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Maurice ALLAIS. The experiments of Dayton C. Miller 1925-1926 and the theory of relativity. 12 March 1996

Essay submitted for competing for the 1996 Annual Gravitation Prize of the Gravity Research Foundation

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.

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 invaнriance 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-аааааа Theа principleаа of Miller'sа experiments* isа theаа sameаа asа for Michelson's experiments.

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 disturнbances (of temperature, for example) or do they present a very real internal coherence?

Second Question: Do they permit to detect variations in the veloнcity of the light according to its direction?

Third Question: Is it possible to deduce the Earth's position on its orbit from these observations?

3.- The very remarkable coherence underlying Miller's observations excluding any perverse effect

1 - A very marked coherence appears when one considers the variaнtions 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 reнpresenting velocities and azimuths in sidereal time are on the whole very remarkable.

The sidereal time θ^* for which the velocity is minimal and the sideнreal time θ^** for which the azimuth A is equal to its Ā mean value and for which dA/dt < 0,а 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 hoнdographs are approximately perpendicular to the directions of the Ā mean azimuths.

For the four periods the calculated hodographs, deduced from the sinusoidal fittings of the velocities and azimuths, are almost exactly perнpendicular to the mean A directions of the azimuths and symmetrical reнlatively to those directions. аIndeed that is an even more remarkable cirнcumstance.

4 - Finally, the figures change gradually from one period to another. They attain their maximum dimensions around September 21 which corнresponds 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 marнked coherence underlying Miller's observations allow to give an unquesнtionably affirmative answer to the first two fundamental questions of з 2.3 above.

It is therefore absolutely wrong to consider that Michelson's expeнriment, 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 areаа the maximum and minimum velocities V_m and

V_m, the Ā 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 sinuнsoidal fittings all occur around the March 21 equinox.

3 -ааааа 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 maxiнmum 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 numeнrous observations.

The statistical significance of the whole of these results for semiнannual 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 з 2.3 above.

5.- Interpretation of Miller's observations

1 -ааааа 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).

Thirdly, the velocity of the light is not invariant in all direcнtions.

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

2 -ааааа 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 Ц Ā differences,

and does not provide any explanation for the mean deviations Ā 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 Ā;

- 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 experiнment, the invariance of the speed of light in all directions, and the imнpossibility 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 direcнtions, 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 transнlation 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 inнvalidated 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 preнmises 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 (з3.2)

Legend:

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 (з 3.2)

Legend:

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. OBSERVATIONS OF MILLER Sinusoidal fittings with a 24 hour period (з3.2)

Velocities

Azimuths

Estimations of θ* and θ** (in sidereal time)

Legend :

R = correlation coefficient

θ^* = sidereal time of the velocity minimum

θ^** = sidereal time of the equality A = Ā with dA/dt < 0

Sources : Calculations of Charts I and II.

The correlations were calculated in February 1996

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

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

Table II. FUNDAMENTAL CHARTS OF MILLER GRAPHICAL ESTIMATIONS OF VELOCITIES AND AZIMUTHS (з4.1)

Velocities (in km per sec.)

Azimuths (in degrees)

Legend:аааа V_m and V_m : maximum and minimum values of velocities

A_m and A_mаа : maximum and minimum values of azimuths

Aа =(A_m + A_m )/2 A^*_M = (A_M Ц A_m )/2

A^* = A Ц Ā

Sources : These estimations of V_m , V_m , A_m , 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

1881ааааааааа 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

1887ааааааааа 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

1895ааааааааа Versuch einer Theorie des Elektrischen und Optischen Erscheinrungen in bewegter Körperm

Leiden ; Enzyklop. d. math. Wiss., V., 1903, p. 2, Art. 14.

1904ааааааа 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

1905аааааааа Zur Elektrodynamik bewegter Körper
Annalen der Physik, 17, p. 891.

1916аааааааа Die Grundlage der Allgemeinen Relativistätsheorie

Annalen des Physik, 49, p. 765.

A. MICHELSON and H. GALE

1925ааааааа The Effect of the Earth's Rotation on the Velocity of Light The Astrophysical Journal, April 1925, p. 137-145

Dayton C. MILLER

1925ааааааааа The Ether-Drift Experiments at Mount Wilson

Proceedings of the National Academy of Sciences, Vol. II, 28 April 1925, p. 306-314

1926ааааааааа Significance of the Ether-Drift Experiments of 1925 at Mount Wilson

Science, Vol. LXIII, April 1926, n░ 1635, p. 433-443

1933ааааааааа 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)

1927ааааааааа The Astrophysical Journal, Vol. LXVIII, December 1928, p. 341-402<

Maurice ALLAIS

1959ааааааа 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 (з4.3)

Series	P	R	1ЦR2
VM	6	Ц 0,772	0,404
(VM+Vm)/2	6	Ц 0,607	0,632
Ā	6	+ 0,834	0,305
Ā + A*M	6	+ 0,744	0,447
Ā Ц A*M	6	+ 0,880	0,225
Averages : а= 0,767аааааааа а= 0,403
Vm	12	+ 0,880	0,225
VMЦVm	12	Ц 0,9994	0,0012
Vm/VM	12	+ 0,980	0,041
A*M	12	Ц 0,924	0,145
Averages: а= 0,946аааааа =0,103
Overall averages : а= 0,847аа = 0,269

Legend

P = period in months

R = correlation coefficient

Sources: Estimations of Table II.

* Dayton C. Miller : The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth,аа Reviews of Modern Physics, Vol. 5, July 1933, n░ 3, p. 203-242

Book of M.Allais, fr. (1997)