tessel@um.bot wrote:

> On Sun, 8 Jan 2006, John Bell wrote:
[snip}

> > (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.
After due reflection, I must admit that I find your analogy argument

far less than rigorous in terms of pure mathematics, physics, or even

philosophy. Although analogy with light (EMR) is sometimes used for

teaching purposes where we already know that gravity behaves similarly,

this analogy takes us into deep and dangerous waters when used to

explore the unknown. When we move like poles together in EM their

potential energy increases. When we move *like poles* together in

gravity, their potential energy decreases. We would arrive at precisely

the wrong conclusion if we attempted to deduce this property of gravity

by analogy with EM.

In your case, you have assumed that the assumption of positive energy g

waves is correct, and then used the EM analogy to conclude that this

would remain positive if propagating at -c. You have forgotten, in the

process, that we know perfectly well, in the EM case, that the later

participant gains energy via the interaction. In the g case, we know

only that the participant (eg the binary pulsar) loses energy.

Consequently, both by energy conservation rules, and by a more rigorous

EM analogy, we are forced to conclude that the energy of this wave must

be negative if propagating at a speed of -c. You can then *prove* by

re-application of your EM analogy, that this energy must remain

negative if propagating at a speed of +c. You can thus *prove* that a g

wave propagating at a speed of +c would violate the Einstein energy

conservation constraint. (See what I mean by deep & dangerous waters?).

For more on this constraint, see discussion with Eric Grisse

John Bell