sorry, the simplifications that you are attempting don't work, for the reasons explained above. I know you have very good intentions but we need to do this proof the hard way (with math).

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    Let's put this in math since you won't accept it otherwise

    Obtain the metric for a rotating frame of reference

    For light set and for a suitable choice of origin we can also set
    Thus

    And thus the coordinate speed of light

    No difference at all, certainly not a difference in each arm of the experiment.

    ETA: hadn't read your last post while writing this (had trouble with the latex), i hope this works better?

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    Quote Originally Posted by caveman1917 View Post
    Let's put this in math since you won't accept it otherwise

    Obtain the metric for a rotating frame of reference

    For light set and for a suitable choice of origin we can also set
    Thus

    And thus the coordinate speed of light
    Yes, this is correct, it agrees with my earlier statement (that coordinate light speed does NOT depend on the angular speed) and it disagrees with your earlier statement, the one I objected to:

    Quote Originally Posted by caveman1917
    Alternatively, since the coordinate speed of light in the rotating frame depends on the angular velocity of the light wrt inertial coordinates,
    So, we are on the same page now.

    No difference at all, certainly not a difference in each arm of the experiment.
    While this is correct, it doesn't bring us any closer to a proof because coordinate speed of light is judged from the perspective of an observer at the center of the experiment. In that system of coordinates the arms of the interferometer can be (and are) subjected to different amounts of length contraction. Anyways, I did the complete proof, what I am looking for is references to papers/books that did it before me.

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    Quote Originally Posted by macaw View Post
    No, that's just as false as before. I think I can trace your error to attempting to apply the calculations of Kennedy-Thorndike (done for frames in linear motion) to rotating frames. To convince yourself, consider a loop made of fiberoptic cable going over two spindles of very, very small diameters. The area of the loop (or, in your parlay, the projection of the path segment) is zero.
    The area is zero, but not the projection of the path segment on its direction of velocity. For the "straight" parts of the loop, the projection equals the path segment length. The velocity vector of the path is in the same direction as the path.


    It doesn't, it is invariant wrt the angular velocity. Nikolic proved that it doesn't in this paper:

    H.Nikolic, “Relativistic contraction and related effects in non-inertial frames”, Phys.Rev. A, 61, (2000)

    I can reproduce the proof in one page of calculations. Perhaps you are thinking about the closing speed , ?
    Not sure what exactly you're getting at here, , isn't that what we need in order to get the phase shifts along each leg?

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    Quote Originally Posted by macaw View Post
    The standard textbook explanation uses linear motion, I am looking for a reference that uses the realistic, rotating motion even if the approximation by a linear motion is "pretty close". I am looking for the exact treatment, if it exists. I couldn't find it, I am asking for help.
    Wiki has a list of similar experiments from 2009 all the way back to the original. At least a few of them should have the explanation of the rotating frame correction, or at least why they arent sources of error. I would imagine that you are going to need to look at an experiment done since the invention on the maser, since it wasnt until than that the rotation of the Earth would be a comparatively large source of error.

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    Quote Originally Posted by caveman1917 View Post

    Not sure what exactly you're getting at here, , isn't that what we need in order to get the phase shifts along each leg?
    No, it isn't, is the closing speed, not the coordinate speed. I don't need a derivation, I already have the correct derivation, I need some references.

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    Quote Originally Posted by macaw View Post
    it agrees with my earlier statement (that coordinate light speed does NOT depend on the angular speed) and it disagrees with your earlier statement, the one I objected to
    I see what went wrong, i meant as opposed to a standard sagnac experiment where we let the light make a complete 'tour' and in that case we get the depence on angular velocity.

    While this is correct, it doesn't bring us any closer to a proof because coordinate speed of light is judged from the perspective of an observer at the center of the experiment.
    It can if we can show it is invariant under a translation of origin, which is the second part i'm trying to think of how to show.

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    Quote Originally Posted by korjik View Post
    Wiki has a list of similar experiments from 2009 all the way back to the original. At least a few of them should have the explanation of the rotating frame correction, or at least why they arent sources of error. I would imagine that you are going to need to look at an experiment done since the invention on the maser, since it wasnt until than that the rotation of the Earth would be a comparatively large source of error.
    Thank you, do you mean this?
    I am very familiar with all the papers, none of them contains the theory of the experiment in rotating frames.
    Last edited by macaw; 2011-Jun-06 at 12:09 AM.

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    Quote Originally Posted by macaw View Post
    I don't need a derivation, I already have the correct derivation, I need some references.
    Can't help you with that, i don't even have the correct derivation yet

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    Quote Originally Posted by caveman1917 View Post
    Can't help you with that, i don't even have the correct derivation yet
    Thank you, I am always interested in alternative approaches.
    An obvious approach would be to show that in the rotating frame of the lab two-way light speed is isotropic. Combined with the fact that the proper lengths of the interferometer arms are equal, the proof is complete.

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    Quote Originally Posted by macaw View Post
    Thank you, do you mean this?
    I am very familiar with all the papers, none of them contains the theory of the experiment in rotating frames.
    If none of them discuss rotating frames, then you may be out of luck. It is possible that no one has bothered to worry about the rotation.

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    Would Dayton Miller have better results and be a worth looking at?
    http://www.orgonelab.org/miller.htm

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    Quote Originally Posted by fosborn View Post
    Would Dayton Miller have better results and be a worth looking at?
    http://www.orgonelab.org/miller.htm
    No. I can tell from the URL.

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    Quote Originally Posted by fosborn View Post
    Would Dayton Miller have better results and be a worth looking at?
    http://www.orgonelab.org/miller.htm
    No. Besides, "Orgonelab" is a fringe site. DeMeo is a crank.

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    More of a combover site. A thin layer of attempted respectability you can generally see through, but that might just be able to convince a casual passer by.

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    For an M-M experiment rotating about its center, we can have a circular mirror stretching all the way around from the center at radius r. We rotate it and split the photon paths in any two directions from the center and then the photons rejoin there to travel to the detector. According to an inertial observer in the same frame as the rotating M-M apparatus, two sets of photons will be emitted and split at the center simultaneously, both sets travel at c and strike the mirror simultaneously, and then travel at c along the same path back to the center (unless the mirror somehow deflects the photons from this path), and reach the center simultaneously again, then travel together to the detector, so there will be no phase shift, gaining a null result, and all observers will agree. However, this is for rotating the apparatus around its own center only. I'm not sure how it might work out by rotating it around some other point, such as when it is placed upon the surface of the Earth while the Earth rotates, so rotating around Earth's center.

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    Quote Originally Posted by grav View Post
    However, this is for rotating the apparatus around its own center only.
    This is not what the OP question was about.


    I'm not sure how it might work out by rotating it around some other point, such as when it is placed upon the surface of the Earth while the Earth rotates, so rotating around Earth's center.
    This is what the OP is about.

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    Is this correct?

    Let's use z as axis of rotation, and as polar coordinates on a z=constant plane.
    Inertial reference frame:


    Now, switching to a rotating observer, we note that he relates through a lorentz transform to the inertial observer by length contraction along the axis and time dilation, both of which depend on the angular speed at his location. (*)

    Thus



    Getting us


    For light


    And define


    Light speed


    ETA: (*)
    It's the simplest approach possible. The reasoning for it is that, when doing an actual full treatment in rotating frames, different rotating clocks just won't stay synchronized no matter what you try. So at some point you'll need to make the assumption that the experiment is very small, all close to zero. So why not make the assumption from the start? And just treat it as an instantaneous lorentz transform between inertial observers.
    Last edited by caveman1917; 2011-Jun-09 at 06:47 PM. Reason: added explanation for simplistic approach

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