Our reply to s.vik

s.vik says:

April 13, 2013 at 16:59 (Edit)

Well what if the are no GW. Does that mean that GR needs to be modified?
Can GR be changed with “new geometry” are still match currents results??

Nonobservation of GW is not a reason to modify GR. It is rather opposite, because GR (Einstein’s equations) does not have a wave solution, and non-existence (GW were not observed) of such a phenomenon in nature is confirmed by many experiments during the last half of century.

Einstein’s GR is a system of nonlinear equations, and it is a well-known mathematical fact that not all nonlinear equations can be solved starting from some linear approximation. In case of GR, unsuitability of a linear approximation, that has a wave solution, was demonstrated long time ago – the non-renormalizability of GR (where the first approximation is exactly one with a wave solution). So, already in 80s it was proven that, at least, a linear approximation, which corresponds to the wave solution of Einstein’s equation, is not appropriate, and either different linear approximation must be used or there is no linear approximation at all that can lead to a solution of GR equations. Arguments in support of the latter scenario can be given. Perhaps one additional argument for people familiar with the Hamiltonian formulation of GR is: the Hamiltonians of full GR and so-called spin-2 model (a linear approximation) are fundamentally different and there is no continuous transition from one into another.

We would also like to add that Einstein’s name was and continues to be used as one of major arguments for existence of GW in his GR (especially in “scientific” writings for general public). This is just wrong, because during almost four decades after 1916 his opinions changed. He did not die in 1916 (either physically or scientifically). Einstein’s understanding of GR was evolving, including his views on GW, quantization, a role of non-linearity (again, ahead of his time), general covariance, etc.

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6 Responses to Our reply to s.vik

  1. anonymous says:

    What about Robinson-Trautman solutions?

    • If we understood you correctly, you refer to the solution for the special case: the Robinson-Trautman metric. There is a number of special metrics for which the solutions can be found (e.g., the Schwarzschild solution for a static spherically symmetric space-time), but all of them are preserved only under particular subsets of coordinate transformations. In particular, for the Robinson-Trautman solutions, see H. Stefani, et al “Exact Solutions of Einstein’s Field Equations”, Ch. 28, where such a set of transformations is given. By the way, Robinson and Trautman in their paper (Proceedings of the Royal Society of London, A 265, 1962, 463-473) wrote:

      “The geometric conditions imposed on our solutions, however, are too stringent to allow for completely realistic fields.”

      If one considers GR as a valid theory and wants to confirm its results by experiment, then these results should obey general covariance, i.e. they should be expressed in quantities which do not change under arbitrary coordinate transformations.

      Maybe, we were not precise when we wrote that Einstein’s equations do not have a wave solution. They might have a solution similar to what another nonlinear equation, e.g., Korteweg-de Vries’ equation, has – a solitary wave, but any solution of Einstein’s equations, which is to be related to observation, should be invariant under general coordinate transformations. For example, it is possible to consider a linear approximation of Einstein’s equation, or weak perturbation of a metric around a flat space-time, and find a plane wave solution, but there always exists a coordinate transformation (among all possible coordinate transformations) such that a plane wave solution disappears. In plane words, if we choose a coordinate system which oscillates together with a wave, then an observer in such a frame of reference will not “see” a gravitational wave. This is in contrast to the electro-magnetic theory. The solutions of Maxwell’s equations are invariant under Lorentz transformations, and consequently, there is no such a Lorentz transformation that can destroy a wave solution.

  2. s.vik says:

    Thanks for your explanation.
    So you are saying that there are other solution that may not be “waves” at all.
    Could there be fractal gravity field solutions to how two binary stars loose energy in their death spiral?

    The earth/moon orbits separate instead of spiraling inwards, due to tides! Could a binary system
    with a large and small star have the same effect?

    Can there really be gravity waves at 50 to 300 K Hz?? I though they were sub 1 Hz.

    • Einstein’s equations are integrable, but so far nobody found a general solution to them; but waves are not solutions to Einstein’s equations. They are solutions of some invalid approximations (like linear approximation) and/or contradictory to the spirit of GR assumptions, for example, general covariance.

      What is “fractal gravity”? Why is Einstein’s gravity not good and needed to be modified?

      Of course, if gravitational waves will be observed (at whatever frequency), then Einstein’s GR has not to be modified, but rather fully abandoned. In 1919, Einstein wrote:

      “The chief attraction of the theory [GR] lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible.”

      Albert Einstein, Ideas and Opinions (Wings Books, New York, 1954), p. 66.

      A half of century search of gravitational waves does not produce any threat to Einstein’s theory, and there should be a good reason for any alternative to GR (including “fractal gravity”).

      If gravitational waves are not observable, it does not matter at how many Hertzs to search them.

  3. Andrei says:

    Do you have new posts coming soon ?

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