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Michelson-Morley Experiments
An Enigma for Physics and the History of Science
Maurizio Consoli
National Institute for Nuclear Physics, Italy
Alessandro Pluchino
University of Catania, Italy

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British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.
The cover shows the scheme of the modern Michelson–Morley experiment by H. Müller et al. in Phys. Rev. Lett. 91 (2003) 020401 with the portraits of Albert Einstein and Hendrik Anton Lorentz.
MICHELSON–MORLEY EXPERIMENTS An Enigma for Physics and the History of Science Copyright © 2019 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.
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Preface
Subtle is the Lord but malicious He is not. A. EINSTEIN, 1921
The Lord whose oracle is at Delphi neither reveals nor conceals but gives a sign. HERACLITUS, V Century B. C.
In 1887 Michelson and Morley tried to detect in laboratory a small diﬀerence of the velocity of light propagating in diﬀerent directions that, according to classical physics, should have revealed the motion of the earth in the ether (“ether drift”). The result of their measurements, however, was much smaller than the classical prediction and considered as a typical instrumental artifact: a “null result”. This was crucial to stimulate the ﬁrst, pioneering formulations of the relativistic eﬀects and, as such, represents a fundamental step in the history of science.
Nowadays, this original experiment and its early repetitions performed at the turn of 19th and 20th centuries (by Miller, Kennedy, Illingworth, Joos...) are considered as a venerable, well understood historical chapter for which, at least from a physical point of view, there is nothing more to reﬁne or clarify. All emphasis is now on the modern versions of these experiments, with lasers stabilized by optical cavities that, apparently, have conﬁrmed the null result by improving by many orders of magnitude on the limits placed by those original measurements.
v

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vi

Michelson-Morley Experiments

Though, this is not necessarily true. In the original measurements, light was propagating in gaseous systems (air or helium at atmospheric pressure) while now, in modern experiments, light propagates in a high vacuum or inside solid dielectrics. Therefore, in principle, the diﬀerence with the modern experiments might not depend on the technological progress only but also on the diﬀerent media that are tested thus preventing a straightforward comparison.
This is even more true if one takes into account that, in the past, greatest experts (as Hicks and Miller) have seriously questioned the traditional null interpretation of the very early measurements. The observed “fringe shifts”, although much smaller than the predictions of classical physics, were often non negligible as compared to the extraordinary sensitivity of the interferometers. Therefore, in some alternative scheme, the small residuals could acquire a deﬁnite physical meaning.
By starting from this observation, in the last few years we have formulated a new theoretical framework where these residual eﬀects could represent the ﬁrst experimental indication for the earth motion within the Cosmic Microwave Background (CMB). In fact, in this alternative scheme, the small observed residuals show surprising correlations with the direct observations of the CMB dipole anisotropy with satellites in space.
The possibility of ﬁnally linking the CMB with the existence of a fundamental reference frame for relativity, and the substantial implications for the interpretation of non-locality in the quantum theory, would be of paramount importance. Therefore, we should preliminarily explain at least the key ingredients of our alternative scheme.
First of all, one should not compare the data with the classical predictions but impose that all measurable eﬀects vanish exactly if the velocity of light cγ propagating in the various interferometers, or more precisely its two-way combination c¯γ, coincides with the basic parameter c entering Lorentz transformations. This is the ideal vacuum limit of a refractive index N = 1 where no ether drift should be observed. Instead if c¯γ ̸= c, as for instance in the presence of matter, where light gets absorbed and then re-emitted, nothing would really prevent a non-zero light anisotropy ∆c¯θ = c¯γ(π/2 + θ) − c¯γ(θ) ̸= 0.
Then, in the inﬁnitesimal region N = 1 + , which corresponds for instance to gaseous systems, one can expand ∆c¯θ in powers of the two small parameters and β = v/c, v being the velocity of the laboratory system with respect to the hypothetical preferred frame. By simple symmetry arguments, this expansion leads to the relation |∆c¯θ| ∼ β2 which is much
c

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Preface

vii

smaller than the estimate |∆c¯θ|class ∼ β2/2 of the classical calculation. To
c
have an idea, for experiments in air at room temperature and atmospheric pressure, where ∼ 2.8 · 10−4, and for the typical projection v ∼ 300 km/s of the earth cosmic motion where β2 = 10−6, our estimate would still be about 17 times smaller than the classical prediction for the much smaller traditional orbital value v = 30 km/s where β2 = 10−8. For helium at room temperature and atmospheric pressure, where ∼ 3.3 · 10−5, our expectation would even be 150 times smaller. This could now explain the order of magnitude of the observed eﬀects.
The other peculiar aspect of our analysis concerns the time dependence of the data. Here, the traditional view is that, for short-time observations of a few days, where there are no sizeable changes in the orbital motion, a genuine physical signal should precisely follow the slow and regular modulations induced by the earth rotation. The fringe shifts instead were showing an irregular behavior indicating sizeably diﬀerent directions of the drift at the same hour on consecutive days so that statistical averages were much smaller than all individual values. Within the traditional view, this has always represented a strong argument to interpret the measurements as mere instrumental artifacts.
Again, however, there might be a logical gap. The relation between the macroscopic earth motion and the microscopic propagation of light in a laboratory depends on a complicated chain of eﬀects and, ultimately, on the physical nature of the vacuum. By comparing with the motion of a body in a ﬂuid, the standard view corresponds to a form of regular, laminar ﬂow where global and local velocity ﬁelds coincide. Instead, some arguments suggest that the physical vacuum might rather behave as a stochastic medium which resembles a highly turbulent ﬂuid where large-scale and small-scale ﬂows are only indirectly related.
In this diﬀerent perspective, with forms of turbulence which, as in most models, become statistically isotropic at small scales, the direction of the local drift is a completely random quantity that has no deﬁnite limit by combining a large number of observations. Thus, one should ﬁrst analyze the data in phase and amplitude (which give respectively the instantaneous direction and magnitude of the drift) and then concentrate on the latter which is a positive-deﬁnite quantity and remains non-zero under any averaging procedure. In this alternative picture, a non-vanishing amplitude (i.e. deﬁnitely larger than the experimental resolution) is the signature to separate an irregular, but genuine, signal from instrumental noise.

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viii

Michelson-Morley Experiments

By implementing these two ingredients, the classical experiments in

gaseous systems can now become consistent with the earth velocity of 370

km/s deduced from the direct CMB observations. In particular, from a ﬁt

to Joos’s 1930 very precise observations (data collected during all 24 hours

to cover the full sidereal day and recorded automatically by photocamera),

we have also obtained some information on the angular parameters of the

earth motion, namely right ascension α(ﬁt − Joos) = (168±30) degrees and

angular declination γ(ﬁt − Joos) = (−13±14) degrees, to compare with the

present values α(CMB) ∼ 168 degrees and γ(CMB) ∼ −7 degrees. This

consistency gives good motivations for a new generation of dedicated exper-

iments to reproduce the experimental conditions of those old measurements

with today’s much greater accuracy.

Meanwhile, waiting for this deﬁnitive test, we have tried to obtain a

diﬀerent check with modern experiments in vacuum. The point is that in

the physical vacuum the velocity of light may still diﬀer from the para-

meter c of Lorentz transformations. This might be due to several reasons.

For instance, some authors have suggested that the curvature observed in a

gravitational ﬁeld might represent a phenomenon which emerges from a fun-

damentally ﬂat space-time. This would be in analogy with some condensed-

matter systems (such as moving ﬂuids, Bose-Einstein condensates...) at

length scales much larger than the size of their elementary constituents.

In this picture, one expects a tiny vacuum refractivity v ∼ 10−9 which

accounts for the diﬀerence between an apparatus in an ideal freely-falling

frame and an apparatus on the earth surface.

Then, if our interpretation of the classical experiments is correct, we

would also expect a very small anisotropy |∆c¯θ|v
c

∼

vβ2 ∼ 10−15 which

could be detected by measuring the frequency shift of two vacuum optical

resonators. More precisely, in our picture, this is the expected magnitude of the instantaneous, irregular signal. Its statistical average |⟨∆c¯θ⟩v| after
c
many observations should instead be much smaller, say 10−18, 10−19..., and

vanish in the limit of an inﬁnite statistics. As we will illustrate, this expec-

tation is consistent with the most recent room temperature and cryogenic

vacuum experiments thus providing further support for our alternative in-

terpretation.

Now, as it is well known, symmetry arguments give often a good de-

scription of phenomena independently of the underlying physical mecha-

nisms. As such, our view of the classical experiments in gaseous systems, in terms of a light anisotropy |∆c¯θ| ∼ β2, does not necessarily contradict
c
the standard interpretation of those old measurements as due to thermal

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Preface

ix

disturbances. Indeed, these disturbances are also known to become smaller and smaller when → 0.
For this reason, and for the overall consistency of the data, the small temperature variations of a millikelvin in the air of the optical arms assumed by various authors (and never fully understood) to explain Miller’s Mt. Wilson observations might have a non-local origin somehow associated with an absolute earth velocity v. After all, our motion within the CMB gives the same order of magnitude [∆T (θ)]CMB ∼ ±3 mK. As we will show, this thermal interpretation could provide a dynamical basis for the enhancement found in the gas case (i.e. the observed magnitudes |∆c¯θ|air = O(10−10) for
c
air and |∆c¯θ|helium = O(10−11) for gaseous helium vs. the much smaller vac-
c
uum value |∆c¯θ|v 10−15) and, at the same time, could also help to under-
c
stand the diﬀerences and the analogies with the most precise experiment in solid dielectrics where again an instantaneous value |∆c¯θ|solid 10−15 (as in
c
the vacuum case) is presently observed. In this way, symmetry arguments, on the one hand, would motivate and, on the other hand, would ﬁnd justiﬁcation in underlying physical mechanisms, with an overall increase of our understanding.
We emphasize that this book is primarily a monograph about the physics of these experiments. However, the history of this research is also interesting and sometimes even dramatic for the strong personal commitment of some scientist. For this reason, several historical accounts have been included as a useful supplementary material.
In conclusion, our work should motivate the reader to sharpen his own understanding of both classical and modern Michelson-Morley experiments. Then, it will become evident that their standard null interpretation, presented in all textbooks and specialized reviews as the most evident scientiﬁc truth, is very far from obvious and most probably wrong. This is why these experiments represent an enigma for physics and the history of science. In view of their fundamental importance, we hope that our book will induce to reﬁne substantially the experimental tests and the analysis of the data thus contributing to reach a higher level of collective awareness.

Acknowledgments
We thank our friends and colleagues Evelina Costanzo, Caroline Matheson, Angelo Pagano, Lorenzo Pappalardo and Andrea Rapisarda for many useful discussions and their precious collaboration.

b2530 International Strategic Relations and China’s National Security: World at the Crossroads
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Contents

Preface

v

1. Chapter One

1

1.1 Premise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Lorentz vs. Einstein . . . . . . . . . . . . . . . . . . . . . 5 1.3 Classical ether-drift experiments: Just null results? . . . . 7 1.4 A universal thermal gradient, the CMB and the vacuum
structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2. Chapter Two

15

2.1 Some historical notes on the (a)ether . . . . . . . . . . . . 15 2.2 Descartes . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Kant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Young and Fresnel . . . . . . . . . . . . . . . . . . . . . . 26 2.6 Maxwell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.7 The turbulent-ether model . . . . . . . . . . . . . . . . . . 34

3. Chapter Three

37

3.1 The idea of the ether drift . . . . . . . . . . . . . . . . . 37 3.2 Albert A. Michelson and his ﬁrst 1881 experiment . . . . 38 3.3 The 1887 Michelson-Morley experiment . . . . . . . . . . 44 3.4 A closer look at the Michelson-Morley data . . . . . . . . 51

4. Chapter Four

59

4.1 The ﬁrst Lorentzian version of relativity . . . . . . . . . . 59

xi

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4.2 1905: Einstein’s special relativity . . . . . . . . . . . . . . 62 4.3 Einstein and the ether . . . . . . . . . . . . . . . . . . . . 65

5. Chapter Five

71

5.1 After Michelson-Morley: Morley−Miller (1902-1905) . . . 71 5.2 Miller 1920−1925 . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 Tomaschek 1924 . . . . . . . . . . . . . . . . . . . . . . . . 77 5.4 Miller 1925−1926 . . . . . . . . . . . . . . . . . . . . . . . 78 5.5 Kennedy-Illingworth 1926-1927 . . . . . . . . . . . . . . . 84 5.6 Piccard and Stahel 1926-1928 . . . . . . . . . . . . . . . . 88 5.7 Michelson-Pease-Pearson 1926−1929 . . . . . . . . . . . . 92 5.8 Joos 1930 . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.9 Criticism of Shankland’s criticism of Miller’s work . . . . 96

6. Chapter Six

99

6.1 The non-trivial vacuum of present particle physics . . . . 99 6.2 The Cosmic Microwave Background . . . . . . . . . . . . . 104 6.3 General aspects of the ether-drift experiments . . . . . . . 108 6.4 A modern version of Maxwell’s calculation . . . . . . . . . 111 6.5 A stochastic form of ether-drift . . . . . . . . . . . . . . . 115 6.6 Reconsidering the classical experiments . . . . . . . . . . . 119 6.7 Reanalysis of the Piccard-Stahel experiment . . . . . . . . 121 6.8 Reanalysis of the MPP experiment . . . . . . . . . . . . . 125 6.9 Reanalysis of Joos’s experiment . . . . . . . . . . . . . . . 128 6.10 Summary of the classical ether-drift experiments . . . . . 140 6.11 A modern experiment with He-Ne lasers . . . . . . . . . . 142

7. Chapter Seven

145

7.1 Modern experiments with vacuum optical resonators . . . 145 7.2 An eﬀective refractivity for the physical vacuum . . . . . . 148 7.3 Simulations of experiments with vacuum optical resonators 155 7.4 Gaseous media vs. vacuum and solid dielectrics . . . . . . 160 7.5 Summary and conclusions . . . . . . . . . . . . . . . . . . 165

Bibliography

171

Index

179

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Chapter 1

You, my honored Herr Michelson began this work when I was only a small boy, not even a meter high. It was you who led the physicists into new paths, and through your marvelous experimental labors prepared for the development of the relativity theory. You uncovered a dangerous weakness in the ether theory of light as it then existed, and stimulated the thoughts of H. A. Lorentz and Fitzgerald from which the special theory of relativity emerged.
A. EINSTEIN, Speech in honor of Michelson, Pasadena,15 January 1931.

1.1 Premise

The Michelson-Morley experiment [1] was designed to check Maxwell’s clas-

sical prediction [2] that if the earth drifts in the ether with a velocity v there

should

be

an

anisotropy

|∆c¯θ| c

∼

v2 c2

of

the

two-way velocity

of

light

in

the

earth frame1. Michelson’s idea was to detect this tiny eﬀect by observing

the interference fringes of two light rays propagating back and forth along

perpendicular directions.

To introduce the argument, let us consider the two-way velocity of light

c¯γ(θ). This is the only one that can be measured unambiguously and is

1Actually, Maxwell’s estimate is larger by a factor of two than the standard classical

prediction

|∆c¯θ | c

∼

v2 2c2

, see Chapt.3.

1

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2

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Fig. 1.1 The typical scheme of Michelson’s interferometer.

deﬁned in terms of the one-way velocity cγ(θ) as

c¯γ (θ)

=

2 cγ(θ)cγ(π + θ) cγ(θ) + cγ(π + θ)

(1.1)

where θ represents the angle between the direction of light propagation and

the earth velocity with respect to the hypothetical preferred frame Σ.

By introducing the anisotropy

∆c¯θ = c¯γ(π/2 + θ) − c¯γ(θ)

(1.2)

there is a simple relation with the time diﬀerence ∆t(θ) for light propagation

back and forth along perpendicular rods of length D (see Fig.1.1)

∆t(θ) =

2D − 2D c¯γ(θ) c¯γ(π/2 + θ)

∼

2D c

∆c¯θ c

(1.3)

(where, in the last relation, we have assumed that light propagates in a

medium of refractive index N = 1 + , with 1). This gives the fringe

patterns (λ is the light wavelength)

∆λ(θ) ∼ 2D ∆c¯θ

(1.4)

λ

λc

and could be measured, in principle, by rotating the apparatus.

The classical prediction (see e.g. [3] for a simple derivation) was

∆λ(θ) λ

class

∼

D λ

v2 c2

cos 2θ

(1.5)

and, for the Michelson-Morley apparatus, the relevant value was (D/λ) ∼

2·107. Therefore, for v = 30 km/s (the earth orbital velocity about the sun,

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Chapter One

3

and consequently the minimum anticipated drift velocity) where v2/c2 = 10−8, under a 90 degree rotation, one was expecting a shift

∆λ(0) λ

−

∆λ(π/2) λ

∼
class

2D λ

v2 c2

∼

0.4

(1.6)

that would have been about hundred times larger than the extraordinary sensitivity of the apparatus, about ±0.004 [1, 4, 5].
Instead, in the various experimental sessions, the observed shifts were about 10 ÷ 20 times smaller than expected [6, 7]. By using Eq.(1.5), these values were indicating earth velocities of about 6 ÷ 10 km/s which have no obvious interpretation. In addition, the observed pattern was irregular because observations performed at the same hour on consecutive days were showing sizeable diﬀerences. The simultaneous presence of these two aspects gave a strong argument to consider the data as typical instrumental eﬀects, i.e. a “null” result.
The acceptance of this view, indicating a failure of the classical ideas and/or the non-existence of the ether, had a strong impact on the scientiﬁc ambiance and was crucial to stimulate the ﬁrst, pioneering formulations of the relativistic length contraction and time dilation eﬀects, by Fitzgerald in 1889 [8], Lorentz in 1895 [9] and 1899 [10], Larmor in 1897 [11] and 1900 [12]. These original developments of the theory of the electromagnetic ether induced Lorentz in 1904 [13] and Poincar´e in 1905 [14] to derive a particular set of transformations of the space-time coordinates (Lorentz Transformations) : “Applying one of such transformations amounts to an overall translation to the whole system. Then two frames, one at rest in the ether and one in uniform translation, become the perfect images of each other”. This statement of Poincar´e in 1905 was the precise formalization of the Principle of Relativity, already proposed by him in La Science et l’Hypothese (Flammarion, Paris 1902) and at the 1904 St. Louis Conference [15]2.

2Poincar´e’s precise words to formulate this principle in his 1904 address are:“The principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer ﬁxed, or for an observer carried along in a uniform movement of translation; so that we have not and could not have any means of discerning whether or not we are carried along in such a motion” [16]. In the same address, Poincar´e was also concluding that “From all these results, if they are conﬁrmed, would arise an entirely new mechanics, which would be, above all, characterized by this fact, that no velocity could surpass that of light, any more than any temperature could fall below the zero absolute, because bodies would oppose an increasing inertia to the causes, which would tend to accelerate their motion; and this inertia would become inﬁnite when one approached the velocity of light” [16].

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4

Michelson-Morley Experiments

This ﬁrst historical phase and its relation with special relativity [17] can be well described by quoting, twice, Einstein himself. The ﬁrst quotation is from his address to Michelson during a social gathering of scientists at the California Institute of Technology in mid-January 1931:“You, my honored Herr Michelson began this work when I was only a small boy, not even a meter high. It was you who led the physicists into new paths, and through your marvelous experimental labors prepared for the development of the relativity theory. You uncovered a dangerous weakness in the ether theory of light as it then existed, and stimulated the thoughts of H. A. Lorentz and Fitzgerald from which the special theory of relativity emerged” [18].
The second quotation is from an Einstein’s interview delivered in 1955, a few months before his death. When asked, once more, about his original view and the relation with previous work he said:“ There is no doubt that the theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already observed that the transformations which later were known by his name were essential for the analysis of Maxwell equations and Poincar´e had even penetrated deeper into these connections. Concerning myself, I knew only Lorentz’ important work of 1895 but not his later work nor the consecutive investigations by Poincar´e. In this sense my work of 1905 was independent. The new feature of it was the realization that the bearing of Lorentz transformations transcended its connection with Maxwell equations and was concerned with the nature of space and time in general. The new result was that Lorentz invariance was the general condition for any physical theory” [19].
Thus, one could summarize as follows: (i) the Michelson-Morley experiment was crucial for the ﬁrst formulation of the relativistic eﬀects within the theory of the electromagnetic ether (ii) later on, by Einstein, relativity was recognized as a doctrine of nature and formulated in an axiomatic form, free of any association with ether and electromagnetism3.
3Over the years, Einstein made diﬀerent statements about the inception of relativity and the possible inﬂuence that the Michelson-Morley experiment had on his views. For instance, Holton [5] reports the following sentence: “In my own development Michelson’s result has not had a considerable inﬂuence. I even do not remember if I knew of it at all when I wrote my ﬁrst paper on the subject (1905). The explanation is that I was, for general reasons, ﬁrmly convinced that there does not exist absolute motion and my problem was only how this could be reconciled with our knowledge of electrodynamics. One can therefore understand why in my personal struggle Michelson’s experiment played no role or at least no decisive role”. At the same time, this other statement is reported by van Dongen [20]: “As a young man I was interested, as a physicist, in the question what is the nature of light, and, in particular, what is the nature of light with respect to bodies. That is, as a child I was already taught that light is subordinate to the oscillations of the

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Chapter One

5

Such premise is essential to properly frame the Michelson-Morley experiment in the history of physics. At the same time, nowadays, there is the tendency to consider this fundamental experiment, and its classical repetitions at the beginning of 20th century by Miller [7], Illingworth [21], Joos [22] ... as an old, well understood historical chapter for which there is nothing more to reﬁne or clarify. All emphasis is now on the modern versions of these experiments, with lasers stabilized by optical cavities (see e.g. [23] for a review), which apparently have improved by orders of magnitude on those original measurements [24].
However, a basic aspect has been overlooked by most authors. The various measurements were performed in diﬀerent conditions, i.e. with light propagating in gaseous media (as in [1, 7, 21, 22]) or in a high vacuum (as in [25–27]) or inside dielectrics with a large refractive index (as in [24, 30]) and there could be physical reasons which prevent a straightforward comparison. In this case, the diﬀerence between old experiments (in gases) and modern experiments (in vacuum or solid dielectrics) might not depend on the technological progress only but also on the diﬀerent media that were tested. Then, if the small residuals of those original experiments were not mere instrumental artifacts, there would be substantial implications for both physics and history of science.

1.2 Lorentz vs. Einstein
Before going deeper into the analysis of the experiments, we want to add some general comment about Lorentz’ and Einstein’s views of relativity. Apart from all historical aspects, the basic diﬀerence could simply be phrased as follows. In a “Lorentzian” approach, the relativistic eﬀects originate from the individual motion of each observer S’, S”...with respect to some preferred reference frame Σ, a convenient redeﬁnition of Lorentz’ ether. Instead, according to Einstein, eliminating the concept of the ether as a preferred frame leads to interpret the same eﬀects as consequences of the relative motion of each pair of observers S’ and S”.
light ether. If that is the case, then one should be able to detect it, and thus I thought about whether it would be possible to perceive through some experiment that the earth moves in the ether. But when I was a student, I saw that experiments of this kind had already been made, in particular by your compatriot, Michelson. He proved that one does not notice anything on earth that it moves, but that everything takes place on earth as if the earth is in a state of rest”. In spite of these contradictions, we trust in our synthesis (points i) and ii) above) which derives from two consistent Einstein’s citations and ﬁts well with the historical evolution of the scientiﬁc ideas.

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In spite of this diﬀerence, it is generally assumed that there is a substantial phenomenological equivalence between the two formulations. This point of view was, for instance, already clearly expressed by Ehrenfest in his lecture ‘On the crisis of the light ether hypothesis’ (Leyden, December 1912) as follows: “So, we see that the ether-less theory of Einstein demands exactly the same here as the ether theory of Lorentz. It is, in fact, because of this circumstance, that according to Einstein’s theory an observer must observe exactly the same contractions, changes of rate, etc. in the measuring rods, clocks, etc. moving with respect to him as in the Lorentzian theory. And let it be said here right away and in all generality. As a matter of principle, there is no experimentum crucis between the two theories”. In fact, independently of all interpretative aspects, the basic quantitative ingredients, namely Lorentz transformations, are the same in both formulations.
Then, one may get the impression that the present supremacy of Einstein’s interpretation depends on the null interpretation of the ether-drift experiments where one attempts to measure the “absolute” earth velocity with respect to the hypothetical Σ. Though, this is not true. In a Lorentzian perspective, if the velocity of light cγ propagating in the various interferometers coincides with the basic parameter c entering Lorentz transformations, relativistic eﬀects conspire to make undetectable the individual velocity parameter of each observer. For this reason, a null result of the ether-drift experiments should not automatically be interpreted as a conﬁrmation of special relativity. The motion with respect to Σ might well remain unobservable, yet one could interpret relativity ‘a´ la Lorentz’. As emphasized by Bell [31], see also [32, 33], this change of perspective, which may be useful for pedagogical reasons, could also be crucial to reconcile faster-than-light signals with causality [34, 35] and thus provide a very diﬀerent view of the apparent non-local aspects of the quantum theory [36].
In our context of the ether-drift experiments, we want to add one more remark about Einstein’s and Lorentz’ points of views. According to Einstein, the original hypothesis of a real, physical length contraction along the direction of motion, to compensate the diﬀerence of the light velocity and thus explain the failure of the classical relation (1.5), was important from a historical point of view but highly unsatisfactory as ultimate explanation. For him, it was preferable to build the theory by postulating the impossibility-in-principle of discovering an absolute state of motion, or equivalently of assigning “a velocity vector to a point in empty space where electromagnetic processes take place” [17]. For Lorentz, on the other

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Chapter One

7

hand, only a conspiracy of eﬀects, associated with the equality cγ = c, was preventing to detect the motion with respect to the ether which, however diﬀerent might be from ordinary matter, is nevertheless endowed with a certain degree of substantiality. For this reason, in his view, “it seems natural not to assume at starting that it can never make any diﬀerence whether a body moves through the ether or not” [37].
Adopting such a “Lorentzian” open mind was for us an important motivation to undertake a re-analysis [38] of the early ether-drift experiments in gaseous media and check the claims of those experts [6,7] that over the years have seriously questioned the standard null interpretation. In their opinion, in fact, the fringe shifts were much smaller than the classical predictions but not always negligible as compared to the extraordinary sensitivity of the interferometers. This means that, in some alternative model, the small residuals can acquire a deﬁnite physical meaning.

1.3 Classical ether-drift experiments: Just null results?

For our analysis of the ether-drift experiments, we shall rely on two basic

assumptions, namely (i) the existence of a preferred frame Σ where light

propagation is seen isotropic and (ii) the validity of Lorentz transforma-

tions. This means that any anisotropy in the earth frame S′ should vanish

identically either when the earth velocity v = 0 (i.e. S′ ≡ Σ) or when

N = 1, i.e. when cγ ≡ c4. The reason for the substantial suppression of

the fringe shifts can then be understood by exploring the possible func-

tional forms for the two-way velocity of light in the limit of refractive index

N = 1 + . With our premise, in fact, for 1, one can expand in powers

of and β = v/c and it is elementary to show, see [38, 40] and the follow-

ing Chap.6, that the leading term for a possible anisotropy of the two-way

velocity of light is

∆c¯θ ∼ β2 cos 2θ. c

(1.7)

Therefore, the fringe shifts are now predicted

∆λ(θ) ∼ D λλ

2 v2 c2

cos

2θ

(1.8)

and are suppressed by the tiny factor 2 with respect to Eq.(1.5). As such,

this basic diﬀerence can be reabsorbed into an observable velocity

vo2bs ∼ 2 v2

(1.9)

4Actually, De Abreu and Guerra have shown [39] that the null result of a Michelson-

Morley experiment in an ideal vacuum can be deduced without using Lorentz transfor-

mations, but only from general assumptions on the choice of the admissible clocks.

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which depends on the refractive index and is the one traditionally reported

in the classical analysis of the data.

More precisely, one can deﬁne the observable velocity vobs through the relation

∆λ(θ) λ

∼

D λ

vo2bs c2

cos

2θ

(1.10)

to make clear that this is the velocity extracted from the fringe shifts.

In classical physics one has vobs = v, where v is the kinematical velocity. However, in other contexts the two quantities are diﬀerent.

In any case, due to the formal properties of the two way velocity of light,

the fringe shifts should represent a 2nd-harmonic eﬀect, i.e. periodic in θ

in the range [0, π], with amplitude

A2

∼

D λ

vo2bs c2

.

(1.11)

Notice also that in the classical experiments, where one was always assuming the identity vobs = v, it was customary to formulate predictions for the orbital earth velocity v = 30 km/s. For this reason, we will often refer to the classical expected amplitude

Ac2lass ∼

D λ

(30 km/s)2 c2

(1.12)

as a convenient reference value to compute the observable velocity from the

experimental amplitude AE2 XP through the relation

vobs ∼ 30 km/s

AE2 XP Ac2lass

.

(1.13)

The main conclusion of this discussion is that those small observable velocities obtained from the measured fringe shifts, typically vobs = 6 ÷ 10 km/s for experiments in air (where is about 2.8 · 10−4) and vobs = 2 ÷ 3 km/s for experiments in helium (where is about 3.3 · 10−5), can now become consistent with the average kinematical earth velocity v ∼ 370 km/s obtained by studying, with aircraft and satellites, the Cosmic Microwave Background (CMB).
Apart from the order of magnitude of the fringe shifts, another important aspect concerns the time dependence of the data. Traditionally, it has been always assumed that, for short-time observations of a few days, where there are no sizeable changes in the earth orbital velocity, the time

dependence of a genuine physical signal should reproduce the slow and

regular modulations induced by the earth rotation. The data instead, for

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Chapter One

9

both classical and modern experiments, have always shown a very irregular behavior. As a consequence, all statistical averages are much smaller than the instantaneous values. This diﬀerence, between individual measurements and statistical averages, has always represented a strong argument to interpret the data as mere instrumental artifacts.
However, again, could there be an alternative interpretative scheme? A possibility, would be to characterize the signal as in the standard simulations adopted to model turbulent ﬂows. This idea derives from realizing that, at the most fundamental level, light propagation (e.g. inside an optical cavity) takes place in that substratum which we could call physical vacuum5. This is dragged along the earth motion but, so to speak, is not rigidly connected with the solid parts of the apparatus as ﬁxed in the laboratory. Therefore, if one would try to characterize its local state of motion, say vµ(t), this does not necessarily coincide with the projection of the global earth motion, say v˜µ(t), at the observation site. The latter is a smooth function while the former, vµ(t), in principle is unknown. By comparing with the motion of a body in a ﬂuid, the equality vµ(t) = v˜µ(t) amounts to assume a form of regular, laminar ﬂow where global and local velocity ﬁelds coincide.
Though, this is not necessarily true. For instance, it would be natural to compare the physical vacuum to a ﬂuid with vanishing viscosity (or inﬁnite Reynolds number for any ﬂow velocity). But, within the framework of the Navier-Stokes equation, the picture of a laminar ﬂow is by no means obvious due to the subtlety of the zero-viscosity limit, see for instance the discussion given by Feynman in Sec. 41.5, Vol.II of his Lectures [41]. The reason is that the velocity ﬁeld of such a hypothetical ﬂuid cannot be a diﬀerentiable function [42]. Instead, one should think in terms of a continuous, nowhere diﬀerentiable function6, similar to an ideal Brownian path [43]. This leads to the idea of the vacuum as a fundamental stochastic medium, somehow similar to a highly turbulent ﬂuid, consistently with some basic foundational aspects of both quantum physics and relativity [45].
For these reasons, it becomes conceivable that, as in turbulent ﬂows, the local vµ(t) exhibits random ﬂuctuations while the global v˜µ(t) just determines its typical limiting boundaries. Although the random vµ(t) cannot
5Maxwell’s original argument in favor of an ether was indeed considering this basic aspect of light propagation [2].
6Onsager’s argument relies on the impossibility, in the zero-viscosity limit, to satisfy the inequality |v(x + l) − v(x)| < (const.)ln, with n > 1/3. Kolmogorov’s theory [44] corresponds to n = 1/3.

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be computed exactly, one could still estimate its statistical properties by numerical simulations [38, 45]. To this end, one could start by assuming forms of turbulence or intermittency which, as it is generally accepted in the limit of zero viscosity, become statistically isotropic at small scales. In this way, see the following Chap.6, one could easily explain the irregular character of the data because, whatever the macroscopic earth motion, the average of all vectorial quantities (such as the fringe shifts at the various angles) would tend to zero by increasing more and more the statistics. In this framework, is not surprising that from instantaneous measurements of given magnitude one ends up with smaller and smaller statistical averages. This trend, by itself, might not imply that there is no physical signal.

1.4 A universal thermal gradient, the CMB and the vacuum structure
Now, it is well known that symmetry arguments, of the type used to derive Eq.(1.7), can provide a successful description of phenomena independently of the particular dynamics. Still, one may wonder about the underlying physical mechanisms. Namely, when considering light propagation in a gas, why there should be an anisotropy in the earth laboratory where (the container of) the gas is at rest?
For instance, a possibility is that the electromagnetic ﬁeld of the incoming radiation produces diﬀerent polarizations in diﬀerent directions depending on the state of motion of the medium. Such mechanism should act in both weakly bound gaseous matter and strongly bound solid dielectrics with the ﬁnal conclusion that light anisotropy would increase proportionally to the refractivity of the medium. This is in contrast with the result of the Shamir-Fox [30] experiment in perspex where no particular enhancement was observed (with respect to the Michelson-Morley experiment in air).
As an alternative possibility, it was noted in [38, 40] (see also Chap.6) that the trend in Eq.(1.7) is just a special case of a more general structure where light anisotropy originates from convective currents of the gas molecules, along the optical paths, associated with an absolute velocity v. Therefore, on the basis of the traditional thermal interpretation7 of the residuals, and of the consistency of the kinematical velocities obtained
7The idea that temperature diﬀerences along the optical paths could be crucial dates back to Helmholtz, already at the time of the ﬁrst 1881 Michelson [46] experiment in Potsdam. The same emphasis on temperature diﬀerences is also found in the critical reanalysis of Miller’s observations performed by Shankland et al. [47].

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Chapter One

11

from measurements in diﬀerent laboratories and diﬀerent conditions, it becomes conceivable that such universal eﬀect in gaseous systems reﬂects the existence of a non-local thermal gradient.
At the beginning, the ultimate explanation for the sought non-local thermal gradient was searched for [38, 40] in the fundamental energy ﬂow which, on the basis of general arguments, is expected in a quantum vacuum which is not exactly Lorentz invariant and thus sets a fundamental preferred reference frame (see Chap.6).
Later on, however, it was argued [48] that the required physical mechanism could perhaps be related to the temperature variations associated with the CMB kinematic dipole [49–51] . This is interpreted as a Doppler eﬀect due to a motion of the solar system with average velocity v ∼ 370 km/s toward a point in the sky of right ascension α ∼ 168o and declination γ ∼ −7o and produces angular variations of a few millikelvin which would ﬁt well with the typical magnitude of the periodic temperature diﬀerences in the air of the optical arms, about (1 ÷ 2) mK [47, 52], which in principle could explain away the typical fringe shifts observed by Miller at Mount Wilson8.
To check this interpretation, a new generation of dedicated experiments is needed to reproduce the experimental conditions of those early measurements with today’s much greater accuracy. The essential ingredient is that the optical resonators which nowadays are coupled to the lasers should be ﬁlled by gaseous media. Such experiments would be along the lines of ref. [53] where just the use of optical cavities ﬁlled with diﬀerent forms of matter was considered as a useful complementary tool to study deviations from exact Lorentz invariance.
In these modern ether-drift experiments one looks for a possible anisotropy of the two-way velocity of light through the relative frequency shift ∆ν(θ) of two orthogonal optical resonators (for a review see e.g. [23]). In units of their natural frequency ν0, we thus predict a frequency shift

∆ν(θ) ∼ ν0 gas

∆c¯θ c

∼ (Ngas − 1) (v2/c2) cos 2θ.
gas

(1.14)

8We emphasize that our interpretation of light anisotropy

∆c¯θ c

∼

v2/c2 in gaseous sys-

tems, as originating from a non-local thermal gradient, applies to all classical ether-drift

experiments and not just to Miller’s Mount Wilson measurements. This is an important

diﬀerence with the standard point of view, deriving from the article of the Shankland

team [47], which tends to distinguish sharply Miller’s observations from all other ex-

periments. These aspects will be discussed in great detail in the following Chaps.5, 6

and 7.

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Michelson-Morley Experiments

This type of thermal interpretation would also explain why the same
trend ∆c¯θ ∼ (N − 1)v2/c2 does not extend to experiments in solid di-
c
electrics, where the refractivity N − 1 is of order unity, as with the men-

tioned Shamir-Fox [30] experiment in perspex (N = 1.5). In this case, in

fact, a small temperature gradient would mainly dissipate by heat conduc-

tion without generating any appreciable particle motion or light anisotropy

in the rest frame of the apparatus. Hence, the non-trivial physical dif-

ference between classical experiments (in gaseous systems) and modern

experiments (in a very high vacuum or in solid dielectrics).

Now, conceptually, explaining the residuals of the classical ether-drift

experiments as non-local thermal eﬀects, eventually related to the CMB

temperature dipole, is diﬀerent from introducing a preferred frame through

a Lorentz-non-invariant vacuum state. To try to disentangle the two mech-

anisms, we have thus started to look at experiments where optical cavities

are maintained in an extremely high vacuum, both at room temperature

and in the cryogenic regime. The reason is that, in this limit, where any

residual gaseous matter is totally negligible, a temperature gradient of a

millikelvin cannot produce any observable light anisotropy. Therefore, if

some inﬁnitesimal eﬀect still persists, the idea of a fundamental preferred

frame would ﬁnd additional support.

As a deﬁnite scenario to analyze these experiments, one can again con-

sider the same scheme where c¯γ ̸= c so that the ideal equality N = 1 does

not hold exactly in the physical vacuum. As a possible motivation, it was

proposed [57] that an eﬀective vacuum value Nv = 1 + v, with v ∼ 10−9, could reveal the diﬀerent refractivity between an apparatus in an ideal

freely-falling frame and an apparatus on the earth surface. This diﬀerence

is expected if the curvature observed in a gravitational ﬁeld is an emergent

phenomenon from a fundamentally ﬂat space-time. Then, the existence

of a preferred frame would imply in our picture a deﬁnite, instantaneous

|∆c¯θ| ∼
c

vβ2 ∼ 10−15 which coexists with a much smaller statistical aver-

age |⟨ ∆c¯θ ⟩| 10−15. By assuming the same form of cosmic motion as for

c

the classical experiments, in the following Chap.7, this expectation will be

shown to be consistent with our numerical simulations of the most recent

room temperature and cryogenic vacuum experiments.

Likewise, the existence of a fundamental 10−15 instantaneous signal,

with very precise measurements, should also show up in solid dielectrics

where, as anticipated, there should be no particular enhancement with re-

spect to the vacuum case. This expectation is consistent with the cryogenic

experiment of ref. [24] where most electromagnetic energy propagates in a

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Chapter One

13

solid with a refractive index N ∼ 3 (at microwave frequencies) but again a 10−15 instantaneous signal is observed.
To conclude this introductive chapter, we emphasize that, apart from its relevance for our view of relativity and for the history of science, a check of our predictions could have other non-trivial implications. In fact, suppose some future experiment would conﬁrm the unambiguous detection of a universal signal in gaseous systems as in Eq.(1.14). In our interpretation, this would mean that light propagation in gaseous systems is modiﬁed due to a non-local temperature gradient, somehow associated with our motion within the CMB. But, of course, all physical systems on the moving earth would also be exposed to the same energy ﬂow. This is very weak today but was substantially larger in the past when the temperature of the CMB was much higher. For this reason, one may speculate [58] on the role that this gradient might have played for the chemistry of liquid water. More in general, it is known [59, 60] that an external energy ﬂow can induce forms of spontaneous self-organization in matter. In this sense, a universal thermal gradient could increase the eﬃciency of physical systems and provide a microscopic, dynamical mechanism to produce those macroscopic aspects (self-organized criticality, large-scale ﬂuctuations, fat-tailed probability density functions...) which characterize the behavior of many complex systems, see e.g. [61–65] .
In the following, we will start in Chap.2 with some historical accounts on the ether conceptions that ﬁnally, at the end of XIX century, gave the motivation for the ether-drift experiments.
In Chap.3, we will concentrate on Michelson, on his early attempts to measure an ether-drift and on the original Michelson-Morley experiment.
In Chap.4, we will brieﬂy comment on the inception of relativity and on its implications for the analysis of the experiments.
In Chap.5 we will report on the early repetitions of the MichelsonMorley experiment and on their traditional interpretation.
In Chap.6, we will re-consider the whole issue from scratch by introducing a modern formalism to re-interpret both the classical ether-drift experiments and the modern versions with optical resonators.
Finally, in Chap.7, we will extend our analysis to the present experiments in vacuum and solid dielectrics by discussing in more detail the various aspects brieﬂy illustrated above.