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I Why special relativity is unsuitable to describe gravity

  1. Jul 8, 2017 #1
    I am trying to understand why the special relativity is not suitable for describing the gravity.
    Consider a counterexample assuming it is the suitable and the space-time containing a gravitational mass is flat. Then one could describe the acceleration of a test particle from his inertial frame of reference (FOR) where the gravitational mass is located in the center of this coordinates system. If, however, there is another observer moving relative to the first system with a constant speed, he can still calculate the acceleration of the test particle relative to his new coordinates. However, this gives different acceleration because the acceleration is frame dependent according to SR which may not agree with the fact that the different value of new acceleration must also match the value given by ##g=G\frac{M}{r^2}## and ##M## should be larger relative to the moving observer. This drove Einstein to think about the general covariance principle where only the free falling observer has the privilege to consider his frame inertial which leads to considering all other frames non-inertial and hence the curved space-time emerged.
    Is this a true argument?
     
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  3. Jul 8, 2017 #2

    Ibix

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    The problem with Newtonian gravity in special relativity is that its effects are instantaneous at any distance, but instantaneous is a frame-dependent thing in relativity. Attempts to fix this by adding a propagation speed to gravity didn't work.

    Experimental tests on semi-Newtonian theories also ended up predicting the wrong deflection of light, where GR predicted correctly.
     
  4. Jul 8, 2017 #3
    Hi. Fake gravitation such as motions of constant acceleration or rotation can be fully understood by applying SR. Real gravity seems to have similar behaviour with fake ones thus introduced GR. Best.
     
  5. Jul 8, 2017 #4

    FactChecker

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    I think that another difference is that the SR acceleration vectors would all be parallel whereas gravity "acceleration" vectors are all pointing away from the gravitational mass and are not parallel. And the nature of the vector magnitudes are different in SR and GR. Keeping track of geodesic paths in GR is a significant problem.
     
  6. Jul 9, 2017 #5

    PeterDonis

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    If you assume that ##M## is relativistic mass, yes, ##M## will be larger in the moving frame. But the coordinate acceleration will also be larger in the moving frame. Also, the distance ##r## will be length contracted in the moving frame. It's not clear just from stating those facts whether things will still end up working out in the moving frame.

    That's not the principle of general covariance; in fact it contradicts it, by picking out a special class of frames (the inertial ones). The principle of general covariance says you can pick any frame you like--inertial, non-inertial, it doesn't matter--and the laws of physics will still look the same. Giving a special status to inertial frames is what special relativity does, not general relativity.
     
  7. Jul 9, 2017 #6

    PeterDonis

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    Ibix gave the correct answer: instantaneous propagation speed. That is inconsistent with SR, and trying to fix it by just adding a propagation delay to Newtonian gravity gives a theory that is grossly inconsistent with observations (for example, such a theory predicts that planetary orbits in the solar system should be unstable on fairly short time scales).
     
  8. Jul 9, 2017 #7
    I don`t understand why there should be an instantaneous propagation speed in a solar system where the mass of the sun is stable over the time. I do not feel this is the correct answer, what I missed here?. Even from the history, Einstein looked at it from different view point. He thought that there is no point to restrict ourselves to particular frame of reference when we describe the general motion in physics. And by general motion here, I mean movement with constant velocity or acceleration. This means any arbitrarily frame can describe the law of physics correctly. But the inertial frame in a gravity-free space is also equivalent to a free falling frame according to the principle of equivalence. This give the relation between the general relativity motion and the gravitation. see Stanford encyclopedia section2/5 https://plato.stanford.edu/entries/spacetime-iframes/
    This drives me to ask another question, is that all about the gravity alone? how about other general physical movement or actions in physics? is gravity the only force that undermines the concept of general covariance?
     
  9. Jul 9, 2017 #8

    Ibix

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    ##F=GMm/r^2## has no propagation term. It implies that a change in the position or mass of one a body should be reflected in its gravitational effect instantly everywhere else in the universe. That's inconsistent with relativity, which doesn't have a universal definition of "instantly".
    The special thing about gravity in the historical sense is that it is the only force for which we ever had a non-relativistic theory. Maxwell's equations are Lorentz-covariant not Galileo-covariant, although that wasn't understood at the time Maxwell developed them, and the strong and weak force theories were developed after Einstein.

    So it isn't that gravity "undermines the concept of general covariance", it's that relativity undermines Newtonian gravity. That, in turn, means that Newtonian gravity can only be an approximation to something else that respects relativity's speed limits. That something else turns out to be General Relativity.
     
  10. Jul 9, 2017 #9
    This mean that not only the change in the sun mass, but also the information about the change in its position still needs to propagate in the form of gravitation wave. If, so can we detect this wave knowing that the sun is moving inside the galaxy?
     
  11. Jul 9, 2017 #10
    And more importantly, will the free faller detect the gravitational wave if the sun suddenly disappears? If so, how can he explain that wave?
     
  12. Jul 9, 2017 #11

    Nugatory

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    Instaneous propagation is inherent in Newton's ##F=Gm_1m_2/r^2##. To evaluate the force on an object at any moment, you need to know the positions of all the other masses in the universe at that moment - and that assumption implies absolute simultaneity, which is equivalent to instaneous propagation.

    Another way of seeing the problem is to consider that force is a vector, so it has a direction. The earth is moving relative to the sun. Does the force vector acting on the earth point along a line between the earth and where the sun is now relative to the earth; or does it point along a line between the earth and where the sun was relative to the earth a moment ago? The former implies instaneous propagation and the latter implies a finite speed of propagation, with larger values of "a moment ago" corresponding to larger propagation delays. Stable orbits (and there is no doubt that the planetary orbits are stable) require that the vector always point along the line between where the sun and the earth are right now with no propagation delay, so even in a system in which the mass of the sun is stable we are stuck with instaneous propagation.
     
  13. Jul 9, 2017 #12

    Ibix

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    I don't know much about gravitational waves; however I think the answer is that it's not that simple. Just "moving" isn't enough - gravitational waves come from changing quadropole moments, which means that it's motion relative to other masses that's important. I'll have to leave others to answer this.
    Energy conservation is built in to Einstein's field equations. They literally cannot describe the Sun just disappearing. If it were to go nova or something, you would notice nothing gravitationally until mass and energy from the nova started passing you, at which point you would have ample explanation for changes in the gravitational field.
     
  14. Jul 9, 2017 #13
    So the free faller will not notice the gravitational wave. Why? the wave is a physical wave propagates outward from the center of the sun and the faller moves inward to the center of the sun, so logically they should meet!
     
  15. Jul 9, 2017 #14

    Ibix

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    I did not say that. I just said that there's no change in gravity at your location until some of the energy and matter from a stellar explosion has passed you. Gravitational waves and electromagnetic radiation travel at the same speed - c, in a vacuum.
     
  16. Jul 9, 2017 #15
    I got it, thank you. But again, why the absolute simultaneity does not hold in general relativity where the sun bends the space around it far away from the center?
     
  17. Jul 9, 2017 #16

    Nugatory

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    GR describes the motion of a body based on the spacetime curvature at the point where the body is at a given moment; the positions of distant objects at that moment don't matter. Of course that spacetime curvature is affected by where the distant objects were in the past, but that is consistent with a propagation delay so we don't need absolute simultaneity.

    You might reasonably ask how we can have stable orbits with propagation delay in GR but we can't have stable orbits with propagation delay with Newtonian gravity. The answer is that GR predicts different (only very slightly different for planets orbiting a sun-sized mass) orbits than Newtonian gravity; we see this in the precession of Mercury's orbit because it is closest to the sun and the tiny difference is most visible there. The GR-predicted orbits are stable even with a propagation delay.
     
  18. Jul 9, 2017 #17
    Hi Nugatory:

    I am guessing that you are intentionally for pedagogical reasons ignoring the fact that gravitational waves (GWs) make orbits unstable in the sense that over time an orbit shrinks due to the loss of kinetic energy from the moving bodies due to the GWs they generate.

    Regards,
    Buzz
     
  19. Jul 9, 2017 #18

    Dale

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    There are other gravitating objects in the solar system besides the sun.
     
  20. Jul 9, 2017 #19

    FactChecker

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    Is it correct to think that in a Sun-centered coordinate system, the time-space distortion is essentially fixed and not "propagating". (Ignoring smaller gravitational objects.) Alternatively, in a planet-centered coordinate system, the Sun is moving and the time-space distortion effects propagate at the speed of light?
     
  21. Jul 9, 2017 #20
    Hi Adel:

    Another small nit. The mass of the sun is not stable over time. The sun is constantly losing mass, and it has been doing so almost ever since it came into existence. The photon energy it radiates, as well as the mass particles it radiates, reduce it's mass continuously. (There may have been a relatively short period when the mass of in falling matter exceeded the mass loss.)

    Regards,
    Buzz
     
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