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A Einstein, Mach's Principle, and the Speed of Light Limit

  1. Aug 29, 2016 #1
    I am confused about Einstein's thinking. I understand when he formulated his general theory of relativity, he wanted to incorporate 3 foundations for his theory: The relativity principle, the equivalence principle, and Mach's Principle. He believed that inertia and weight were essentially the same phenomenon, that inertia was a function of the surrounding mass of the universe. Spin a rock tied to a string, he believed the centrifugal force tugging on your fingers was essentially a gravitational effect caused by the rotation of the rock relative to the cosmic mass of the univers. Here is my confusion. All of his professional life he insisted that nothing-- light, physical causality,etc. could ever exceed the speed of light. So why would he even attempt to implement Mach's principle, knowing that no effect, wave, field,etc. could travel faster than c?
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  3. Aug 29, 2016 #2

    Paul Colby

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    I've always thought that the way the distribution of mass and energy in the universe determines the local metric in GR is consistent at least in spirit with Mach's principle. I've always been told by people that know that this view is simply incorrect. So, if one were to spin up the distant stars respecting the speed of light and all, wouldn't frame dragging eventually effect the water in a initially non-rotating Newton's pail? Whatever....
  4. Aug 30, 2016 #3
    Again, I'm not sure what Einstein was thinking. If the local metric is already determined by the total cosmic mass-energy distribution of the universe, then was he thinking that acceleration with respect to the local metric pre-determined by distant mass-energy is what actually causes the inertial force, not acceleration with respect to the distant mass-energy distribution? I don't know. Can someone throw some more light on this problem, specifically, the speed of light restriction and causality due to distant mass-energy. Inertial reactions are instantaneous reactions, so something local must be causing it. Therefore, how could Einstein try to weave Mach's principle into GR without overstepping the light speed restriction? Remember, Einstein rediculed spooky-action-at-a-distance in quantum mechanics pertaining to quantum entanglement.
  5. Aug 30, 2016 #4


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    Excellent question!

    I think a lot of people believe Einstein rejected the notion of an ether as soon as he published his special theory, but this is not the case. E.g., in 1920 he lectured in Leiden where he stated that "if inertia determines the accelerations of masses far away, this implies an action at a distance, which is unacceptable for a modern physicist". As such he proposed to reincarnate the idea of an ether. See e.g. Walter Isaacson's biography, chapter 14. As I understand it now, in that lecture he proposed to do so because his theory of GR is not Machian; you will feel inertial forces when you rotate in an empty universe, as you can check by transforming the geodesic equation in an empty universe for an inertial observer by going to rotating coordinates. So whereas Newton proposed that one rotates wrt absolute space, Einstein proposed that you will rotate wrt the metric field (which is a substructure of spacetime), which in some sense serves as an "ether" (although it is not the same concept as before!).

    It's not a satisfactory answer to your question, but if I find more about this in Isaacson's biography, I'll let you know.
  6. Aug 30, 2016 #5

    Paul Colby

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    I certainly can't comment on what Einstein was thinking or even grasp why one should care so much. In the limit that light might shine both ways, how is it that GR is not an answer to the above question? In EM the local fields are determined by the global sources in a causal way, why is GR different? The Wiki discussion throws up Godel's rotating universe as some grand counter example. That one can find some special solution of the GR field equations that tweak poor Mach in a way he wouldn't be able to understand doesn't surprise. Mach didn't understand either relativity theory given the time period when he was writing. People tend to speak about these things like the progenitor of a theory has some choice in how the theory turns out? The facts drive the (successful) theories not the will of researcher.
  7. Aug 30, 2016 #6
    Thank you for the response. I will have to investigate deeper into his papers on the Einstein Paper's website on his ideas concerning an ether.
  8. Aug 30, 2016 #7
    There is a simple scenario that counters Mach's idea.
    Two spheres separated by space, spinning in a common plane, with opposite and equal rotations.
    If the reciprocal effect was due to the remaining mass of the universe spinning with the opposite rotation, the net rotation would be zero.
    The spheres would still experience centrifugal effects.
  9. Aug 30, 2016 #8

    Paul Colby

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    Does this assume that the two spheres are the only mass in the universe? It would seem required to counter Mach's idea.
  10. Sep 1, 2016 #9
    Mach would attribute equivalent centrifugal effects of a rotating mass m
    if the universal mass (M-m) rotated in the opposite direction and m had no rotation.
    Two masses m1 and m2, with equal rates of rotation but opposite directions, would not work per his principle.
    There is also the distinction between allowed physical behavior of matter, and perception.
    The distant stars rotating at speeds >c is perception, or reality confined to the mind.
  11. Sep 1, 2016 #10

    Paul Colby

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    Agreed. Is this due to Mach predating the relativities? If Mach was aware and understood the relativities wouldn't GR have address Mach's philosophical stand?
  12. Sep 1, 2016 #11


    Staff: Mentor

    According to the equations of GR, yes (with some caveats related to what "spin up the distant stars" would actually mean). I suggest checking out Cuifolini and Wheeler's book Gravitation and Inertia. It goes into this general issue in excruciating detail.
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