Hindsight does wonderful things to aging eyes, so it's good to go back
and check old material. This past week, while travelling on business, I
revisited Anderson et al's 2002 report for a slow, careful look. In
particular, a question that I should have looked carefully at back in
1998, but could not because their 1998 article didn't explain the
background, and in 2002, I had too many other things on my mind.

How did they arrive at the sunward acceleration? What was the actual
data, and what were the steps of inference?

Baez's open questions list and Ned Wright's pages only discuss the
acceleration conclusion. Data questions have been painstakingly
reviewed and reported by NASA themselves in the 2002 report, and
there's been little to add. Virtually all the rest of us have been
however taking their inference to be too simple and open (at least as
of the 2002 report) to be wrong, and conjecturing or trying to come up
with various ways to explain the conclusion itself.

Looking back at the report, section V B in particular, I finally see
what they did - and while it's a bit unforgiving, please remember that
all of us have been equally befuddled or deluded as well:

1. CHASMP identifies a negative frequency drift, -6 x 10^{-9} Hz / s,
in the round trip loop having uplink and downlink frequencies of 2.11
and 2.23 GHz, respectively.

A negative drift means (and this is definitional, no room for argument
here!) that the returning signal kept falling in frequency, even though
the outbound signal was constant (for the purpose of explaining the
drift). If we hadn't sent the signal in the first place, we'd have very
likely called this a redshift drift, which is why I, and several others
in 1998-2001 timeframe, treated the anomaly as a redshift, and came up
with solar system expansion implications.

2. The NASA/JPL team then divides this negative frequency drift by the
signal frequency to get a normalized value. However, since the units
now become s / s^2 (since the drift was Hz / s = 1/s^2), so the team
calls this a "clock acceleration". The value is a path-average of -6 x
10^-9 / 2.11 G and -6 x 10^-9 / 2.23 G, and comes out to -2.84 x 10^-18
s / s^2.

The result still carries a -ve sign - so it's really still a clock
deceleration, i.e. a redshift.

3. Now that they have an acceleration with respect to time, the team
decides to apply the old relativity formula to convert it to an
acceleration with respect to space - just multiply or divide by 'c' to
get the right dimensions. In this case, s/s^2 x m/s = m/s^2 , so they
multiply by 'c' to arrive at their famous acceleration. So to
summarize:

[red drift] -6 x 10^-9 s^-2 --> -6 x 10^-9 s^-2 / {2.11,2.23 G} = -2.84
x 10^-18 s/s^2 [clock]

[clock drift] -2.84 x 10^-18 s/s^2 * 3 x 10^8 m/s = -8.4 x 10^-10
m/s^2 [acceleration!]

So how did it become sunward, which would mean a blueshift as people
started pointing out in 2000s? It was just the negative sign hanging
over from the negative frequency drift, where it DID mean a drift
towards the red. So did we miss something in step (3)? I don't think
so - multiplying by 'c' is simply a dimensional transform from time to
space. No hidden slight of physics or math here. In hindsight, there
SHOULD have been physical reasoning when multiplying by 'c' - reasoning
that would have dispensed with the sign because when we change
dimensions, we must reexamine our sign conventions to fit the new
dimensions. That the NASA/JPL team evidently forgot.


So is there an anomaly to be explained? Of course. But is it red or
blue? A blueshift is incompatible with a negative clock drift at or
from the same location, relativistically or otherwise. A redshift, on
the other hand, is NOT a sunward acceleration, but motion away from the
sun, as in fact immediately suggested in 1998 by Rosales and
Sanchez-Gomez, and would match a solar system scale cosmological
acceleration (or quintessence if you must), as also already suggested
by others in 1998-1999. A blueshift, on the other hand, is a mystery
because it can never simultaneously explain the CHASMP equivalence to a
clock slowdown (term used in Anderson et al's 1998 paper), and is
therefore a very exotic beast - belonging only in fairy tales.

Perhaps there's another lesson as well. The NASA/JPL team's driving
motivation seems to have been solar system tests of relativity. When
one looks for an acceleration that matches the pattern of gravitation,
that's exactly what one gets, by hook or by folly. WY(want to)SIWYG. We
humans do that all the time!


-prasad