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General relativity with infinite speed of light?

  1. Sep 23, 2010 #1
    Are there any consistent theory in which the speed of light is infinity,
    but the space-time is curved?
    Let us imagine a history of mankind in which GR is invented before special relativity (SR).
  2. jcsd
  3. Sep 23, 2010 #2
    There is a difference between a theory and a fantasy. If it is not based on reality it is not a theory. Since the speed of light is not infinite this is simply a fantasy.
  4. Sep 23, 2010 #3
    "Are there any consistent theory in which the speed of light is infinity"

    There is such. You may like to check http://arxiv.org/abs/arXiv:gr-qc/9604054" [Broken] by Christian Rueede and Norbert Straumann. Also search for "Newton-Cartan" and "Galilei general relativity". This way you will find further references.
    Last edited by a moderator: May 4, 2017
  5. Sep 23, 2010 #4
    Not necessarily. For instance you may think that the speed of light may be irrelevant for gravity. That it is relevant is just an assumption justified by a long and mostly successful use of GR. But this fact must not be taken as a "no-no" for trying other assumptions, even if at first look you don't like them.
    Last edited: Sep 23, 2010
  6. Sep 23, 2010 #5
    Do you think that Newtonian theory is fantasy?
    NO! Newton theory is a real theory,
    and describes the real world in the regime v << c.
    The above mentioned theory (GR without SR)
    can describe also the real world in a suitable regime,
    for example gravitational Doppler effect is a situation,
    where we dont need SR but GR is needed
    Last edited: Sep 23, 2010
  7. Sep 23, 2010 #6
    I don't know what you are talking about but last time I checked the speed of light is finite, in fact it is exactly:

    299792458 m / s
  8. Sep 23, 2010 #7
    The question is why the value of the speed of light should affect gravity? It is an assumption of GR that it does. But other assumptions and models are not excluded, and other theories are being tried.
  9. Sep 23, 2010 #8
    Yes they are excluded because the speed of light is not infinite, as is established by experiment.
  10. Sep 23, 2010 #9
    They are not excluded, because they do not claim that the speed of light is infinite. They claim that it is irrelevant for a theory of gravity. Speed of light enters Maxwell's equation. And it can be well what it is. But equations for the gravitational field is something else.
  11. Sep 23, 2010 #10


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    Theoretical physicists sometimes investigate theories known to be incompatible with observation if it illuminates the mathematical properties of more realistic theories...for example, considering the 2+1 dimensional analogue of general relativity, or adding an extra time dimension to M theory which may reveal some symmetries which are hidden in the ordinary version. For a simpler example consider the exercise of http://www.physics.princeton.edu/~mcdonald/examples/mechanics/lee_ajp_43_434_75.pdf [Broken], which results in a transformation which has an adjustable parameter in the place of c which can either be given an infinite value (in which case the transformation reduces to the Galilei transformation of Newtonian physics) or a finite value (in which case it reduces to something like the ordinary Lorentz transformation).
    Last edited by a moderator: May 4, 2017
  12. Sep 23, 2010 #11
    Quoting from http://image.sciencenet.cn/upload/blog/file/2010/8/201081019170575880.pdf" [Broken]:

    "As may be recalled, there is a space-time formulation of Newtonian gravitational theory originally provided by Cartan [7], and further studied independently by Friedrichs [14] and Trautman [40], in which the Newtonian version of the equivalence principle is directly incorporated into the geometrical description. (See Ref. 12 for an up-to-date account.) The Cartan geometric formulation of Newtonian gravitational theory is indeed the appropriate one for taking into account the subtleties of (what remains of) the principle of general covariance and the principle of equivalence. (For example, the Newton-Cartan space-time of a constant non-zero Newtonian gravitational field has an identical geometry to that of the zero gravitational field, but it differs from a non-uniform Newtonian field which produces tidal effects.) It has been pointed out by Christian [8] that the Newton-Cartan framework provides a valuable setting for exploring some of the fundamental problems of unifying quantum theory with gravitational theory without, at this stage, the more severe difficulties of general relativity having to be faced. Christian argues that this framework indeed sheds important light on the role of gravity in the measurement problem.
    As it turns out, the criterion for quantum state reduction that we shall be led to here is independent of the value of the speed of light c."
    Last edited by a moderator: May 4, 2017
  13. Sep 23, 2010 #12
    Sorry, I mean Newtonian theory instead of SR, but its the same.
    I am talking about special relativity which is not good in describing gravitation,
    therefore you can say that its just a fantasy :) ???
  14. Sep 23, 2010 #13
    Special relativity was not invented for describing gravitation. Similarly you could say that gravitation is not good in describing quantum phenomena. So what? Different frameworks are invented for different purposes.
  15. Sep 23, 2010 #14


    Staff: Mentor

    It would help if you clarified: Do you mean "consistent with observation" or "self-consistent".

    The Newton Cartan formulation that arkajad mentioned is just a geometrical reformulation of Newtonian gravity, so it doesn't mention c at all. It is self-consistent, but it is not consistent with observation since it is just a reformulation of Newtonian gravity and therefore makes all of the same wrong (and right) predictions.

    AFAIK, there is no theory of gravity consistent with observation that does not use a finite c.
  16. Sep 23, 2010 #15
    Yes, and GR without SR was not invented for describing gravitation with system with large velocities!

    I mean "self-consistent".

    (But I think, that we have nothing consistent with all observations yet)
  17. Sep 23, 2010 #16
    But Newton Cartan theory predict the right formula for gravitational Doppler-effect, or doesnt?
  18. Sep 23, 2010 #17


    Staff: Mentor

    What observation is inconsistent with GR?
  19. Sep 23, 2010 #18
    I mean that GR is not the theory of everything, but this is not the subject of this post
  20. Sep 23, 2010 #19
    Newton-Cartan theory is not dealing with light. Maxwell's theory is. Similarly GR tells you nothing about Maxwell equations and propagation of electromagnetic waves. You need a separate theory of electromagnetism. Then, when you have both, you can try to relate the structure of one to the structure of the other.
  21. Sep 23, 2010 #20


    Staff: Mentor

    For clarity, do you understand:
    a) GR is self-consistent and also consistent with observation
    b) Newton Cartan is self-consistent and not consistent with observation
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