Tom Roberts:
> David Jones:
>
> > Also, 'messy data' (with big sources of random error)
> > remains a problem with solutions that are mainly ad-hoc
> > (such as, when Roberts offers analyses that drop large
> > fractions of the data).
>
> I did not "drop large fractions of the data", except that
> I analyzed only 67 of his data runs, out of more than
> 1,000 runs.

So you did not include 93% of data, for the reason stated
below:

> As my analysis requires a computer, it is necessary to
> type the data from copies of Miller's data sheets into the
> computer. I do not apologize for doing that for only a
> small fraction of the runs (I had help from Mr. Deen).
> The 67 runs in section IV of the paper are every run that
> I had.

What I regret is that you selected the 67 runs from
disparate experiments, instead of from the ones Miller
considered his best (and might prove his
worst!) -- performed on Mt. Wilson. Are you certain you did
not pick some of the sheets recording laboratory tests of
the interferometer, including those to determine the effect
of temperature irregularities, rather than actual ether-
drift measurements?

> It is drifting, often by large amounts -- so large that in
> most runs Miller actually changed the interferometer
> alignment DURING THE RUN by adding weights to one of the
> arms (three times in the run of Fig. 1).

To avoid the wrong imporession, he /never/ readjusted the
interferometer mid-turn, but always during a special
calibaration turn, when no observations were being made. In
other words, those adjustments took place /between/ complete
full-turn series of observations and no doubt contribute
large and sudden discontinuitites into your error-difference
functions, for I think you did not sew-together the
observation turns separated by such calibration turns, prior
to fitting the model of systematic drift. These
calibration-caused irregularities may have a negative effect
upon the fitting of combined systematic drift.

> Even so, there are often jumps between adjacent data
> points of a whole fringe or more -- that is unphysical,
> and can only be due to an instrumentation instability.

Not all the errors are systematic, as Miller himself noticed
the action of sound in disturbing the air in the
interferometer light path, let alone those due to the
hypothetical aether wind, which, if partially entrained,
will be affected by atmospheric turbulances, as well as show
the typical instabilities occuring when a laminar flow meets
with obstacles.

> Modern interferometers are ENORMOUSLY more stable. In the
> precision optics lab I manage, we have a Michelson
> interferometer that is ~ 10,000 times more stable than
> Miller's. We use it to stabilize lasers, not search for an
> aether. That stability includes a lack of 12-hour
> variations, with a sensitivity of ~ 0.00002 fringe (~
> 10,000 times better than Miller's).

How interesting. Is it installed in a basement and/or
screened off from the hyphothetical aether by metal? I
should like to see it installed in a triple-glass casement
on Mt. Wilson and left for an entire year. Hardly possible,
of course...

> By taking advantage of the 180-degree symmetry of the
> instrument, only 8 orientations are used.

No, I think you are taking advantage of the 180-degree
symmetry of the hypothesised effect rather than of the
instrument, which itself may be asymmetrical due to many
factors, including an asymmetrical air flow and temperature
in the aether house.

> Note I did NOT do the simple and obvious thing: use the
> data for the first 1/2 turn as the values of the
> parameters. That would reintroduce signal(orientation) and
> make the analysis invalid.

The subtraction of the first turn has but one effect -- that
of offsetting each of the eight error-difference curves by a
constant value, equal to the observation in the first turn
at the corresponding azimuth. It has /no/ effect on the
forms of those curves. Since your fitting consists in
finding the seven relative vertical offsets between these
curves, it may safely be applied to the raw drifts at each
combined mark, in which case the seven fit parameters will
represent the pure signal, if any!

Tom Roberts:
> David Jones:
>
> > I have heard some non-statistical experts in other
> > fields just using "chi-squared" to mean a sum of squared
> > errors.
>
> I used the term as it is commonly used in physics. It is a
> sum of squared differences each divided by its squared
> errorbar.

So you used a weighted form the of least-squares. But then
a complete enumeration is unnecessary, becuase least-squares
is designed to be an analitical method with linear
complexity: you simply write the smoothness function as a
sum of weighted squared differences over the tabulated data
and optimise it the usual way via partial derivatives.
Notice, however, that large discontinuitites between runs
due to interferomenter calibration are likely to dominate
the fitting.

> But criticism about using just 67 runs out of >1,000 is
> valid.

That critisicm is mine, Tom, and I would clarify that the
entire set of the Mt. Wilson experimenets, consisting of
some 350 runs, would make happy.

Tom Roberts:
> David Jones:
>
> > If this were a simple time series, one mainstream
> > approach from "time-series analysis" would be to present
> > a spectral analysis of a detrended and prefiltered
> > version of the complete timeseries, to try to highlight
> > any remaining periodicities.
>
> Fig. 6 is a DFT of the data considered as a single time
> series 320 samples long, for the run in Fig. 1.

Unfortunatly, this is affected by the discontinuities due to
the several calibration turns, which is why I recommended
that you sew them together beforehand.

> Similar experiments with much more stable interferometers
> have detected no significant signal.

Were they performed according to Michelson's and Miller's
emphatic instructions not to obstruct the light path and the
aether flow, which includes raising the device as well as
possible above any terrestrial features?

> Arxiv says it was last revised 15 Oct 2006; the initial
> submission year and month are enshrined in the first four
> digits of the filename.

Which is why I thought it was published in 2006 rather than
in 1986. The earlier dates explains a lot.

> > Anton Shepelev wrote: there are no time readings in
> > Miller's data.
>
> Yes, but that doesn't matter, as time is not relevant;
> orientation is relevant, and that is represented by
> successive data points, 16 orientations for each of 20
> turns.

It is of some relevance where you consider it continuous
between turns, ignoring the unrecorded calibration turns,
are observing instabilities of high rate and magnitude at
points where two observations turns were interrupted by a
calibration turn.

> Note that Miller never presented plots of his data (as I
> did in Fig. 2).

I see that has the adjustments included, as I am sure you
had to do for the statiscical reanalysis in section IV as
well. Did you do it?

> Had he displayed such plots, nobody would have believed he
> could extract a signal with a peak-to-peak amplitude < 0.1
> fringe.

Why not? Assuming, as Miller did, the plot to consist of
signal, linear drift, and random noise, they would well
believe that oversampling would help rescue the signal,
produducing the nice smooth curves that Miller had.

What is your opinion regarding the claimed galactic
orientation of the measured drift, as plotted in fig. 22 of
the 1933 paper? Can an instumental error have a concistent
half-periodic dependency on 1) time of day and 2) the season
of the year so as to point into a fixed direction in the
galaxy?

> > [further analysis is] impossible without Miller's
> > original data
>
> Miller's original data sheets are available from the CWRU
> archives. They charge a nominal fee for making copies.
> IIRC there are > 1,000 data sheets. Transcribing them into
> computer-readable form is a daunting

I believe doing even the 67 was tiring. Do you know anyone
who could help me in obtaining the 350 sheets from the Mt.
Wilson experiements if I cannnot travel to CWRU in person?
I will pay the costs, of course.

Tom Roberts:
> Anton Shepelev:
>
> > Exactly, and I bet it is symbolic parametrised funtions
> > that you fit, and that your models include the random
> > error (noise) with perhaps assumtions about its
> > distribution.
>
> I don't know what you are trying to say here, nor who
> "you" is.

This is because you have chosen to reply to everybody in one
huge message. It was Rich Ulrich I was addressing.

> But yes, my model has no explicit noise term because it is
> piecing together the systematic error from the data with
> the first 1/2 turn subtracted; any noise is already in
> that data. Virtually all of the variation is a systematic
> drift, not noise, and I made no attempt to separate them.

And your argument for a neglibible noise is -- that the
systematic drift as you estimated it explains alone most of
the raw observed data?

> Note the quantization was imposed by Miller's method of
> taking data, not anything I did.

Sure.

Tom Roberts:

> Anton Shepelev:
>
> > Roberts jumped smack dab into the jaws of the curse of
> > dimensionality where I think nothing called for it!
>
> I have no idea of what you mean.

I mean the following:
https://en.wikipedia.org/wiki/Curse_of_dimensionality

Tom Roberts:
> Anton Shepelev:
>
> > Miller, considering the level of statistical science in
> > 1933, did a top-notch job. Both his graphs and results
> > of mechanical harmonic analysis[1] show a dominance of
> > the second harmonic in the signal, albeit at a much
> > lower magnitude that initially expected.
>
> See section III of my paper for why the second harmonic
> dominates -- his analysis algorithm concentrates his
> systematic drift into the lowest DFT bin, which "just
> happens" to be the second harmonic bin where any real
> signal would be.

In section III, analysing Miller data-reduction's in
frequency domain, you write:

...And finally the two halves of the 16 point 1-turn
signal are averaged to an 8-point 1/2-turn signal.
That is another comb filter that retains only the
even-numbered frequency bins, giving the final
spectrum shown in Fig. 9; the 1/2-turn signal bin is
now number 1
[...]
A conspicuous feature of these spectra is that they
all have decreasing amplitude with increasing
frequency. And in the final plot the frequency bin in
which the real signal would appear is bin 1, the
lowest nonzero frequency bin. [...] This is a simple
consequence of the fact that the 1/2-turn Fourier
component is the lowest frequency retained by the
algorithm, and it will dominate because of the falling
spectrum. When a single frequency bin dominates the
Fourier spectrum, the signal itself looks
approximately like a sinusoid with that period. Using
this data reduction algorithm, any noise with a
falling spectrum will end up looking like an
approximately sinusoidal "signal" with a period of 1/2
turn -- precisely what Miller was looking for.

While correct in themselves, your inferences are based on
the assumption that Miller folded the turn's (orientation)
data in two /prior to/ harmonic analyis, which he did not,
except "the purpose of a preliminary study of the
observations" (Miller, 1933).

These charted "curves" of the actual observations
contain not only the second-order, half-period ether-
drift effect, but also a first-order, full-period
effect, any possible effects of higher orders,
together with all instrumental and accidental errors
of observation. The present ether-drift investigation
is based entirely upon the second order effect, which
is periodic in each half revolution of the
interferometer. This second-order effect is completely
represented by the second term of the Fourier harmonic
analysis of the given curve. In order to evaluate
precisely the ether-drift effect, each curve of
observations has been analyzed with the Henrici
harmonic analyzer for the first five terms of the
Fourier series.

Figure 21 in the 1933 article clearly shows the second
harmonic to dominate over both the first and the higher-
order ones.

> Go look at my Fig. 2 -- do you seriously think you can
> extract a sinewave signal with amplitude ~ 0.1 fringe from
> that data?

I will need the entire Mt. Wilson runs to decide that
myself.

> BTW I still have these 67 runs on disk. If anyone wants
> them, just ask.

Yes, please, I shall be most grateful!

> I am surprised that the analysis program source is not
> also there, but it isn't, and I doubt it is still
> accessible. IIRC it was about 10 pages of Java.

I do not uderstand -- if you wrote the article 1986, how can
it be in Java?

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