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In article <C0p70n.15z@well.sf.ca.us> metares@well.sf.ca.us (Tom Van Flandern) writes:
>and lip@s1.gov (Loren I. Petrich) [= "LP" below] replied:
>
:  [LP] I'm not sure that this is quite correct. _Where_ do they state
:  precisely this, if this is what they now conclude?

>     Here is what the authors actually claim in their own words:

>     "Examples of theoretically well motivated theories have recently been
>constructed which have the same post-Newtonian limits as general relativity,
>and can pass the omega-dot/gamma/P-sub-b-dot test without fine tuning, while
>still differing markedly from Einstein's theory because of the strong self-
>gravity effects in the pulsar and its companion."  [Damour, Class.Quant.Grav.
>9, p. 55 (1992)]

	I'm looking forward to seeing more details.

	It is a bit difficult for me to imagine a theory with the
post-Newtonian parameters (gamma) and (beta) being very close to 1 for
low-density sources, but noticeably different from 1 for neutron
stars, but I guess I'd have to see what Damour had had to say about
that.

>     "The omega-dot/gamma/P-sub-b-dot test is a mixed one which combines
>strong-field and radiative effects in an indistinct way, so that one cannot
>logically conclude, when a test is satisfied, that both the specific strong-
>field and radiative predictions of general relativity have been independently
>confirmed."  [Taylor and Weisberg, AstrophysJ 345, p. 434 (1989)]

	If one treats post-Newtonian and radiative effects with
appropriate fudge factors like the aforementioned (beta) and (gamma),
that is indeed correct. However, various theories put constraints on
these fudge factors, thus allowing potential tests.

>     "Damour and Esposito-Farese have recently constructed examples of other
>theories that can also pass the test, as well as all known tests of gravity
>in the weak-field limit, while differing substantially from general
>relativity in the strong-field regime.  They call attention to an inherent
>complication of the omega-dot/gamma/P-sub-b-dot test: it necessarily mixes
>quasi-stationary strong field effects (related to omega-dot and gamma) with
>radiative ones (related to P-sub-b-dot).  If a theory fails, the test, one
>gains no hints as to whether its problems lie in the (quasi-stationary)
>strong field or the radiative regime."  [Taylor, Wolszczan, Damour, Weisberg,
>Nature 355, p. 132 (1992)]

	I agree that that is a potential problem at the current level
of accuracy, but Shapiro time delay and eccentricity effects may well
offer additional tests, as I have commented, though that would take
pulsar-timing accuracies of at least a few microseconds to see the
basic effects and about 100-300 nanoseconds to see the eccentricity
effects for moderately large (~0.5) eccentricities.

: > A part of the difference of viewpoint here centers on exactly what is
: > "the GR result for G-wave emission."  The Yu paper [Yu Xin (A. Yu), "Does
: > Einstein's G.R. theory predict gravitational radiation of PSR 1913+16?",
: > Astrophys. & SpaceSci. 194, 159-163 (1992)], for example, argues that
: > G-wave emission in GR must actually be zero.

:  [LP] what is Yu's argument?

>     Next, Yu derives the quadrupole radiation formula (-dE/dt = ...),
>emphasizing its one-body nature.  Then he says, "However, for a finite
>neutral particle system, the theory proves illusory ...,"

	How?

...and he proceeds to
>show that the right-hand side in that equation must reduce to zero for such a
>system.

	I am told that he made an error, by going from momentum
conservation to concluding that the reduced quadrupole moment does not
change.

	Conservation of momentum leads to:

	Sum_a m[a]*x[a]_i = M*X0_i + P_i*t

	while the reduced quadrupole moment is

	Q_ij = Sum_a m[a]*(x[a]_i*x[a]_j - 1/3*delta_ij*x[a]^2)

	It is easy to show that conservation of momentum does not
cause this quantity to be a simple function of time.

	The metric perturbation h_ij is proportional to
(d^2/dt^2)Q_ij, to within some projection operators for getting into
some appropriate gauge, like the transverse-traceless one. The energy
output is proportional to the square of (d^3/dt^3)Q_ij, and this is
nonvanishing for binary-star systems.

Quoting again, "That is, there is no energy transported due to
>gravitational radiation; or, shall we say, the Einstein approximation scheme
>gives no gravitational radiation.  The argument goes with any particle system
>by induction.  ...  The claim that observed data from PSR 1913+16 has
>verified Einstein's gravitational radiation theory is, therefore,
>groundless."

	I've yet to see any mentions of radiation reaction.

:  [ST] I believe the error in Yu is that statement 3.1 (momentum is
:  conserved) does not imply 3.2 (reduced quadrupole moment vanishes).

>     This is right at the heart of Yu's argument.  Your statement is not
>obvious.  Could you please elaborate carefully, since a lot hinges on this
>matter.

	This statement is correct for a _single_ particle, but is
_not_ correct for a binary star system. It is easy to show that Q_ij
for such a system is mr * (r_i*r_j - 1/3*delta_ij*r^2), where mr is
the reduced mass and r is the separation. This is from x1 = -
m2*r/(m1+m2) and x2 = + m1*r/(m1+m2), from conservation of momentum.
mr = m1*m2/(m1+m2). For a circular orbit, r_i = a*(e1_i*cos(l) +
e2_i*sin(l)), where e1 and e2 are two perpendicular unit vectors, a is
the orbit radius and l is the orbit longitude.

	Q_ij = mr*a^2*((1/2)*(e1_i*e1_j + e2_i*e2_j) - (1/3)*delta_ij)

	+ mr*a^2*(1/2)*(e1_i*e1_j - e2_i*e2_j)*cos(2*l)

	Only the second term contributes to the time derivatives of
Q_ij and to the energy. For elliptical orbits, the principle is the
same, though the calculations are more involved. One can also derive
angular momentum loss; the change in J_i is proportional to
epsilon_ijk (d^2/dt^2)Q_jl (d^3/dt^3)Q_kl.

: > There is still considerable vagueness about exactly what comprises the
: > medium through which G-waves propagate.  Gravity waves are supposed to be
: > "ripples in spacetime."  But is this the same spacetime through which
: > electromagmetic signals propagate?  Then what distinguishes a G-wave from
: > an electromagnetic signal of very long wavelength?

:  [LP] Yes, it is the same spacetime :-)  How are they distinguished? By the
:  field that does the "waving". Electromagnetism is a separate field that
:  propagates in spacetime, while a gravitational field is (according to GR)
:  the spacetime itself.

>     So how does a gravity *wave* (not field) differ from an electromagnetic
>wave if both are waves of spacetime?  I argued that the properties of
>spacetime cannot be the same for both.  For example, we know that local
>(gravitationally bound) spacetime doesn't expand with the universe, but
>distant spacetime does.  [I refer to the known result from radar and
>spacecraft data that the solar system is not expanding at the Hubble rate.]
>Does the "density" (e.g., zero-point energy) of distant spacetime decrease as
>the universe expands?  What is the observable difference between expanding or
>non-expanding spacetime?  Surely you see the conceptual problems I'm pointing
>to.  Math can't answer such questions of concept or logic.

	Electromagnetism is a _separate_ field from the metric-tensor
field.

	The Solar System doesn't expand because (among other things)
it's too small. The Universe expands because the galaxies are flying
away from each other; this effect can be modeled (yes, modeled) as
expanding space.

	The zero-point energy density of the Universe is expected to
be unchanging. What does decline as the Universe expands is the
density of its contents.

:  [LP] A question about this criticism is why linearized GR would give the
:  right results for these Newtonian and post-Newtonian effects but not for
:  G-waves.

>     G-waves are a separate and unrelated phenomenon whose very existence is
>still debated.  As you see from Yu's argument and the preceding, there is
>even doubt about what GR predicts about G-waves.  It is not at all like the
>static field, the nature of which is not in doubt in GR, since additional
>assumptions about the medium must be made when discussing G-waves.

	That is not correct. In the "shallow wave" case, G-waves can
be treated as perturbations on a background spacetime; the waves
propagate on this background.

	G-wave solutions _do_ exist in GR.

	And I may add that radiative solutions are predicted along
with the quasi-static Newtonian and post-Newtonian effects in
linearized theory.

:  [LP] And it looks like you need a refresher course in GR, so you can
:  understand what it's all about.

>     Insults are out of place in a scientific discussion, and no one
>following this technical thread appreciates them.  Presumably we are spending
>our time on this because we are all learning some new things as we proceed.
>If you think I and others reading this would benefit from reading a different
>perspective, please provide a suitable reference for the benefit of all.
>     -|Tom|-

	I'm sorry if I insulted you, but it seemed like you were
making some rather elementary mistakes about GR, which seemed a bit
annoying to me to see from someone so insistent on critiquing that theory.

	I don't know any good (non-Mickey-Mouse) introduction to GR
that does not involve a _lot_ of mathematics, but if one can handle
(say) Jackson's _Classical Electrodynamics_, then one shouldn't have
too much trouble with GR. Books recommended:

	Misner, Thorne, and Wheeler's _Gravitation_ (comprensive, but
heavy going in places, and parts get into some rather arcane issues).
One chapter features the canonical derivation of G-waves in GR. You
might want to examine the MTW proof to see if you can find any errors
or less-than-warranted assumptions.

	Weinberg's _Gravitation and Cosmology_

	Ohanian's _Gravitation and Spacetime_ (?)

	Lightman, Press, Teukolsky (?) Problem Book in Relativity and
-- 
/Loren Petrich, the Master Blaster
/lip@s1.gov