On Sun, 15 Sep 2024 20:04:34 +0000, Paul.B.Andersen wrote:
(in response to Richard)
https://paulba.no/paper/Hafele_Keating.pdf
>
The _measured_ average drift of the four clocks was 8e-13.
But the drift of each clock was higher, so the precision
of the clocks was in the order 1e-12, or better.
>
But during 65 hours the uncertainty would be ±235 ns
so it would obviously be impossible to measure anything
with such a clock without some kind of calibration.
>
And of course Hafele and Keating knew that, they were not stupid
even if you think they were.
>
This was what they did:
Before the Eastward trip, they compared the clocks to the standard clock
at the US Naval Observatory (USNO) for 240 hours, and noted their drift.
They did the same for 150 hours between the trips, and again for 110
hours after the Westward trip.
This way they could interpolate the drift during the trips.
>
https://paulba.no/paper/Hafele_Keating.pdf
See fig.1 and fig.3 and READ the text!
A serious complication that H&K needed to compensate for, is that
in addition to fluctuations in rate due to shot noise in the beam
tubes, early cesium clocks frequently exhibited "more or less well
defined quasi-permanent changes in rate. The times at which these
rate changes occur typically are separated by at least 2 or 3 days for
good clocks." Due to the stresses of travel, these random jumps in
rate occurred more frequently than for clocks in a stable laboratory
environment.
Fortunately, a time-honored technique exists for detecting and
compensating for rate glitches in otherwise stable clocks. This is the
technique of "correlated rate-change analysis", first used by Newcomb
in 1874 to detect changes in the Earth's rotational period.
During the 636 hours of the experiment
- H&K took over 5000 inter-clock comparisons while the clock was on
the ground as well as in flight.
- While on the ground, they took hourly comparisons of each clock with
USNO time.
Their continuous inter-clock comparisons enabled them to pinpoint the
times and magnitudes of the rate jumps for each clock.
To illustrate how correlated rate change analysis works, consider the
following made-up data from a hypothetical ensemble of three clocks.
Clock 0 initially runs a bit fast, while clocks 1 and 2 run a bit slow
compared with the ensemble mean. The following table presents, in
columnar format, data for the three clocks. The columns marked "t"
show hourly clock readings, which are compared with the ensemble means
to their right.
At a certain time during the run, one of the clocks exhibited a rate
change. Which clock exhibited the rate change, when did the rate
change occur, and did the clock speed up or slow down?
Clock 0 Clock 1 Clock 2
t mean t mean t mean
4 3.9650 4 4.0052 4 4.0294
5 4.9564 5 5.0065 5 5.0367
6 5.9478 6 6.0079 6 6.0441
7 6.9392 7 7.0093 7 7.0514
8 7.9306 8 8.0106 8 8.0588
9 8.9220 9 9.0120 9 9.0661
10 9.9134 10 10.0132 10 10.0732
11 10.9081 11 11.0129 11 11.0789
12 11.9028 12 12.0126 12 12.0845
13 12.8976 13 13.0123 13 13.0902
14 13.8923 14 14.0120 14 14.0959
15 14.8870 15 15.0117 15 15.1015
16 15.8817 16 16.0114 16 16.1072
I note that Richard considers himself to be an Excel expert. It is
quite easy to analyze this data using Excel. If Richard plots the
differences of each individual clock reading from the ensemble means,
then it should be apparent that at Hour 10, Clock 0 experienced a
rate slowdown of 0.5%. This caused the ensemble mean rate to decrease
by 0.17%. The result is that Clock 0 showed a net slowdown of 0.33%
relative to the ensemble mean, while Clocks 1 and 2 both showed a net
speed up of 0.17% relative to the ensemble mean.
Hafele and Keating used FOUR clocks rather than the three clocks in my
demonstration. This enabled them to resolve the rare instances where
two clocks might have glitched at the same time.
…