From: lip@s1.gov (Loren I. Petrich)
Subject: Re: Size of Second-Order GR Effects in Binary Pulsars
Organization: LLNL
Date: Mon, 21 Dec 1992 21:14:09 GMT

In article <BzKK19.37I@well.sf.ca.us> metares@well.sf.ca.us (Tom Van Flandern) writes:
>
>lip@s1.gov (Loren I. Petrich) writes:
>
: total energy, momentum, angular momentum, and center-of-mass location (the
: familiar 10 integrals) are well-defined quantities.
>
>     There is apparently some argument about the system of equations being
>over-determined because of an extra identity that has been found.  I can't
>say for certain that Yu's paper is correct, but the matter isn't trivial
>either.

	What extra identity???

: even if the total energy was not a well-defined quantity, one could always
: calculate the effect of the radiation reaction. I have to wonder how Yu's
: paper made it past the referees.
>
>     It would help if you read it and gave us an informed opinion about the
>actual line of reasoning.  Blind shots are not helpful.

	Maybe I'll find it sometime and check it over. But if it is in
some obscure, out-of-the-way journal, you ought to indicate whether or
not it is worth the trouble. In the meantime, you can be reading some
mainstream GR text like Misner, Thorne, and Wheeler's.

: So Yu claims _zero_ G-wave flux?  That is contrary to all the GR literature
: I have ever read.  Any GR textbook will contain derivations in gory detail.
: Here's some books: ...
>
>     Yu is familiar with these derivations, and opens his article by
>repeating the derivation.  The issue is not with the derivation, but with the
>assumptions on which it is based.  Yu reasons that the right-hand side of the
>energy-change equation is vacuous.  He is not alone in thinking this.

	See above about conservation integrals. And does he discuss
radiation reaction? Including _that_ effect gives the right result also.

: There is also the additional problem that GR works very well in the
: post-Newtonian limit in the Solar System, and it is post-Newtonian effects
: that allow the masses of the two Hulse-Taylor objects to be determined, as
: well as the orbit size. Plugging all these, with the eccentricity, into the
: GR G-wave orbit-decay rate formula gives essentially the right value.
: Alternate theories that differ from GR have to suffer some very fine tuning
: to get the right G-wave emission rate.
>
>     It is important to read and understand the 1992 papers by Damour and
>Taylor, as well as Yu.  Ordinary, classical GR with zero gravitational
>radiation is just as consistent with the binary pulsar observations as is GR
>with the Taylor radiation formula.  The other GR effects, the star masses,
>and the orbital elements soak up the difference.  The radiation effects
>cannot be separated out of the solutions, so one cannot say from the
>observations whether they are zero or non-zero.

	That is just plain wrong. See Shapiro and Teukolsky's book,
for example. Here are the parameters determined from observation:

	[Newtonian]

	Period: P = (2[pi])*sqrt(a^3/(M1+M2))

	Rate of change: (dP/dt)

	Projected semimajor axis: a*(M2/(M1+M2))*sin(i)

	Eccentricity:

	Periapsis position: [omega]

	Rate of change: (d/dt)[omega]

	GR prediction: (2[pi]/P)*(3*(M1+M2)/(a*(1-e^2)))

	[Order (v/c) Post-Newtonian]

	[beta] = (M1*M2*(M1+2*M2))/((M1+M2)^2/a)*e

	From the period, the projected semimajor axis, the rate of
periapsis advance, and [beta], one can find four quantities: a,
sin(i), M1, and M2. If one assumes post-Newtonian GR, one has a
_completely_ determined system.

	Assuming GR for G-waves, one can calculate the value of
(dP/dt) as a function of a, e, M1, and M2, determined from the rest of
the observations, and compare it with the observed value. One finds 50
sigmas of agreement so far.

: If one takes the Newtonian orbit parameters: (a1 sin i), P, and e, and adds
: in the redshift effect and the precession rate (assuming the truth of GR's
: post-Newtonian approximation), one uniquely determines the masses, the
: semimajor axis, and the inclination.
>
>     Sorry, that's not so.  You get different values for these parameters
>from the observations depending on whether or not radiation is included in
>the theoretical model.

	That is just plain wrong. See above.

: It just doesn't work out that way. The other elements don't "adjust". They
: are precisely fixed by post-Newtonian GR.

>     The elements and masses are what is called "constants of integration."
>They are completely free parameters.  No theory can predict their values.  If
>observations are compared to a theory with radiation, one set of constants
>gives the best fit.  If a theory without radiation is used, a different best
>fit results.  In other problems one might be able to tell which fit was the
>better.  But not so in this case: the fits are of equal quality.

	And how is a "theory with no radiation" supposed to work out???

	As I had explained above, whether or not (dP/dt) is due to
G-waves has NOTHING to do with the determination of the rest of the
orbit parameters.

	I'll be gone for the next two weeks after tomorrow...

>and matt@physics2.berkeley.edu (Matt Austern) writes:
>
: The argument that Yu makes seems to apply only to the second assertion: he
: is trying to show that a time-dependent quadrupole doesn't radiate.
>
>     That is not the main thrust of his argument.  See if you can get a copy
>of the article and take a look at the math.  -|Tom|-
-- 
/Loren Petrich, the Master Blaster
/lip@s1.gov