Ranging and Pioneer

[[Mod. note -- I have snipped large chunks of quoted material from this
post in the interests of brevity. Posters, please realise that readers
have generally *already* read the article you're quoting -- you don't
have to quote the whole thing verbatim again! Please just quote enough
to establish the context for what you want to say. -- jt]]

Oh No wrote:
Thus spake George Dishman
...
Charles could you clarify the details of your calculation of
the Pioneer effect since it is significantly larger than the
cosmological redshift.
[[Mod. note -- 7 lines snipped. -- jt]]

The basic idea is that quantum theory can be formulated using
conformally flat coordinates. I treat quantum theory as a calculational
[[Mod. note -- 20 lines snipped. -- jt]]
When the final state of one part of the motion is reinterpreted as the
initial state for the next part of the motion, the quantum theory must
be renormalised. This removes a factor of the expansion parameter from
cosmological redshift, yielding the normal linear law for cosmological
redshift.

Thanks, I just about understood the working and
the consequence is clear.

When we measure classical motions local to the earth we can
determine motion to great accuracy. The motion thus consists of many
initial state-final state stages, and reduces to geodesic motion under
the normal affine connection.

Of critical importance is the timescale between initial state and final
state when modelling the motion. This timescale is determined by the
accuracy with which we can measure. Local distances can be measured with
great accuracy, equivalent to a short timescale. Remote distances are
intrinsically less accurate (e.g. radar distance measurements to mars
are accurate to about 12m).

I'm not familiar with the details of Mars
ranging but I have looked at Pioneer in
some detail. I will comment on that as it
may be of interest to you but it doesn't
seem to answer my original question.

The signal from Pioneer uses an effective Doppler frequency of 1MHz,
equivalent to a distance scale of 300m.

Although the final digital analysis is done
around 1MHz, the RF is heterodyned down
to that against the reference. It means that
the measurement resolution is still that of
the 2.291GHz carrier. Further the MDA is
capable of measuring phase to 1/256 of a
cycle or about 0.5mm in range. While the
ranging system itself wasn't available, the
frequency measurements are still taken
from that same hardware and have that
resolution. Note the residuals from Galileo
in Figure 10 of gr-qc/0104064 and the
discussion to the left that indicates
consistency to about 4m over a day.

The actual measurements are limited to a
few metres accuracy mainly due to the
group delay in the somewhat unpredictable
solar plasma and the unknown angle of
refraction through the atmosphere and at
the boundary of the ionosphere, but the
resolution of the instrument which I think
is the determining aspect from the QM
point of view is better than 1mm.

So I am predicting that when the
measurement of distance is accurate to better than 300m, the period of
the signal spans more than one quantum stage, and the standard general
relativistic result is predicted.

That would certainly apply to Pioneer
whichever resolution you adopt.

When measurement of distance is less
accurate than 300m the Doppler signal is measured incorporating the
square law for cosmological redshift.

OK, so I understand those two conditions
to mean either you get the conventional
redshift value for low resolution measurements
or you get no extra redshift locally beacause
we have higher resolution measurements.

In this case the anomalous Pioneer
shift is found.

This was the gist of my original question and
where I am still puzzled. The conventional
linear Hubble law if applied to Pioneer 10
predicts an apparent acceleration some
15000 times smaller than the anomaly given
by the equation a_H = 2 H v. I don't understand
why you think your analysis produces a result
four orders of magnitude larger than the normal
Hubble Law under either of the regimes you
explain above.

Sorry if I'm being a bit slow but it is this factor
of 15000 increase that I cannot fathom.

The apparent inconsistency between these two results is taken up by
cycle slip, or apparent jumps in motion (it is possible that such a jump
has been observed in VLBI measurements of IM Pegasi which appears to
occasionally jump up to 2/3 its radius). Currently cycle slip is treated
as a "blunder point" in the collection of data, and has been discarded
from the analysis of the Pioneer data. If this is right it may be
possible to reanalyse the pioneer archive and show that the discarded
data resolves the anomaly - or it may be that there are also real
blunders in the data such that the analysis becomes impossible :-( .

There will be blunder points due to noise
but might be distinguishable since they
will always be exactly a carrier cycle at
the macroscopic frequency and should
occur randomly given gaussian noise in
the channel.

George