From: lip@s1.gov (Loren I. Petrich)
Subject: Re: That Great Pulsar Timing Flame War
Organization: LLNL
Date: Sat, 9 Jan 1993 01:08:47 GMT

In article <C0IoBJ.4x8@well.sf.ca.us> metares@well.sf.ca.us (Tom Van Flandern) writes:
>lip@s1.gov (Loren I. Petrich) writes:
:  So, we have the following parameters all from observation:
:  - The projected semimajor axis a1*sin(i)
:  - The period P
:  - Its first derivative dP/dt [*]
:  - The eccentricity e
:  - The periapsis angle omega
:  - Its rate of change d(omega)/dt [*]
:  - The redshift parameter gamma = sqrt(a/m)*(mc*(mp+2*mc)/m^2)*e [*]

>     The three parameters I have marked with [*] actually form a single
>solution parameter, according to Taylor and Damour.  There is insufficient
>observational power to separate them.  The masses and orbit must be
>determined from observations along with this single relativistic parameter.
>So the relationship between the three components of the relativistic
>parameter must be set by theory, since it cannot be measured by observations.

	I'm not sure that this is quite correct. _Where_ do they state
precisely this, if this is what they now conclude?

	It is indeed true that the redshift parameter gamma cannot be
distinguished from appropriate changes in the eccentricity and the
periapsis angle _if the periapsis does not precess_.

	However, if it _does_ precess, then this term _can_ be
distinguished. Consider the equation:

	t(delay) = a1*sin(i)*(sin(omega)*(cos(E) - e) +
cos(omega)*sqrt(1-e^2)*sin(E)) + gamma*sin(E)

	where E - e*sin(E) = n*t + 1/2*n'*t^2 (Kepler's equation).

	Notice the two sin(E) terms.

	The eccentricity is quite large, e = 0.617139(5), which should
make it possible to pin down omega without much trouble.

	Currently, the periapsis advances at a rate of 4.2261(7)
deg/yr, which gives 34 degrees of advance from 1974 (when it was
discovered) to 1982 or 76 degrees to now. And this should be _more_
than enough.

	[Source: Shapiro and Teukolsky, _Black Holes, White Dwarfs,
and Neutron Stars_, giving 1982 results]

	And indeed, the 1982 Taylor and Weisberg result quotes a value
of the redshift parameter and a value for the period change rate, as
if they could distinguish these parameters.

	If I understand you correctly, Taylor and Damour now claim
that they _cannot_ distinguish those effects. That's news to the whole
relativeistic-astrophysics community.

:  If one assumes the GR result for G-wave emission, then one predicts an
:  unambiguous result for dP/dt, which is very close to what is observed.
>
>     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.

	It may take it a while before I can get a hold of that paper,
but what is Yu's argument? Ambiguity of total energy in GR? The
illegitimacy of standard derivations of the radiation reaction? What
"errors" does he find in standard arguments?

>     Even if one derives the amount of gravitational radiation in the way you
>prefer, that still makes assumptions that are reasonable, but not confirmed
>by observation or experiment.  These assumptions fall into two categories:
>(1) G-waves will differentially affect two independent masses in a detectable
>way, as opposed to setting up oscillations within a single mass.  That point
>is distinctly arguable.  But note that the whole design of LIGO assumes it is
>true.  That is one reason some of us feel that the LIGO design is premature.

	That is a glaring misunderstanding.

	That opposition between two different masses and oscillations
in a single mass just does not exist. Both effects are predicted by GR
and most alternative gravity theories. As to G-waves interacting
differently with different masses, that is not the case. Two separate
masses are used in some experiments because it is the separation that
counts.

	And why is the LIGO design supposed to be so defective?

>     (2) 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?  It seems more reasonable to
>assume that the carrying media for electromagnetism and gravity are
>distinguishable, and that we will eventually develop the observational
>capability of distinguishing them.  Then we are back to the original
>situation that we can't be sure we know the key properties of the propagating
>medium for G-waves.  We are presently just making unverified assumptions
>based on a highly questionable analogy with electromagnetism.

	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. If you want a "field theory" viewpoint of spacetime,
consider the "metric formulation":

	ds^2 = g_ij dx^i dx^j

	in GR notation. Instead of a vector potential for EM, there is
a symmetric-tensor potential for gravity in GR, the g_ij's.

	The equivalent of Maxwell's equations is Einstein's equation

	G_ij = k*T_ij

	where G_ij is the "Einstein tensor" formed from the g_ij's in
a coordinate-invariant fashion and T_ij is "stress-energy tensor",
which has the function of the charge in EM theory. The "k" is a
constant in GR. Alternative theories of gravity, like the Brans-Dicke
theory, feature extra fields, and usually yield an equation like:

	G_ij = k(f)*(T_ij + T_ij(f))

where f repesents the extra fields.

:  It _might_ be possible that there is some alternate theory of gravity which
:  predicts (say) a value of d(omega)/dt different from GR and a value of
:  G-wave emission different from GR, with the fitted parameters resulting
:  from a1*sin(i), P, gamma, and d(omega)/dt giving _exactly_ the observed
:  value of dP/dt, but it would have to be a very contrived theory.
>
>     Whether or not you agree with Yu's theoretical argument that GR should
>actually predict zero gravitational radiation, you can see that the pulsar
>timing observations do not allow us to disprove Yu's argument.  GR with zero
>gravitational radiation can be made to fit the data equally well.  It was
>common to see the amount of gravitational radiation predicted by GR disputed
>up until the announcement that the binary pulsar had "confirmed" a particular
>value.  We now see that the observations did not confirm a particular value;
>rather, a particular value was assumed to be "the GR value," and that value
>was shown to be in agreement with observations.  But other values make
>equally good fits.

	GR with no G-waves making an equally good fit???

	[More on that above]

>Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
>Meta Research was founded to foster research into ideas not otherwise
>supported because they conflict with mainstream theories in Astronomy.

	And it looks like you need a refresher course in GR, so you
can understand what it's all about.
-- 
/Loren Petrich, the Master Blaster
/lip@s1.gov