Re: Is temporal sign ambiguity inherent in Einstein's general relativistic field equation?
- From: tessel@xxxxxx
- Date: Sun, 22 Jan 2006 23:53:07 +0000 (UTC)
On Sun, 8 Jan 2006, John Bell wrote:
Mathematically speaking, Einstein's general relativistic field equation admits two possibilities for the speed of propagation of gravitational fields/waves, + or - the speed of light (c) (i.e. propagation forwards or backwards in the dimension of time).
Not quite. Rather, relativistic field theories such as gtr possesses time reversal symmetry, because the Lorentz group admits such a symmetry. The symmetry group of Newtonian physics is different from the Lorentz group, but also includes time reversal, so this property is by no means characteristic of relativistic field theories.
If so, it appears to me that this might provide a conceptually simpler/alternative explanation as to why such orbits remain stable, to that given in the physics faq. (although clearly, the real reason for this stability is that Einstein derived the equation from the axiomatic foundations of the theory, under the constraints of energy and impulse conservation)
I don't understand why you think that, but I don't think time reversal symmetry will help understand stability or lack of stability in solar system dynamics, either in Newtonian physics or in relativistic physics. Note that relativistic effects are unlikely to overwhelm Newtonian effects whcih are more important in determining stability or lack of stability. See Solar System Dynamics by Murray and Dermott for an excellent introduction to this topic in the context of Newonian physics.
It seems you might believe that the state of the art in physical theory predicts that our own solar system is "stable". In fact, just the opposite is true. See John Baez's Week 222 and ensuing discussion of the digital orrery project, which includes relativistic effects (but as I said, these probably do not play the most critical role in questions of stability).
(In the case of the decay of binary pulsars, it appears to me at present, that the emission of negative energy gravitational waves with negative propagation speed should be mathematically equivalent to the emission of positive energy waves, with a positive propagation speed)
No, time reveral doesn't turn positive energy waves into negative energy waves. Just consider the simpler example of electromagnetic waves! For example, wiggling a charge here produces an EM wave with spherically expanding wavefronts and positive energy. Time reversal results in an EM wave with spherically contracting wavefronts, but positive energy, which contracts onto a charge and wiggles it. As Feynman noted in his Lectures, that seems pretty bizarre, because the boundary conditions for a wave with collapsing spherical wavefronts is less realistic than the boundary conditions for a wave with expanding spherical wavefronts, but if we could produce the latter, it would indeed wiggle the "target" charge as stated.
"T. Essel"
.
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