🚀 go-pugleaf

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.
|> 

As Loren has already pointed out, this is not correct.  I will try to
explain why a bit more completely.  First, the asterisk after dP/dt is
simply wrong.  The pulsar spin period and binary orbital period have
been confused.  Second, Loren is right in saying that the advance of
periastron "decouples" d(omega)/dt (typically referred to as
"omega_dot") from gamma.  They are instantaneously covariant, but over
the nearly two decades from the discovery of PSR~B1913+16 the
periastron advance has cleanly separated the variables.

The real error here is the claim that Taylor and Damour say that
these parameters form a "single solution parameter" which cannot be
observationally separated. Actually, the orbital period derivative
(P_b_dot), gamma, and omega_dot form a single "test" of GR.  A nice
graphical way to think of this is that each parameter measured defines
(in any gravity theory) a line in the "m_1/m_2" plane (in which the two
axes are the pulsar and companion masses).  Because the masses must
each take on a single value, these three lines must meet at a single
point.  This is indeed found in GR, in Brans-Dicke theory with a large
enough BD parameter, and in Damour et al's "tensor-biscalar" theories
with small enough scalar parameters.  This last case, in particular, is
the one that started this whole thread: Damour et al. pointed out that
the P_b_dot-gamma-omega_dot test does not do a good job of
discriminating between these new tensor- biscalar theories and GR.  No
matter how good the test becomes, as the data continues to come in, you
can always sneak through this alternative theory by making the small
parameters smaller.

Note this is not the end of the story with binary pulsars.  As Taylor and
others pointed out in a Nature article recently, PSR~B1534+12 offers
a new "test" which uses Shapiro time delay measurements rather than
P_b_dot and is thus "nonradiative", and useful in squeezing on a
different set of alternative theories.

As a scientist working in the field, let me restate my own opinion,
offered some weeks ago.  Taylor and Weisberg, in their observations of
the binary pulsar PSR~B1913+16, have demonstrated the existence of
gravity waves beyond any real doubt.  The fact is that a prediction of
an orbital decay rate due to the loss of energy and angular momentum
into gravitational radiation was made, and the measurement was done and
the results matched to better than 1%.  Any serious claim against GR
or gravitational waves must now reproduce this result in a natural
way.  I am all in favor of the continued exploration of alternative
models, done so well recently by Damour.  My PhD thesis included much
discussion of alternative models.  Someday the real limits of GR will
be reached, and it will be quantized and perhaps folded into a GUT, and
I believe this explorations of the underpinning of GR may show the
way.  But in the meantime, there is no reason to believe that the
"standard model" is incorrect.

Steve Thorsett
Caltech

PS. I believe the error in Yu is that statement 3.1 (momentum is conserved)
does not imply 3.2 (reduced quadrupole moment vanishes).  Most of Yu's
paper is non-controversial and not new.  See chapter 36 in MTW for correct
derivation.