Tom Roberts

2005-12-09 04:34:09 UTC

Title: Dayton Miller's Data have no Real Signal

Author: Tom Roberts

Date: December 8, 2005

Introduction

------------

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" [1]. 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 [2]. Since then numerous people have proclaimed

Miller's data are correct, and have built castles in the air based on

that assumption.

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 [1] 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

article.

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

turns.

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

the data.

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 [1]).

Here I discuss a single run, and apply this process to each run

individually.

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

method is:

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.

Conclusion

----------

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

References

----------

[1] Miller, Rev. Mod. Phys., _5_, (July 1933), p203-242.

[2] Shankland et al, Rev. Mod. Phys., _27_, 2, (April 1955), p167-178.

Author: Tom Roberts

Date: December 8, 2005

Introduction

------------

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" [1]. 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 [2]. Since then numerous people have proclaimed

Miller's data are correct, and have built castles in the air based on

that assumption.

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 [1] 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

article.

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

turns.

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

the data.

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 [1]).

Here I discuss a single run, and apply this process to each run

individually.

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

method is:

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.

Conclusion

----------

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

References

----------

[1] Miller, Rev. Mod. Phys., _5_, (July 1933), p203-242.

[2] Shankland et al, Rev. Mod. Phys., _27_, 2, (April 1955), p167-178.