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C-5639** 12 March 1996
Maurice ALLAIS THE EXPERIMENTS OF DAYTON C. MILLER
1925-1926 AND THE THEORY OF RELATIVITY
Essay submitted for competing for the 1996 Annual Gravitation Prize of the Gravity Research Foundation

THE EXPERIMENTS OF DAYTON C. MILLER 1925-1926
AND THE THEORY OF RELATIVITY
Summary
The interferometric observations of Dayton C. Miller in 1925-1926 reveal a very real internal coherence, independent of any perverse effect ;
They demonstrate that the velocity of light is not the same in all directions ;
They demonstrate the possibility of determining the motion of the Earth on its orbit from purely terrestrial experiments ;
Accordingly, Miller's experiments invalidate the very foundation of the Theory of Relativity.

THE EXPERIMENTS OF DAYTON C. MILLER 1925-1926
AND THE THEORY OF RELATIVITY
1.- The Genesis of the Theory of Relativity
1 - In 1900 it was considered, as "well-established", that all attempts to detect, by purely terrestrial experiments, the motion of translation of the Earth had failed.
To explain this negative outcome, Lorentz presented his hypotheses of the contraction of bodies according to their velocities and of the local time, and, following Lorentz, Einstein developed his Special Theory of Relativity (1905), and subsequently, his General Theory of Relativity (1916).
From the formulation of the Special Theory of Relativity stem both the impossibility of detecting the Earth's motion on its orbit and the inva¬ riance of the velocity of light in all directions.
2 - Today, it is everywhere admitted without reservation, as postulates, that the velocity of light is independent of its direction, and that no purely terrestrial experiment can detect the velocity of translation of the Earth or even simply its position on its orbit.
2.- The reputedly "negative"outcome of Michelson's experiment and Miller's experiments
1- The principle of Miller's experiments* is the same as for Michelson's experiments.
(*) Dayton C. Miller : The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth, Reviews of Modern Physics, Vol. 5, July 1933, n° 3, p. 203-242

According to this principle, the interferometer makes it possible to measure the difference of the velocity of the light for two perpendicular directions.
2 - In his 1933 paper, Miller presented his observations in the form of eight Charts, four for the azimuths and four for the velocities, in sidereal time, for four periods of continued observations during six or eight days (1933, p. 229).
3 - Any appreciation of the scope of Miller's observations boils down to three utterly fundamental questions :
First Question : Do Miller's observations result from mere disturbances (of temperature, for example) or do they present a very real internal coherence ?
Second Question : Do they permit to detect variations in the velocity of the light according to its direction ?
Third Question : Is it possible to deduce the Earth's position on its orbit from these observations ?
5.- The very remarkable coherence underlying Miller's observations excluding any perverse effect
1 - A very marked coherence appears when one considers the variations in the azimuths and velocities, not in civil time, but in sidereal time.
2 - The fittings, with sinusoids of a period of 24 hours, of the curves representing velocities and azimuths in sidereal time are on the whole very remarkable.

The sidereal time θ* for which the velocity is minimal and the side­ real time θ** for which the azimuth A is equal to its A mean value and for which dA/dt < 0, are very similar for the four considered periods.
3 - If one represents the hodographs of velocities for the four periods on the basis of the hourly values of velocities and azimuths in sidereal time, it is remarkable that on the whole the figures representing the ho­ dographs are approximately perpendicular to the directions of the A mean azimuths.
For the four periods the calculated hodographs, deduced from the sinusoidal fittings of the velocities and azimuths, are almost exactly per­ pendicular to the mean A directions of the azimuths and symmetrical re­ latively to those directions. Indeed that is an even more remarkable cir­ cumstance.
4 - Finally, the figures change gradually from one period to another. They attain their maximum dimensions around September 21 which cor­ responds to the autumn equinox, and their minimum dimensions around March 21 corresponding to the spring equinox. They are therefore dependent on the Earth's position on its orbit.
5. All these properties which indisputably correspond to a very mar­ ked coherence underlying Miller's observations allow to give an unques­ tionably affirmative answer to the first two fundamental questions of § 2.3 above.
It is therefore absolutely wrong to consider that Michelson's expe­ riment, as taken up by Miller, gives a negative outcome.

4.- The very significant Correlation of Miller's Observations with the Earth's Position on its Orbit
1- The most significant parameters characterizing Miller's eight fundamental Charts are the maximum and minimum velocities VM and Vm, the A mean values of the A azimuths, and the amplitudes A*M of their variations around their mean values.
I made graphically direct estimations of these parameters through the photographic enlargement of Miller's eight fundamental Charts, quite independently of any hypothesis or any theoretical interpretation whatsoever.
2 - A thorough harmonic analysis of these parameters shows that all have a marked semi-annual or annual periodical structure.
The maximum and minimum values of the corresponding sinusoidal fittings all occur around the March 21 equinox.
3 - For lack of space, I must limit myself to commenting on the fittings of the observed data with sinusoids for a period of six or twelve months, all having their maximum on March 21.
Although each of the two groups of fittings corresponding to six or twelve-month periods relates to only one reference sinusoid with a maximum on March 21, all the correlation coefficients are relatively high.
4 - They are all the more significant as the considered parameters do not correspond to isolated observations but to the averages of very numerous observations.

The statistical significance of the whole of these results for semiannual or annual periods corresponding to fittings to the same functions is very high and amounts to a quasi-certainty.
5 - Thus it may be considered as perfectly established that the observations corresponding to the four series of experiments have a semi-annual or annual periodicity centered on March 21, the date of the spring equinox, and that it is possible, through purely terrestrial experiments, to determine the Earth's position on its orbit.
An affirmative answer must therefore be given, in all certainty, to the Third Question of § 2.3 above.

5.- Interpretation of Miller's observations

1 - The above analysis leads to a fourfold conclusion :

Firstly, there is a considerable and absolutely indisputable coherence between Miller's interferometric observations, and it corresponds to a very real phenomenon.

Secondly, it is quite impossible to attribute this very marked coherence to fortuitous causes or to perverse effects (of temperature, for example).

tions.

Thirdly, the velocity of the light is not invariant in all direc-

Fourthly, all Miller's observations display a very marked correlation with the Earth's position on its orbit.

2 - These conclusions are independent of any hypothesis and of any theoretical analysis whatsoever.
Most of the results, on which these conclusions are founded, particularly the most significant ones, were not perceived by Miller.

3 - On the basis of his own analysis, Miller considered it possible to provide an estimation of the cosmic velocity of the Earth in relation to its orbital velocity (Miller, 1933, p. 230-237).
However, Miller's analysis only considers the A – A differences, and does not provide any explanation for the mean deviations A of the azimuths and their variations from one period to another (Miller, 1933, p. 234-235).
Consequently, the interpretation given by Miller to his observations cannot be considered as valid.
4 - In fact, it is possible to show that the observed velocities and azimuths can be explained by the conjunction of two effects :
- an optical anisotropy of the space of direction A ;
- an effect proportional to the total velocity of the Earth (orbital velocity + cosmic velocity toward the Hercules Constellation).
6.- The Significance and Scope of Miller's Observations
1 - The very basis of the Special and General Relativity Theory rests on a triple postulate: the reputedly "negative" result of Michelson's experiment, the invariance of the speed of light in all directions, and the impossibility to detect the absolute motion of the Earth through any purely terrestrial experiment.
However, with regard to the analysis above, it is certain that it is impossible to maintain that interferometric experiments provide a "negative" outcome, that the velocity of the light is invariant in all directions, and that any purely terrestrial experiment cannot determine the motion of translation of the Earth.

Consequently, the Special and General Theory of Relativity resting on postulates invalidated by the observation data cannot be considered as scientifically valid.
As Einstein himself wrote in 1925 in the"Science" review :
"If Dr Miller's observations were confirmed, the Theory of Relativity would be at fault. Experience is the ultimate judge".
2- The "positive" outcome of Miller's experiments means that there is no distinction to be made between the rotation of the Earth and its translation as maintained by the Theory of Relativity. Both can be detected through purely terrestrial experiments.
3 - Rejection of the Special and General Theory of Relativity as being incompatible with observation data cannot in any way mean that all Einstein's contributions should be rejected.
It only means that all theoretical developments based on data invalidated by experimental data should be discarded as such.
Those contributions of Einstein that appear to have been confirmed by experience should naturally be preserved, but, quite obviously, they must be given a theoretical justification other than that of the Theory of Relativity.
4 - A theory is only worth what its premises are worth. If the premises are wrong, the theory has no real scientific value. Indeed, the only scientific criterion of the scientific validity of a theory is its confrontation with experimental data.

CALCULATIONS CORRESPONDING TO SECTIONS 3 AND 4
OF THE ESSAY AND REFERENCES

Charts I

HOURLY OBSERVATIONS OF MILLER DAILY VELOCITY AND AZIMUTH CURVES
in sidereal time (§3.2)

Sources : Hour by hour values of the running averages of Miller's Charts (Miller, 1933, p. 229) The fittings were calculated in February 1996.

HOURLY OBSERVATIONS OF MILLER DAILY VELOCITY AND AZIMUTH CURVES
in sidereal time (§ 3.2)
Sources : Hour by hour values of the running averages of Miller's Charts (Miller, 1933, p. 229) The fittings were calculated in February 1996.

Table I
Velocities
Azimuths

OBSERVATIONS OF MILLER Sinusoidal fittings with a 24 hour period
(§3.2)

R

1–R2

February 8 0,361

April 1

0,981

August 1 0,882

September 15 0,854

0,869 0,0377 0,223 0,271

R

1–R2

February 8 0,856

April 1

0,939

August 1 0,970

September 15 0,927

0,267 0,118 0,0593 0,141

Estimations ofθ*andθ**(in sidereal time)
θ*

θ** θ** – θ*

February 8 17,65

April 1

14,55

August 1 16,50

September 15 17,59

18,56 15,48 15,83 17,78

0,91 0,93 –0,67 0,29

Legend :

R = correlation coefficient θ* = sidereal time of the velocity minimum θ** = sidereal time of the equality A = A with dA/dt < 0

Sources : Calculations of Charts I and II. The correlations were calculated in February 1996

Charts III

5

OBSERVATIONS OF MILLER

OBSERVED HODOGRAPHS OF HOURLY VALUES

AND CALCULATED HODOGRAPHS DEDUCED FROM THE FITTINGS

OF VELOCITIES AND AZIMUTHS

(§ 3.3)

Charts IV OBSERVATIONS OF MILLER
OBSERVED HODOGRAPHS OF HOURLY VALUES AND CALCULATED HODOGRAPHS DEDUCED FROM THE FITTINGS
OF VELOCITIES AND AZIMUTHS (§ 3.3)

Table II FUNDAMENTAL CHARTS OF MILLER
GRAPHICAL ESTIMATIONS OF VELOCITIES AND AZIMUTHS (§4.1)
Velocities (in km per sec.)

VM

Vm

April 1, 1925

10

7,8

August 1, 1925

11,6

6,5

September 15, 1925 9,8

4,2

February 8, 1926

10

7,3

Azimuths (in degrees)

AM

Am

April 1, 1925

60

20

August 1,1925

45

-20

September 15, 1925 90

20

February 8,1926

15

-40

A
40 12,5 55 -12,5

A*M
20 32,5 35 27,5

Legend: VM and Vm : maximum and minimum values of velocities
A M and A m : maximum and minimum values of azimuths
A = ( A M + Am )/2 A*M = (AM – A m )/2
A* = A –A
Sources : These estimations of VM , Vm , AM , and A m were deduced graphically from photographic enlargements of the Charts of Miller (1933, p. 229), independently of any hypothesis. These estimations were made in June 1995, and have been used for all the calculations of Table III.

REFERENCES
A. MICHELSON 1881 The Relative Motion of the Earth and the Luminiferous Aether The American Journal of Science, Third Series, Vol. XXII, Art. XXI, p. 120-129.
A. MICHELSON and E. MORLEY 1887 On the Relative Motion of the Earth and the Luminiferous Aether The American Journal of Science, Third Series, Vol. XXIV, n° 203, Art. XXXVI, p. 333-345.
H.A. LORENTZ 1895 Versuch einer Theorie des Elektrischen und Optischen Erscheinrungen in bewegter Körperm Leiden ; Enzyklop. d. math. Wiss., V., 1903, p. 2, Art. 14.
1904 Electromagnetic Phenomena in a System moving with any Velocity Smaller than that of Light Koninklijke Akademie van Wetenschappen te Amsterdam. Proceedings of the Section of Sciences, Vol. VI, p. 809.
Albert EINSTEIN 1905 Zur Elektrodynamik bewegter Körper Annalen der Physik, 17, p. 891.
1916 Die Grundlage der Allgemeinen Relativistätsheorie Annalen des Physik, 49, p. 765.
A. MICHELSON and H. GALE 1925 The Effect of the Earth's Rotation on the Velocity of Light The Astrophysical Journal, April 1925, p. 137-145
Dayton C. MILLER 1925 The Ether-Drift Experiments at Mount Wilson Proceedings of the National Academy of Sciences, Vol. II, 28 April 1925, p. 306-314
1926 Significance of the Ether-Drift Experiments of 1925 at Mount Wilson Science, Vol. LXIII, April 1926, n° 1635, p. 433-443
1983 The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth Reviews of Modern Physics, Vol. 5, July 1933, n° 3, p. 203-242
CONFERENCE ON THE MICHELSON-MORLEY EXPERIMENT (4-5 February) 1927 The Astrophysical Journal, Vol. LXVIII, December 1928, p. 341-402
Maurice ALLAIS 1959 Should the Laws of Gravitation be Reconsidered ? Aero-Space Engineering, September 1959, n° 9, p. 46-52 ; October 1959, n° 10, p. 51-55 ; November 1959, n° 11, p. 55

Table III
OBSERVATIONS OF MILLER SEMI-ANNUAL OR ANNUAL DOMINANT PERIODICITIES
Fittings to a sinusoid of a period of 6 or 12 months with its maximum on March 21 (§4.3)

Series
VM (VM+Vm)/2

P

R

1–R2

6

– 0,772 0,404

6

– 0,607 0,632

6 + 0,834 0,305

6 + 0,744 0,447

6 + 0,880 0,225

Averages :
Vm VM–Vm Vm/VM

= 0,767
12 12 12 12

= 0,403

+ 0,880 – 0,9994 + 0,980 – 0,924

0,225 0,0012 0,041 0,145

Averages: =0,946

=0,103

Overall averages : = 0,847

= 0,269

Legend P = period in months R = correlation coefficient
Sources : Estimations of Table II.