2005-12-09 04:34:09 UTC
Author: Tom Roberts
Date: December 8, 2005
In the 1920's and 30's Dayton Miller made an enormous number of
measurements using several versions of his Michelson interferometer. In
1933 he published a review article, "The Ether-Drift Experiment and the
Determination of the Absolute Motion of the Earth" . If valid, the
results of that paper would refute SR and GR. Since its publication, no
convincing refutation of that paper has been given, though Shankland et
al tried to do so . Since then numerous people have proclaimed
Miller's data are correct, and have built castles in the air based on
This article explains why Miller, and modern advocates of his anomalous
result, are wrong: there is no real signal in his data at all; his data
and results are completely explained by a large systematic error that
masquerades as a "signal".
I have obtained a significant amount of Miller's raw data (52 runs of 20
turns each), and have been looking at it from a modern data analysis
point of view. This article gives a short summary of what I have found,
giving a very brief overall summary and the primary argument: a simple
and direct model of his systematic error reproduces his data completely,
leaving no room for any real signal at all. In the relatively near
future I will be putting a complete paper about this onto the preprint
servers, and intend to submit it for publication.
Background (summary of other parts of my forthcoming paper)
Modern digital signal processing (DSP) techniques show that Miller's
analysis technique was flawed, and show precisely why his reduced data
show sinusoid-like "signals" with the correct period of 1/2 turn. In
essence, his analysis technique aliased his very large systematic error
into the frequency bin corresponding to 1/2 turn, and the spectrum of
the systematic error forces the result to look sinusoid-like. So it's no
surprise he (and others) thought there was a real signal here. But
that's not the subject of this article.
Miller "determined the absolute motion of the earth" by examining his
voluminous data. A glance at his figures in  shows that the data vary
wildly around the values he found. To a modern eye the striking thing
about these figures is their complete lack of errorbars. In fact, an
analysis of those errorbars shows they are larger than the paper the
plots are printed on. That means that his values for the "absolute
motion" also have large errorbars. Had Miller known the techniques
of including the errorbars and using them in a parametric fit to the
data, he would have found that _ANY_ direction would fit the data
equally well. Yes, there is some direction that fits the data best, and
he apparently found it, but it is not _significantly_ better than any
other direction. Ditto for the speed he obtained. This effect is well
known, and is a major reason why data plots without errorbars are
usually not acceptable today. But this is also not the subject of this
The fundamental difficulty Miller faced is that the data from his
interferometer have a very large systematic error added to whatever
cosmic signal is present. This error can be as large as an excursion of
17 fringes during a single 20-turn run(!), and there are a few turns
during which the data drifted more than 3 fringes(!!). I will simply
accept this systematic error as given, and will not speculate on its
origin -- the data alone tell the story I am discussing. Note also that
there are two runs for which there is essentially no 1/2-turn signal at
all, and for which the systematic error is quite small; they are
atypical, and most runs have a systematic error of 3-5 fringes over 20
In the face of such a large systematic error, it is difficult to find
any real signal of ~0.05 fringe. Modern DSP techniques can often do so,
and it is now simple to perform a digital Fourier transform (DFT) of
each entire run (20 turns, 320 points). Those DFTs, and related
knowledge of DSP techniques, show precisely how his analysis algorithm
biased his result and forced his systematic error to masquerade as
"signal". But they also show that there is indeed a non-zero amplitude
for the 1/2-turn Fourier component, which is where any real signal would be.
The question is: is this a real signal or is it due to that large
systematic error? The best way to determine that is to model the
systematic error and compare its 1/2-turn Fourier amplitude to that of
Modeling the Systematic Error
Miller's data consist of an unknown signal plus a comparatively large
systematic error. The symmetry of his instrument forces the real signal
to be periodic, with a period of exactly 1/2 turn (the rotation of the
earth can be neglected during any single data run, which typically took
~15 minutes). There is no such constraint on the systematic error.
The data were recorded to an accuracy of 1/10 fringe at 16 markers
(orientations) placed uniformly around the circle of rotation of the
interferometer; a series of 20 turns (complete rotations) constitutes a
single run. I have data for 52 such runs, mostly from Cleveland in
August of 1927. This discussion is of that data only, but surely applies
to his other data as well (I include the 1925 run he displayed in figure
8 of ).
Here I discuss a single run, and apply this process to each run
As any real signal is periodic, its value at a given orientation must be
the same for every turn within a run. So by subtracting the first 1/2
turn value of Marker 1 from all 20 of the marker 1 values, the resulting
sequence of turn-by-turn differences has no remnant of the periodic
signal. And because of the symmetry, the marker 9 values can be included
in the same series, giving 40 entries for this orientation. This applies
to the other orientations, giving 8 independent series of 40 entries
each. These series characterize the systematic error at each
orientation, but we don't know how to combine the different orientations
to obtain a model of the complete systematic error (the actual data
contain both the signal and the systematic error, we need just the latter).
What we can do is make an assumption: assume that the systematic error
is as small as possible, consistent with those series of differences.
With that assumption, we can treat the initial 8 values of the 8 series
to be adjustable parameters, and we can adjust them so that the
point-by-point differences are as small as possible on average. So the
a) given the adjustable parameter values, add the measured
differences for each orientation and combine them into a
systematic error with 320 entries (corresponding to the 320
points of the run's raw data).
b) compute the adjacent-point chisquared:
chisq = sum[i=2..320] (systErr[i]-systErr[i-1])2
c) vary the free parameters to minimize the chisquared.
Note that the individual series of differences have one point per 1/2
turn; the chisquared is between adjacent points, which are necessarily
obtained from different series -- each series is a single orientation
and the interferometer was rotating through successive orientations.
This fit converges well for all 52 runs. I won't discuss the details here.
Note this model is as simple as it gets for a model that conforms to the
symmetries of the instrument and also takes advantage of all the
measurements of the systematic error. It is also completely independent
of any real signal -- one could add _ANY_ "signal" (1/2 turn periodic)
to the data and that would not change the modeled systematic error.
Remember the model is determined by the 8 parameters and the
same-orientation differences of the data, so no orientation dependence
of the data is involved in the model, its dependence on orientation is
determined only by the fit.
Comparing the Model of the Systematic Error to the Data
Once the model for the systematic error is obtained for each run, we
simply take the 320-point DFT of the data and of the error model, and
compare. As the only frequency component of interest has period 1/2
turn, this is quite fast.
The best comparison for all runs is a plot of the norms of the 1/2-turn
Fourier amplitudes, plotting the value for the systematic model along
the x axis and the value for the data along the y axis. I cannot display
the plot in this ASCII medium, but it shows that 47 of the 52 runs lie
_exactly_ on the line x=y, ranging from an amplitude of 0.01 fringe to
about 0.15 fringe. That is, for 47 of the runs this simple model of the
systematic error gives the same 1/2 turn Fourier amplitude as does the
data; in fact, in the time domain the systematic error model is
identical to the data for each of these 47 runs -- the model reproduces
the data _exactly_.
There are 5 runs that do not lie on the x=y line, and they are as much
as 0.1 fringe away from it. Looking at the raw data for each of these
runs, it is clear that each of them has several turns during which the
data drifted wildly (more than 1 fringe per turn) -- clearly the
instrument was not stable during these turns. That cannot be interpreted
as any sort of real signal, and it violates the assumption that the
systematic error is as small as possible -- that is the cause, because
removing these unstable turns from the fit makes the error models for
all 5 of these runs reproduce the data exactly.
The simple model of Miller's systematic error accurately and completely
reproduces all of his data that I have (52 runs, 1040 turns of
the interferometer). That means there is no signal of cosmic origin in
any of them -- the only "signal" present is from the systematic error
itself. Analysis I have not discussed here shows precisely how and why
the systematic error masqueraded as "signal", and fooled Miller
and his followers.
Miller could not possibly have known about the DSP ideas used here, nor
how his analysis technique was actually extracting an aspect of his
systematic error, not any real signal. Even if he had known this, the
computations required would have exceeded his ability to perform them
manually. And because the use of errorbars and techniques of using them
were not common in his day, he was unaware of this confusion.
Tom Roberts ***@lucent.com
 Miller, Rev. Mod. Phys., _5_, (July 1933), p203-242.
 Shankland et al, Rev. Mod. Phys., _27_, 2, (April 1955), p167-178.