untitled
A revisit of the papers on the theory of relativity: Reconsideration of 
the hypothesis of ether-dragging 
Masanori Sato 
Honda Electronics Co., Ltd.,  
20 Oyamazuka, Oiwa-cho, Toyohashi, Aichi 441-3193, Japan 
Abstract: This paper revisits previous papers related to the theory of relativity. Afterwards, a 
reconsideration of the hypothesis of ether-dragging is discussed. The ether is compatible with the 
theory of relativity and historical experiments; this paper explains the Michelson-Morley experiment 
using the ether-dragging hypothesis without the orthodox interpretation that the speed c is a fixed 
constant in terms of any system of inertial coordinates. 
Key words: The theory of relativity, ether-dragging, the global positioning system (GPS), the 
earth-centered locally inertial (ECI) coordinate system, aberration, Michelson-Morley experiment, 
Sagnac effect  
PACS numbers: 03.30.+p 
1. Introduction 
The theory of special relativity, proposed by Einstein [1] in 1905, was simple and intuitive. The 
principle is the invariance of the speed of light: light in a vacuum propagates with the speed c (a 
fixed constant) regardless of the motion of the light source. However, the orthodox interpretation of 
the theory of special relativity was derived later from the results of the Michelson-Morley 
experiment [2], which suggested that “the speed c is a fixed constant in terms of any system of 
inertial coordinates”. This orthodox interpretation is rather difficult to illustrate in the theory of 
special relativity: the Michelson-Morley experiment in the gravitational field of the earth cannot be 
discussed in the inertial coordinate; that is, the orthodox interpretation cannot be applied to the 
Michelson-Morley experiment. This is the starting point of this paper.    
The idea that light in a vacuum propagates with the speed c (a fixed constant), regardless of the 
state of motion of the light source was commonly accepted by the end of the 19th and early 20th 
centuries; this idea was represented in Maxwell’s equations and the wave equation as, 
,                                                           (1) 
where E is the amplitude of the wave, and c is the phase velocity of the wave. In those days, 
Maxwell and other scientists considered equation (1) to be defined in stationary coordinates. They 
considered that the speed of light, c, is defined in stationary coordinates, which is in the stationary 
ether. First of all, I would like to make this point clear: the orthodox interpretation is correct on the 
condition of the uniform flow of the ether; this is in the limitation of the theory of special relativity. 
Equation (1) has a solution )(exp kxtiE −∝ ω , (ω: frequency, k: wave number), which has a 
constant phase velocity kc /ω= . This representation indicates that in the ether in uniform flow, the 
phase velocity is always constant. For example, the Doppler shift is detected as not only the 
frequency ω but also the wave number k that satisfy the constant phase velocity, c: this is because the 
wave number k is always proportional to the frequency ω in the inertial coordinate.  
Figure 1 (a) illustrates the idea that light in a vacuum propagates with the speed c regardless of 
the state of motion of the light source. This also illustrates an idea from Einstein's 1905 paper [1]. 
Stationary light source  Moving observer 1  Moving observer 2 
Fig. 1 (b) Moving observers 1 and 2 detect the speed of light c 
Fig. 1 (a) Light in vacuum propagates with the speed c regardless of the 
state of motion of the light source 
Moving light source  
Stationary observer 
Figure 1 (b) shows that moving observers 1 and 2 detect the constant phase velocity of light c 
regardless of their motion. The constant speed of light is satisfied on the condition that both the light 
source and the observer are in inertial motion. As far as wave equation (1) is discussed in the inertial 
coordinate system, the speed of light c is always constant. On the other hand, the interpretation of the 
theory of special relativity that the speed, c, is a fixed constant in terms of any system of inertial 
coordinates is rather ambiguous. This is due to the fact that when we discuss the ether-dragging, we 
have to assume the gravitational field. The ether-wind or ether-drift is not observed in the inertial 
coordinate system; the discussion should be carried out in the theory of general relativity.  
To make the discussion more clear, let us consider an acoustic wave in the atmosphere, which has 
an isotropic constancy: although the earth moves in the solar system, we never consider the speed of 
the acoustic wave to be a fixed constant in any system of inertial coordinates. This is interpreted as 
the acoustic wave traveling in the atmosphere, which is completely dragged by the gravity of the 
earth. Although the motion of the earth in the solar system does not affect the speed of the acoustic 
wave, we never consider that the speed of an acoustic wave is a fixed constant in terms of any 
system of inertial coordinates. This is because, we know the gravitational field of the earth is not in 
the inertial coordinate system. Again, this paper starts from the simple question of how to illustrate 
the orthodox interpretation of this theory. I must conclude that this orthodox interpretation can be 
applied only in the case of a uniform ether. The frame of the wave equation does not appear to 
adhere to stationary coordinates; however, it does adhere to the physical constants of the medium. In 
the case of an acoustic wave in the atmosphere, the inertial coordinates of equation (1) are assumed 
to be the atmosphere. The physical coefficients are the density and the coefficient of stiffness. The 
wave equation of the electromagnetic wave can be interpreted using this analogy; that is, the inertial 
coordinates are the permittivity and the permeability around the earth. 
As a counterargument for the orthodox interpretation, let us consider the earth-centered locally 
inertial (ECI) coordinate system in the global positioning system (GPS) experiment [3]. The reason 
why GPS works precisely in the ECI coordinate system is that the ECI coordinate system can be 
considered as the stationary state. It is difficult to calculate GPS in the solar system; only the ECI 
coordinate system works as the stationary frame. This experimental result is an analogy to an 
acoustic wave in the dragged-atmosphere that is, the electromagnetic wave in the dragged-ether by 
the gravity around the earth.   
Using the analogy of an acoustic wave in the atmosphere, I use a classic hypothesis that the ether 
is the permittivity of free space, ε0, and the permeability of free space, µ0. This classic hypothesis 
was derived from the proposal by Lorentz of luminiferous ether that the absolute stationary 
coordinate is defined in the stationary ether. Thus, to explain the Michelson-Morley experiment, he 
proposed the Lorentz contraction of length. I will also show that the complete ether-dragging 
hypothesis is compatible with the Michelson-Morley experiment. This hypothesis was derived from 
the proposal by Maxwell that the Maxwell equation and wave equation are satisfied in the stationary 
coordinate system, i.e., the stationary ether. Maxwell predicted an ether-wind; however, the GPS 
experiment showed that the ether-wind was not observed at least up to 20,000 km from the ground 
level. Figure 2 shows that the ether is not only dragged, but also modified by gravity. The 
modification of the permittivity and the permeability by gravity causes a decrease in the speed of 
light, 
=c . Diffraction around the gravitational potential of the sun, as observed by 
Eddington [4], can be explained using this proposal that light propagates toward regions of high 
refractive index, that is, toward the sun.  
In the hypothesis that the ether is the permittivity and the permeability, the modification (increase) 
in the permittivity and permeability is used, rather than the curvature of spacetime.  
In the early 20th century, there were many great scientists who held very rigid beliefs in their own 
thoughts. Michelson accepted Einstein's work; however, he believed in the ether. He was not 
satisfied with the results of the Mt. Wilson experiment [2], and he repeated the experiment [5]. He 
worried that "shimmers" of air between the mountains might have fouled his results. In 1930, 
Fig. 2 Gravitational field illustrated by the analogy of the
atmosphere of the earth. The values of the permittivity of free space, 
ε0, and permeability of free space, µ0, vary depending on the height. 
That is, the values are changed in order to satisfy the effect of the
gravitational field on time dilation.  
Michelson’s belief in the ether brought him to his last and most ambitious test [6], the measurement 
of the velocity of light in a partial vacuum. His daughter, Dorothy Michelson Livingston [7], wrote 
that Michelson never gave up his belief in the ether.  
In 1924, Michelson-Gale-Pearson experiment [8] was carried out to observe the effect of the 
earth's rotation on the velocity of light. They assumed a fixed ether and the theory of special 
relativity. A fixed ether means the ether fixed to the ECI coordinate system; that is, the earth rotates 
in the ether. The theory of special relativity means that light in a vacuum propagates with the speed c 
regardless of the motion of the light source. They constructed the experimental setups using long 
pipes of partial vacuum. The experimental results showed the angular velocity of the earth in 
accordance with the theory of special relativity and the fixed ether. In those days, Michelson tried to 
prove the fixed ether experimentally; however the hypothesis of ether gradually disappeared. 
In 1985, on the Sagnac experiment using GPS [9], there was no discussion of the ether. This is 
because Sagnac effect as well as Michelson-Gale-Pearson experiment can be reasonably explained 
without the hypothesis of ether.  
Miller [10] was also a great scientist; he carried out the Michelson-Morley experiment with 
incredible enthusiasm. He was also a great experimentalist, and never changed his belief in the ether. 
In 1933, he reported experimental data that showed a slight seasonal and sidereal periodic fringe 
shift in the Michelson-Morley experiment. However, in 1955, his experimental results were 
re-evaluated and found to be thermal artifacts [11]. As far as the complete ether-dragging hypothesis 
is concerned, the null results are inevitable; thus, I believe that Miller’s experimental results showed 
that the interferometer measurements are affected by the motion of the earth. 
The null results of the GPS experiments were obtained by direct one-way measurement, which has 
a very high sensitivity compared to interferometer measurements. In a one-way (from the GPS 
satellite to the GPS station on earth) direct measurement of the speed of light, the sensitivity to a 
velocity of 30 km/s is calculated as 
4101/000,300/30 −×=÷ skmskm . The sensitivity of the 
Michelson interferometer is estimated as 
1050.0
000,300
1 −×=
vE . 
Thus, the sensitivity of the direct one-way measurement is 4102 × higher than that of the 
Michelson interferometer. The null results are confirmed by one-way direct measurement in the GPS 
experiments.  
At that time, it was hypothesized that ether-dragging occurs around the ground level. To check this 
hypothesis experimentally, the Michelson-Morley experiment was carried out using massive lead 
blocks (one path of the interferometer was set between two lead blocks); there was no fringe shift 
[12]. Michelson, Miller, and others discussed partial ether-dragging at the global magnetic field 
level; today, the GPS experiments show that if there is ether-dragging, it will be observed as an 
ether-wind more than 20,000 km from the ground level. 
In 1951, Dirac [13, 14] referred to the ether in the context of his new electromagnetic theory. He 
suggested describing the ether from the viewpoint of quantum mechanics, that is, quantization of the 
ether. However, his interest in and discussion of the ether gradually disappeared. He wrote a book 
entitled “General Theory of Relativity” in 1975 [15], in which the ether was not described at all. As 
discussed by Dirac in the early 1950’s, the ether may exhibit physical effects in quantum 
phenomena.  
In this paper, a hypothesis of complete ether-dragging that is based on the beliefs of the great 
scientists is described. Thereafter, I will show that the historical experimental results are compatible 
with the ether. Although the hypothesis of no ether is compatible with the historical experimental 
results; however, they do not rule out the ether hypothesis. 
2. Interpretation of historic experiments 
2.1 Aberration of light is compatible with ether-dragging 
The aberration of light was observed by Bradley in 1725. He explained the aberration using 
Newton’s particle property of photons, as shown in Fig. 3. The aberration was considered to be one 
of the experimental results that show there is no ether-dragging around earth. Fresnel explained the 
aberration by assuming that the ether is unaffected by the motion of the earth [16]. This aberration is 
difficult to explain using the wave nature of the photon; however, it is easily explained using the 
particle nature of the photon.  
Let us consider the hypothesis that the refractive index is dragged by the earth. The refractive 
index of air (n) is 1.000292, the speed of light (c) is 300,000 km/s, and the velocity of the earth in 
the solar system (v) is 30 km/s. Thus, using Fresnel’s equation (2), we obtain 
1                                                                 (2) 
912,2990175.0912,29930
000292.1
000292.1
000,3001
−+∴ v
This calculation shows that the refractive index of the air modifies the speed of light. However, the 
contribution from the dragging of the refractive index by the earth is calculated as 
9105839.0912,2990175.0 −×=÷ . 
For simplicity, let us assume a vacuum, that is, n=1. From Fresnel’s equation (2), it can be concluded 
that the speed of light c is not affected by the velocity v. Therefore, we conclude that the aberration 
of light is clearly observed in the ether-dragging scenario.   
  However, according to Fresnel’s equation, the refractive index n depends on the frequency of the 
light. Of course, this dispersion is not observed, as the ether was considered to be 
frequency-independent. Thus, it was said that the aberration cannot be compatible with 
ether-dragging. This shows that it is difficult to interpret the aberration with the wave nature of the 
photon. The wave nature of light does not explain the compatibility between ether-dragging and the 
aberration. This is because the wave property shows that a photon is dragged by the ether.  
Bradley explained the aberration using Newton’s particle property of photons, which gives 
another simple illustration of a photon traveling in a straight line in the moving ether, without 
changing its direction, as shown in Fig. 3. Therefore, the aberration does not rule out ether-dragging. 
The particle property, in the particle-wave duality of the photon, makes the explanation simple.  
2.2. Doppler shift 
In 1842, Doppler proposed the Doppler shift of light in his treatise "On the colored light of the 
binary stars and some other stars of the heaven". If the star is moving toward us, the speed of a 
Fig 3 Aberration of light is observed in the ether-dragging: 
Bradley explained the aberration using Newton’s particle 
property of photons; however, it is difficult to explain using 
the wave nature of the photon. The ether is not only dragged 
but also fixed to the ECI coordinate system. The earth rotates 
in the fixed ether.   
v=30 km/s 
Wave front 
Dragged ether by the earth: Fixed 
ether to the ECI coordinate system 
Photon 
Stationary ether 
The earth 
radiated photon is not changed by the motion of the light source; however, the photon has more 
energy and momentum, observed as the blue Doppler shift. It is interesting that the energy and 
momentum of a photon depend on the motion of the light source. It appears that the energy and 
momentum follow the Lorentz transformation, although the speed of the photon does not. 
The energy and momentum of a photon depend on the motion of the light source: if the star is 
moving toward us, the photon has increased energy and momentum, which is the blue Doppler shift. 
If the observer is moving towards the light source, he detects a higher energy and momentum for the 
photon. Although the speed of a photon does not follow the Galilean transformation, the energy and 
momentum appear to follow the Lorentz transformation.    
Let us discuss the Doppler shift of light. Equation (3) shows the longitudinal Doppler shift, 
0νν .                                                      (3) 
  Here, νD is the Doppler frequency, and ν0 is the frequency of the source in the stationary state. To 
make the discussion simple, both the observer and the source are in free space; furthermore, either 
the observer or the source is in a stationary state, as shown in Fig. 4. The relative velocity is u. Thus, 
equation (3) can be used. The observer detects a Doppler frequency νD.  
Stationary observer      Photon νD              Moving source  
(a) Stationary observer sees moving source 
c                    u 
Moving observer        Photon ν0              Stationary source  
(b) Moving observer sees stationary source 
Fig. 4 The Doppler shift from the viewpoint of quantum mechanics. 
Both the observer and the source are in free space. Either the observer or the 
source is in a stationary state. The relative velocity is u. Thus, equation (3) can 
be used.  
u                c                     
In Fig. 4 (a), a moving source radiates a photon of energy hνD (h: Planck’s constant); in Fig. 4 (b), 
the moving observer detects a photon of energy hνD. Although the speed of light, c, is constant, the 
moving source radiates a photon with higher energy and momentum. The moving observer then 
detects a photon with higher energy and momentum. In quantum mechanics, the phase velocity is 
defined as c=ε/µ, (ε: energy, µ: momentum), thus, the phase velocity is always constant.  
Let us discuss the moving observer in Fig. 4 (b) who detects a photon with speed c. It is possible 
to say that the moving observer detects a modified frequency and wave number as the Doppler shift. 
Thus, the phase velocity becomes a constant, that is, the speed of light, c. This interpretation is 
compatible with constant light speed, regardless of the motion of the light source and the orthodox 
interpretation.  
The discussion of the Doppler shift assumes stationary coordinates. That is, when we use equation 
(3), it is assumed that either the observer or the source is in a stationary state.  
2.3 Sagnac effect in GPS 
Ashby [3] summarized the Doppler shift of carrier and modulated waves in GPS. He described 
that the Doppler shift of modulated wave is proportional to that of carrier. In the GPS, pulse coded 
modulation is used for the measurement of the distance. The Doppler shift of modulated wave is 
observed as the frequency change of modulated wave (i.e., wave packet). The Doppler shift of 
modulated wave is equivalent to the Sagnac effect in GPS. As shown in Fig. 5, the station on earth 
detects the Sagnac effect as well as the Doppler shift of modulated wave (Appendix). 
Sagnac effect shows the distance change between the light source and the observer by the motion 
of the observer. If the observer moves on the flight time of light, the distance between the light 
Fig. 5 Sagnac effect and Doppler shift of modulated wave in GPS  
Station on earth 
GPS satellite 
Modulated wave 
source and the observer is changed. For example, let the distance between the GPS satellite (signal 
source) and the observer on earth set 30,000 km (the distance that light travels at 0.1 second). On the 
equator, the speed of the ground is around 0.47 km/s. Thus the Sagnac effect is 0.047 km at the 
measurement of 30,000 km for the observer on the equator, which means that at the flight time of 
light of 0.1 second, the observer moves 0.047 km. Sagnac experiment using the GPS showed the 
accuracy within 2 % [3, 9].  
From the Sagnac effect, it is assumed that the ether has two properties: 1) the ether is dragged 
with the earth, 2) the ether does not rotate with the earth; the ether is fixed to the ECI coordinate 
system. Thus the earth rotates in the fixed ether as shown in Fig. 5. It looks like a comet. From these 
discussions, there remains two possible selections; one is there is no ether, and the other is fixed 
ether to the ECI coordinate system. The historical experiments do not rule out the ether hypothesis. 
2.4 Summary of the historic experiments revisited 
In this section, the previous experimental results are reconsidered with the hypothesis that the 
ether is the permittivity, ε0, and the permeability, µ0 of free space (i.e., the refractive index n). Table 
1 shows the historic experiments and their interpretation under the ether hypothesis.  
Table 1 Experiments from historical papers 
 Experiments  Comments 
1 Aberration of light 
(1725) 
The particle property of the photon gives a simple illustration; the photon 
travels in a straight line in the moving ether without changing direction. 
The aberration is compatible with the assumption of ether-dragging by the 
earth. 
2 Doppler shift 
(1842) 
The energy and momentum of the photon appear to satisfy the Lorentz 
transformation, although the speed of the photon does not. The moving 
light source causes a Doppler shift. The moving observer also detects the 
Doppler shift. The speed of light appears to be defined in the stationary 
frame; that is, the ether.  
3 Michelson-Morley 
experiment [2] 
(1887) 
In the 1887 experiment, Michelson and Morley ruled out a stationary 
ether. The experimental results (i.e., null results) can be interpreted as 
evidence for complete ether-dragging by the gravitational field of the 
earth. The Michelson-Morley experimental results can be explained using 
ether-dragging. 
4 Sagnac (1913) Sagnac effect is discussed in GPS-Sagnac effect. 
5 Eddington [4] 
(1920) 
Diffraction around the gravitational potential of the sun, as observed by 
Eddington, can be explained with the hypothesis that light propagates 
toward regions of high refractive index, that is, toward the sun.  
6 Michelson-Gale 
-Pearson 
experiment [16] 
(1924) 
Michelson-Gale-Pearson experiment was carried out to observe the effect 
of the earth's rotation on the velocity of light. They assumed a fixed ether 
and the theory of special relativity. The experimental results showed the 
angular velocity of the earth in accordance with the theory of special 
relativity and the fixed ether.  
7 GPS-Sagnac [15] 
(1985) 
Sagnac effect shows the distance change between the light source and the 
observer by the motion of the observer on the flight time of photon. The 
ether is dragged with the earth as well as fixed to the ECI coordinate 
system. The earth rotates in the ether. In the GPS, only the relative 
velocity defined in the ECI coordinate system is correct, we cannot use the 
relative velocity defined in the solar system. This experimental evidence 
reasonably explains the hypothesis of the fixed ether to the earth.  
8. GPS [3] GPS satellites orbit 20,000 km above ground level, at a velocity of 4 km/s. 
GPS uses an earth-centered locally inertial (ECI) coordinate system. This 
coordinate system can be assumed to be a stationary frame. In the GPS 
experiment, 20,000 km from ground level, the ether-wind and Fresnel’s 
ether-dragging are not observed. The Michelson-Morley experiment 
conducted with GPS, i.e., by direct one-way measurement rather than with 
the use of a Michelson interferometer, confirms the constancy of the speed 
of light. The GPS experiments can be considered to be a reconfirmation of 
complete frame-dragging by the gravitational field of the earth. 
As described above, the complete ether-dragging hypothesis is compatible with the historical 
experimental results. 
3. Ether-dragging and the stationary state 
Figure 6 illustrates ether-dragging by the gravitational fields of the earth and the sun. The ECI 
coordinate system (the gravitational field of the earth) drags the ether in the solar system. The solar 
system simultaneously drags the ether in the galaxy, and the galaxy also drags the ether in the cosmic 
microwave background (CMB). Thus, there are many stationary states: the ECI coordinate system, 
the galaxy and the CMB.  
If we leave the gravitational field of the earth, we are in the gravitational field of the sun (solar 
system), that is, the sun-centered locally inertial coordinate system. When we travel at the speed of 
the earth (i.e., the relative velocity to the earth is 0) in the solar system, we observe a time dilation at 
a velocity of 30 km/s. If we reach the gravitational field of mars, we will be in another stationary 
state; that is, we will be in the mars-centered locally inertial coordinate system. When we leave the 
solar system, we will be in the galaxy; if we travel parallel to the solar system, we observe a time 
dilation caused by a speed of 230 km/s (the speed of the solar system in the galaxy). There are many 
stationary states in the solar system, for example, on the earth and mars. This is similar to the 
example of an acoustic wave, in which we have many stationary states, for example, in a moving 
train or in a flying airplane.   
  It is possible that ether-dragging occurs on larger scales (that is, the gravitational field scale) than 
were predicted by Michelson and Miller. They believed in the ether, and it is possible that their belief 
could be confirmed in space physics.   
4. Discussion 
4.1 The wave-particle duality in the theory of relativity 
  In the above discussions, I used the wave and particle properties. It is not easy to explain the 
experimental results using only one property. For example, the aberration is explained using the 
particle property, and I cannot explain the aberration with the wave property. On the other hand, the 
Doppler shift is difficult to explain only by the particle property; the wave property is needed. In the 
interpretation of the theory of relativity, particle-wave duality is required.  
Thus, the ether-dragging hypothesis is explained using the wave-particle duality; I cannot 
consistently explain this hypothesis using only one of the two properties. Therefore, the 
ether-dragging hypothesis should be checked experimentally with space physics. 
4.2 Merits and drawbacks of the ether 
Let us discuss the merits and faults of the ether hypothesis. The faults of the ether hypothesis are 
that it is unnecessary as far as explaining observed phenomena, and that it has never been observed; 
however, it is harmless and eases the understanding of the theory of special relativity. The concept of 
the ether is very convenient; it defines a stationary reference frame. Thus, a relative velocity is also 
defined.  
Fig. 6 Illustration of the ether-dragging by the gravitational fields of the earth 
and the sun. Not only the earth but the sun also drags the ether in the galaxy, 
which moves in the cosmic microwave background (CMB). Thus, there are 
many stationary states; this is because the gravitational fields are the 
stationary states. For examples, the ECI coordinate system, the solar system, 
the galaxy and the CMB.  
ECI coordinate system 
v=230 km/s 
Cosmic microwave background 
Solar system 
v=30 km/s
Galaxy  
v=700 km/s 
As described above, one of the candidates for the ether is the permittivity of free space, ε0, and the 
permeability of free space, µ0. These are very familiar from electromagnetic theory; however, the 
physical meanings of the permittivity and the permeability have not been studied thoroughly enough.  
The merit of the ether hypothesis is that a stationary reference frame can be defined. This 
stationary reference frame is compatible with the theory of special relativity; however, it is not 
compatible with the interpretation of special relativity. I only disagree with the interpretation, which 
is very strong and usually used in the discussion of the gravitational field of the earth. 
  At first, I considered the ether to be an additional concept to aid in understanding the theory of 
special relativity; at this stage, however, I have come to believe in the physical reality of the ether. I 
believe that the ether is compatible with the theory of relativity; the Michelson-Morley experiment 
can be solved using the theory of general relativity without the orthodox interpretation. 
5. Conclusion 
The consideration of the ether began because I could not illustrate the expression “the speed, c, is 
a fixed constant in any system of inertial coordinates.” In this study, I found that many great 
scientists believed in the ether. It was surprising for me to read their splendid papers. The ether is 
compatible with the theory of relativity; furthermore, I think the ether is useful for understanding the 
theory of relativity. Although the ether is said to be superfluous, it appears to have a physical reality. 
I believe that searching for the ether opens up possibilities for new physics. For example, the 
quantization of the ether, as pointed out by Dirac, is very attractive. There is a possibility that 
experiments in space physics may obtain new results regarding the ether. Today, we have new 
information from quantum mechanics and the GPS experiments. In the days of these highly valuable 
historic papers, the authors did not have such information. Therefore, it is important to revisit 
historic papers from the viewpoint of modern physics.       
References 
1) A. Einstein, "On the Electrodynamics of Moving Bodies," Annalen der Physik, 17, 891, (1905), 
in English translation; http://www.fourmilab.ch/etexts/einstein/specrel/www/. 
2) A. Michelson, and E. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether", 
American Journal of Science, Third Series, 34, 333, (1887),  
http://www.aip.org/history/gap/PDF/michelson.pdf.  
3) N. Ashby, “Relativity in the Global Positioning System,”  
www.livingreviews.org/Articles/Volume6/2003-1ashby, (2003). 
4) A. Eddington and C. Davidson, "A Determination of the Deflection of Light by the Sun's 
Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919", Phil. Trans. 
Roy. Soc. A 220, 291, (1920). 
5) A. Michelson, F. Pease, and F. Pearson, "Repetition of the Michelson-Morley Experiment", 
Nature, 123, 88, (1929).  
6) A. Michelson, F. Pease, and F. Pearson: "Measurement of the Velocity of Light in a Partial 
Vacuum", Astrophysical J., 82, 26, (1935). 
7) Dorothy Michelson Livingston, "Master of Light: A Biography of Albert A. Michelson," Univ of 
Chicago Pr (Tx), (1979). 
8) A. Michelson, H. Gale, "The Effect of the Earth's Rotation on the Velocity of Light", The 
Astrophysical Journal, 61, 140-145, (1924), http://adsabs.harvard.edu/abs/1925ApJ....61..140M. 
9) D. Allan, M. Weiss, and N. Ashby, “Around-the-World Relativistic Sagnac Experiment”, 
Science, 228, 69–70, (1985). 
10) D. Miller, "The Ether-Drift Experiment and the Determination of the Absolute Motion of the 
Earth", Reviews of Modern Physics, 5, 203, (1933). 
11) R. Shankland, S. McCuskey, F. Leone, and G. Kuerti, "New Analysis of the Interferometer 
Observations of Dayton C. Miller," Rev. Mod. Phys., 27, 167, (1955). 
12) G. Hammar, "The Velocity of Light within a Massive Enclosure," Physical Review 48, 462, 
(1935). 
13) P. Dirac "Is there an ether?" Nature, 168, 906, (1951). 
14) P. Dirac "Is there an ether?" Nature, 169, 702, (1952). 
15) P. Dirac, "General Theory of Relativity", (Princeton Landmarks in Mathematics and Physics), 
(1975). 
16) C. Misner, K. Thorne, J. Wheeler, “Gravitation”, Freeman, (1973). 
Appendix: Sagnac effect on the group velocity  
Let us discuss the group velocity change depending on the observer’s velocity. Sagnac effect is 
observed as the distance change between the light source and the observer by the motion of the 
observer. Let us consider two observers on the equator. The two observers 1 and 2 are combined by a 
rigid rod of length L as shown in Fig. A. Not only observer 1 but also observer 2 observes the 
Sagnac effect. That is, observer 2 moves during the flight time of light between observers 1 and 2. 
Thus, observer 2 also detects Sagnac effect of 61057.1 −× ; which indicates that a light reaches 
earlier to the observers than in the stationary state.  
Considering the Lorentz transformation, the group velocity is calculated as, 
.                                              (A-1) 
Where, γ is the Lorentz factor, t1 is the time when a light reaches observer 1, t2 is the time when a 
light reaches observer 2, and 12 tttS −=∆ . Let the differential time of stationary observers to set 
0t∆ , thus we obtain,  
The Lorentz factor appears both in length and time; therefore it is cancelled as shown in equation 
(2).  
Figure B shows the Sagnac effect between observers 1 and 2; after observer 1 detects the coded 
wave, observer 2 moves towards the GPS satellite. At the time t2, observer 2 moves vtS ×∆ . From 
Fig. B we obtain,  
vtLct SS ×∆−=×∆ .                                                        (A-2) 
=∆∴ .                                                              (A-3) 
G +=⎟
.                                              (A-5) 
The Sagnac effect in GPS data shows group velocity change due to the motion of the observer. 
Fig. A Sagnac effect on the group velocity measurement 
using GPS: pulse coded signal is detected by observers 1 
and 2. The detected times t1 and t2 suffer the Sagnac 
effect. Thus, the differential time 12 tttS −=∆  
becomes smaller than 0t∆  in which observers 1 and 2 
are in the stationary states.  
Observer 2    Observer 1 
GPS satellite 
Coded wave: group velocity c 
t2     t1 
    L 
Observer’s velocity v 
vtS ×∆  ctS ×∆
Fig. B Derivation of the equation of Sagnac effect: after 
observer 1 detects the coded wave, observer 2 moves 
towards the GPS satellite. At the time t2, when the coded 
wave reaches at observer 2, which moves vtS ×∆ . 
Thus, we obtain vtLct SS ×∆−=×∆ . 
           t2                             t1 
Observer 2                            Observer 1

  This paper revisits previous papers related to the theory of relativity.
Afterwards, a reconsideration of the hypothesis of ether-dragging is discussed.
The ether is compatible with the theory of relativity and historical
experiments; this paper explains the Michelson-Morley experiment using the
ether-dragging hypothesis without the orthodox interpretation that the speed c
is a fixed constant in terms of any system of inertial coordinates.

Introduction 
The theory of special relativity, proposed by Einstein [1] in 1905, was simple and intuitive. The 
principle is the invariance of the speed of light: light in a vacuum propagates with the speed c (a 
fixed constant) regardless of the motion of the light source. However, the orthodox interpretation of 
the theory of special relativity was derived later from the results of the Michelson-Morley 
experiment [2], which suggested that “the speed c is a fixed constant in terms of any system of 
inertial coordinates”. This orthodox interpretation is rather difficult to illustrate in the theory of 
special relativity: the Michelson-Morley experiment in the gravitational field of the earth cannot be 
discussed in the inertial coordinate; that is, the orthodox interpretation cannot be applied to the 
Michelson-Morley experiment. This is the starting point of this paper.    
The idea that light in a vacuum propagates with the speed c (a fixed constant), regardless of the 
state of motion of the light source was commonly accepted by the end of the 19th and early 20th 
centuries; this idea was represented in Maxwell’s equations and the wave equation as, 
,                                                           (1) 
where E is the amplitude of the wave, and c is the phase velocity of the wave. In those days, 
Maxwell and other scientists considered equation (1) to be defined in stationary coordinates. They 
considered that the speed of light, c, is defined in stationary coordinates, which is in the stationary 
ether. First of all, I would like to make this point clear: the orthodox interpretation is correct on the 
condition of the uniform flow of the ether; this is in the limitation of the theory of special relativity. 
Equation (1) has a solution )(exp kxtiE −∝ ω , (ω: frequency, k: wave number), which has a 
constant phase velocity kc /ω= . This representation indicates that in the ether in uniform flow, the 
phase velocity is always constant. For example, the Doppler shift is detected as not only the 
frequency ω but also the wave number k that satisfy the constant phase velocity, c: this is because the 
wave number k is always proportional to the frequency ω in the inertial coordinate.  
Figure 1 (a) illustrates the idea that light in a vacuum propagates with the speed c regardless of 
the state of motion of the light source. This also illustrates an idea from Einstein's 1905 paper [1]. 
Stationary light source  Moving observer 1  Moving observer 2 
Fig. 1 (b) Moving observers 1 and 2 detect the speed of light c 
Fig. 1 (a) Light in vacuum propagates with the speed c regardless of the 
state of motion of the light source 
Moving light source  
Stationary observer 
Figure 1 (b) shows that moving observers 1 and 2 detect the constant phase velocity of light c 
regardless of their motion. The constant speed of light is satisfied on the condition that both the light 
source and the observer are in inertial motion. As far as wave equation (1) is discussed in the inertial 
coordinate system, the speed of light c is always constant. On the other hand, the interpretation of the 
theory of special relativity that the speed, c, is a fixed constant in terms of any system of inertial 
coordinates is rather ambiguous. This is due to the fact that when we discuss the ether-dragging, we 
have to assume the gravitational field. The ether-wind or ether-drift is not observed in the inertial 
coordinate system; the discussion should be carried out in the theory of general relativity.  
To make the discussion more clear, let us consider an acoustic wave in the atmosphere, which has 
an isotropic constancy: although the earth moves in the solar system, we never consider the speed of 
the acoustic wave to be a fixed constant in any system of inertial coordinates. This is interpreted as 
the acoustic wave traveling in the atmosphere, which is completely dragged by the gravity of the 
earth. Although the motion of the earth in the solar system does not affect the speed of the acoustic 
wave, we never consider that the speed of an acoustic wave is a fixed constant in terms of any 
system of inertial coordinates. This is because, we know the gravitational field of the earth is not in 
the inertial coordinate system. Again, this paper starts from the simple question of how to illustrate 
the orthodox interpretation of this theory. I must conclude that this orthodox interpretation can be 
applied only in the case of a uniform ether. The frame of the wave equation does not appear to 
adhere to stationary coordinates; however, it does adhere to the physical constants of the medium. In 
the case of an acoustic wave in the atmosphere, the inertial coordinates of equation (1) are assumed 
to be the atmosphere. The physical coefficients are the density and the coefficient of stiffness. The 
wave equation of the electromagnetic wave can be interpreted using this analogy; that is, the inertial 
coordinates are the permittivity and the permeability around the earth. 
As a counterargument for the orthodox interpretation, let us consider the earth-centered locally 
inertial (ECI) coordinate system in the global positioning system (GPS) experiment [3]. The reason 
why GPS works precisely in the ECI coordinate system is that the ECI coordinate system can be 
considered as the stationary state. It is difficult to calculate GPS in the solar system; only the ECI 
coordinate system works as the stationary frame. This experimental result is an analogy to an 
acoustic wave in the dragged-atmosphere that is, the electromagnetic wave in the dragged-ether by 
the gravity around the earth.   
Using the analogy of an acoustic wave in the atmosphere, I use a classic hypothesis that the ether 
is the permittivity of free space, ε0, and the permeability of free space, µ0. This classic hypothesis 
was derived from the proposal by Lorentz of luminiferous ether that the absolute stationary 
coordinate is defined in the stationary ether. Thus, to explain the Michelson-Morley experiment, he 
proposed the Lorentz contraction of length. I will also show that the complete ether-dragging 
hypothesis is compatible with the Michelson-Morley experiment. This hypothesis was derived from 
the proposal by Maxwell that the Maxwell equation and wave equation are satisfied in the stationary 
coordinate system, i.e., the stationary ether. Maxwell predicted an ether-wind; however, the GPS 
experiment showed that the ether-wind was not observed at least up to 20,000 km from the ground 
level. Figure 2 shows that the ether is not only dragged, but also modified by gravity. The 
modification of the permittivity and the permeability by gravity causes a decrease in the speed of 
light, 
=c . Diffraction around the gravitational potential of the sun, as observed by 
Eddington [4], can be explained using this proposal that light propagates toward regions of high 
refractive index, that is, toward the sun.  
In the hypothesis that the ether is the permittivity and the permeability, the modification (increase) 
in the permittivity and permeability is used, rather than the curvature of spacetime.  
In the early 20th century, there were many great scientists who held very rigid beliefs in their own 
thoughts. Michelson accepted Einstein's work; however, he believed in the ether. He was not 
satisfied with the results of the Mt. Wilson experiment [2], and he repeated the experiment [5]. He 
worried that "shimmers" of air between the mountains might have fouled his results. In 1930, 
Fig. 2 Gravitational field illustrated by the analogy of the
atmosphere of the earth. The values of the permittivity of free space, 
ε0, and permeability of free space, µ0, vary depending on the height. 
That is, the values are changed in order to satisfy the effect of the
gravitational field on time dilation.  
Michelson’s belief in the ether brought him to his last and most ambitious test [6], the measurement 
of the velocity of light in a partial vacuum. His daughter, Dorothy Michelson Livingston [7], wrote 
that Michelson never gave up his belief in the ether.  
In 1924, Michelson-Gale-Pearson experiment [8] was carried out to observe the effect of the 
earth's rotation on the velocity of light. They assumed a fixed ether and the theory of special 
relativity. A fixed ether means the ether fixed to the ECI coordinate system; that is, the earth rotates 
in the ether. The theory of special relativity means that light in a vacuum propagates with the speed c 
regardless of the motion of the light source. They constructed the experimental setups using long 
pipes of partial vacuum. The experimental results showed the angular velocity of the earth in 
accordance with the theory of special relativity and the fixed ether. In those days, Michelson tried to 
prove the fixed ether experimentally; however the hypothesis of ether gradually disappeared. 
In 1985, on the Sagnac experiment using GPS [9], there was no discussion of the ether. This is 
because Sagnac effect as well as Michelson-Gale-Pearson experiment can be reasonably explained 
without the hypothesis of ether.  
Miller [10] was also a great scientist; he carried out the Michelson-Morley experiment with 
incredible enthusiasm. He was also a great experimentalist, and never changed his belief in the ether. 
In 1933, he reported experimental data that showed a slight seasonal and sidereal periodic fringe 
shift in the Michelson-Morley experiment. However, in 1955, his experimental results were 
re-evaluated and found to be thermal artifacts [11]. As far as the complete ether-dragging hypothesis 
is concerned, the null results are inevitable; thus, I believe that Miller’s experimental results showed 
that the interferometer measurements are affected by the motion of the earth. 
The null results of the GPS experiments were obtained by direct one-way measurement, which has 
a very high sensitivity compared to interferometer measurements. In a one-way (from the GPS 
satellite to the GPS station on earth) direct measurement of the speed of light, the sensitivity to a 
velocity of 30 km/s is calculated as 
4101/000,300/30 −×=÷ skmskm . The sensitivity of the 
Michelson interferometer is estimated as 
1050.0
000,300
1 −×=
vE . 
Thus, the sensitivity of the direct one-way measurement is 4102 × higher than that of the 
Michelson interferometer. The null results are confirmed by one-way direct measurement in the GPS 
experiments.  
At that time, it was hypothesized that ether-dragging occurs around the ground level. To check this 
hypothesis experimentally, the Michelson-Morley experiment was carried out using massive lead 
blocks (one path of the interferometer was set between two lead blocks); there was no fringe shift 
[12]. Michelson, Miller, and others discussed partial ether-dragging at the global magnetic field 
level; today, the GPS experiments show that if there is ether-dragging, it will be observed as an 
ether-wind more than 20,000 km from the ground level. 
In 1951, Dirac [13, 14] referred to the ether in the context of his new electromagnetic theory. He 
suggested describing the ether from the viewpoint of quantum mechanics, that is, quantization of the 
ether. However, his interest in and discussion of the ether gradually disappeared. He wrote a book 
entitled “General Theory of Relativity” in 1975 [15], in which the ether was not described at all. As 
discussed by Dirac in the early 1950’s, the ether may exhibit physical effects in quantum 
phenomena.  
In this paper, a hypothesis of complete ether-dragging that is based on the beliefs of the great 
scientists is described. Thereafter, I will show that the historical experimental results are compatible 
with the ether. Although the hypothesis of no ether is compatible with the historical experimental 
results; however, they do not rule out the ether hypothesis. 
2. Interpretation of historic experiments 
2.1 Aberration of light is compatible with ether-dragging 
The aberration of light was observed by Bradley in 1725. He explained the aberration using 
Newton’s particle property of photons, as shown in Fig. 3. The aberration was considered to be one 
of the experimental results that show there is no ether-dragging around earth. Fresnel explained the 
aberration by assuming that the ether is unaffected by the motion of the earth [16]. This aberration is 
difficult to explain using the wave nature of the photon; however, it is easily explained using the 
particle nature of the photon.  
Let us consider the hypothesis that the refractive index is dragged by the earth. The refractive 
index of air (n) is 1.000292, the speed of light (c) is 300,000 km/s, and the velocity of the earth in 
the solar system (v) is 30 km/s. Thus, using Fresnel’s equation (2), we obtain 
1                                                                 (2) 
912,2990175.0912,29930
000292.1
000292.1
000,3001
−+∴ v
This calculation shows that the refractive index of the air modifies the speed of light. However, the 
contribution from the dragging of the refractive index by the earth is calculated as 
9105839.0912,2990175.0 −×=÷ . 
For simplicity, let us assume a vacuum, that is, n=1. From Fresnel’s equation (2), it can be concluded 
that the speed of light c is not affected by the velocity v. Therefore, we conclude that the aberration 
of light is clearly observed in the ether-dragging scenario.   
  However, according to Fresnel’s equation, the refractive index n depends on the frequency of the 
light. Of course, this dispersion is not observed, as the ether was considered to be 
frequency-independent. Thus, it was said that the aberration cannot be compatible with 
ether-dragging. This shows that it is difficult to interpret the aberration with the wave nature of the 
photon. The wave nature of light does not explain the compatibility between ether-dragging and the 
aberration. This is because the wave property shows that a photon is dragged by the ether.  
Bradley explained the aberration using Newton’s particle property of photons, which gives 
another simple illustration of a photon traveling in a straight line in the moving ether, without 
changing its direction, as shown in Fig. 3. Therefore, the aberration does not rule out ether-dragging. 
The particle property, in the particle-wave duality of the photon, makes the explanation simple.  
2.2. Doppler shift 
In 1842, Doppler proposed the Doppler shift of light in his treatise "On the colored light of the 
binary stars and some other stars of the heaven". If the star is moving toward us, the speed of a 
Fig 3 Aberration of light is observed in the ether-dragging: 
Bradley explained the aberration using Newton’s particle 
property of photons; however, it is difficult to explain using 
the wave nature of the photon. The ether is not only dragged 
but also fixed to the ECI coordinate system. The earth rotates 
in the fixed ether.   
v=30 km/s 
Wave front 
Dragged ether by the earth: Fixed 
ether to the ECI coordinate system 
Photon 
Stationary ether 
The earth 
radiated photon is not changed by the motion of the light source; however, the photon has more 
energy and momentum, observed as the blue Doppler shift. It is interesting that the energy and 
momentum of a photon depend on the motion of the light source. It appears that the energy and 
momentum follow the Lorentz transformation, although the speed of the photon does not. 
The energy and momentum of a photon depend on the motion of the light source: if the star is 
moving toward us, the photon has increased energy and momentum, which is the blue Doppler shift. 
If the observer is moving towards the light source, he detects a higher energy and momentum for the 
photon. Although the speed of a photon does not follow the Galilean transformation, the energy and 
momentum appear to follow the Lorentz transformation.    
Let us discuss the Doppler shift of light. Equation (3) shows the longitudinal Doppler shift, 
0νν .                                                      (3) 
  Here, νD is the Doppler frequency, and ν0 is the frequency of the source in the stationary state. To 
make the discussion simple, both the observer and the source are in free space; furthermore, either 
the observer or the source is in a stationary state, as shown in Fig. 4. The relative velocity is u. Thus, 
equation (3) can be used. The observer detects a Doppler frequency νD.  
Stationary observer      Photon νD              Moving source  
(a) Stationary observer sees moving source 
c                    u 
Moving observer        Photon ν0              Stationary source  
(b) Moving observer sees stationary source 
Fig. 4 The Doppler shift from the viewpoint of quantum mechanics. 
Both the observer and the source are in free space. Either the observer or the 
source is in a stationary state. The relative velocity is u. Thus, equation (3) can 
be used.  
u                c                     
In Fig. 4 (a), a moving source radiates a photon of energy hνD (h: Planck’s constant); in Fig. 4 (b), 
the moving observer detects a photon of energy hνD. Although the speed of light, c, is constant, the 
moving source radiates a photon with higher energy and momentum. The moving observer then 
detects a photon with higher energy and momentum. In quantum mechanics, the phase velocity is 
defined as c=ε/µ, (ε: energy, µ: momentum), thus, the phase velocity is always constant.  
Let us discuss the moving observer in Fig. 4 (b) who detects a photon with speed c. It is possible 
to say that the moving observer detects a modified frequency and wave number as the Doppler shift. 
Thus, the phase velocity becomes a constant, that is, the speed of light, c. This interpretation is 
compatible with constant light speed, regardless of the motion of the light source and the orthodox 
interpretation.  
The discussion of the Doppler shift assumes stationary coordinates. That is, when we use equation 
(3), it is assumed that either the observer or the source is in a stationary state.  
2.3 Sagnac effect in GPS 
Ashby [3] summarized the Doppler shift of carrier and modulated waves in GPS. He described 
that the Doppler shift of modulated wave is proportional to that of carrier. In the GPS, pulse coded 
modulation is used for the measurement of the distance. The Doppler shift of modulated wave is 
observed as the frequency change of modulated wave (i.e., wave packet). The Doppler shift of 
modulated wave is equivalent to the Sagnac effect in GPS. As shown in Fig. 5, the station on earth 
detects the Sagnac effect as well as the Doppler shift of modulated wave (Appendix). 
Sagnac effect shows the distance change between the light source and the observer by the motion 
of the observer. If the observer moves on the flight time of light, the distance between the light 
Fig. 5 Sagnac effect and Doppler shift of modulated wave in GPS  
Station on earth 
GPS satellite 
Modulated wave 
source and the observer is changed. For example, let the distance between the GPS satellite (signal 
source) and the observer on earth set 30,000 km (the distance that light travels at 0.1 second). On the 
equator, the speed of the ground is around 0.47 km/s. Thus the Sagnac effect is 0.047 km at the 
measurement of 30,000 km for the observer on the equator, which means that at the flight time of 
light of 0.1 second, the observer moves 0.047 km. Sagnac experiment using the GPS showed the 
accuracy within 2 % [3, 9].  
From the Sagnac effect, it is assumed that the ether has two properties: 1) the ether is dragged 
with the earth, 2) the ether does not rotate with the earth; the ether is fixed to the ECI coordinate 
system. Thus the earth rotates in the fixed ether as shown in Fig. 5. It looks like a comet. From these 
discussions, there remains two possible selections; one is there is no ether, and the other is fixed 
ether to the ECI coordinate system. The historical experiments do not rule out the ether hypothesis. 
2.4 Summary of the historic experiments revisited 
In this section, the previous experimental results are reconsidered with the hypothesis that the 
ether is the permittivity, ε0, and the permeability, µ0 of free space (i.e., the refractive index n). Table 
1 shows the historic experiments and their interpretation under the ether hypothesis.  
Table 1 Experiments from historical papers 
 Experiments  Comments 
1 Aberration of light 
(1725) 
The particle property of the photon gives a simple illustration; the photon 
travels in a straight line in the moving ether without changing direction. 
The aberration is compatible with the assumption of ether-dragging by the 
earth. 
2 Doppler shift 
(1842) 
The energy and momentum of the photon appear to satisfy the Lorentz 
transformation, although the speed of the photon does not. The moving 
light source causes a Doppler shift. The moving observer also detects the 
Doppler shift. The speed of light appears to be defined in the stationary 
frame; that is, the ether.  
3 Michelson-Morley 
experiment [2] 
(1887) 
In the 1887 experiment, Michelson and Morley ruled out a stationary 
ether. The experimental results (i.e., null results) can be interpreted as 
evidence for complete ether-dragging by the gravitational field of the 
earth. The Michelson-Morley experimental results can be explained using 
ether-dragging. 
4 Sagnac (1913) Sagnac effect is discussed in GPS-Sagnac effect. 
5 Eddington [4] 
(1920) 
Diffraction around the gravitational potential of the sun, as observed by 
Eddington, can be explained with the hypothesis that light propagates 
toward regions of high refractive index, that is, toward the sun.  
6 Michelson-Gale 
-Pearson 
experiment [16] 
(1924) 
Michelson-Gale-Pearson experiment was carried out to observe the effect 
of the earth's rotation on the velocity of light. They assumed a fixed ether 
and the theory of special relativity. The experimental results showed the 
angular velocity of the earth in accordance with the theory of special 
relativity and the fixed ether.  
7 GPS-Sagnac [15] 
(1985) 
Sagnac effect shows the distance change between the light source and the 
observer by the motion of the observer on the flight time of photon. The 
ether is dragged with the earth as well as fixed to the ECI coordinate 
system. The earth rotates in the ether. In the GPS, only the relative 
velocity defined in the ECI coordinate system is correct, we cannot use the 
relative velocity defined in the solar system. This experimental evidence 
reasonably explains the hypothesis of the fixed ether to the earth.  
8. GPS [3] GPS satellites orbit 20,000 km above ground level, at a velocity of 4 km/s. 
GPS uses an earth-centered locally inertial (ECI) coordinate system. This 
coordinate system can be assumed to be a stationary frame. In the GPS 
experiment, 20,000 km from ground level, the ether-wind and Fresnel’s 
ether-dragging are not observed. The Michelson-Morley experiment 
conducted with GPS, i.e., by direct one-way measurement rather than with 
the use of a Michelson interferometer, confirms the constancy of the speed 
of light. The GPS experiments can be considered to be a reconfirmation of 
complete frame-dragging by the gravitational field of the earth. 
As described above, the complete ether-dragging hypothesis is compatible with the historical 
experimental results. 
3. Ether-dragging and the stationary state 
Figure 6 illustrates ether-dragging by the gravitational fields of the earth and the sun. The ECI 
coordinate system (the gravitational field of the earth) drags the ether in the solar system. The solar 
system simultaneously drags the ether in the galaxy, and the galaxy also drags the ether in the cosmic 
microwave background (CMB). Thus, there are many stationary states: the ECI coordinate system, 
the galaxy and the CMB.  
If we leave the gravitational field of the earth, we are in the gravitational field of the sun (solar 
system), that is, the sun-centered locally inertial coordinate system. When we travel at the speed of 
the earth (i.e., the relative velocity to the earth is 0) in the solar system, we observe a time dilation at 
a velocity of 30 km/s. If we reach the gravitational field of mars, we will be in another stationary 
state; that is, we will be in the mars-centered locally inertial coordinate system. When we leave the 
solar system, we will be in the galaxy; if we travel parallel to the solar system, we observe a time 
dilation caused by a speed of 230 km/s (the speed of the solar system in the galaxy). There are many 
stationary states in the solar system, for example, on the earth and mars. This is similar to the 
example of an acoustic wave, in which we have many stationary states, for example, in a moving 
train or in a flying airplane.   
  It is possible that ether-dragging occurs on larger scales (that is, the gravitational field scale) than 
were predicted by Michelson and Miller. They believed in the ether, and it is possible that their belief 
could be confirmed in space physics.   
4. Discussion 
4.1 The wave-particle duality in the theory of relativity 
  In the above discussions, I used the wave and particle properties. It is not easy to explain the 
experimental results using only one property. For example, the aberration is explained using the 
particle property, and I cannot explain the aberration with the wave property. On the other hand, the 
Doppler shift is difficult to explain only by the particle property; the wave property is needed. In the 
interpretation of the theory of relativity, particle-wave duality is required.  
Thus, the ether-dragging hypothesis is explained using the wave-particle duality; I cannot 
consistently explain this hypothesis using only one of the two properties. Therefore, the 
ether-dragging hypothesis should be checked experimentally with space physics. 
4.2 Merits and drawbacks of the ether 
Let us discuss the merits and faults of the ether hypothesis. The faults of the ether hypothesis are 
that it is unnecessary as far as explaining observed phenomena, and that it has never been observed; 
however, it is harmless and eases the understanding of the theory of special relativity. The concept of 
the ether is very convenient; it defines a stationary reference frame. Thus, a relative velocity is also 
defined.  
Fig. 6 Illustration of the ether-dragging by the gravitational fields of the earth 
and the sun. Not only the earth but the sun also drags the ether in the galaxy, 
which moves in the cosmic microwave background (CMB). Thus, there are 
many stationary states; this is because the gravitational fields are the 
stationary states. For examples, the ECI coordinate system, the solar system, 
the galaxy and the CMB.  
ECI coordinate system 
v=230 km/s 
Cosmic microwave background 
Solar system 
v=30 km/s
Galaxy  
v=700 km/s 
As described above, one of the candidates for the ether is the permittivity of free space, ε0, and the 
permeability of free space, µ0. These are very familiar from electromagnetic theory; however, the 
physical meanings of the permittivity and the permeability have not been studied thoroughly enough.  
The merit of the ether hypothesis is that a stationary reference frame can be defined. This 
stationary reference frame is compatible with the theory of special relativity; however, it is not 
compatible with the interpretation of special relativity. I only disagree with the interpretation, which 
is very strong and usually used in the discussion of the gravitational field of the earth. 
  At first, I considered the ether to be an additional concept to aid in understanding the theory of 
special relativity; at this stage, however, I have come to believe in the physical reality of the ether. I 
believe that the ether is compatible with the theory of relativity; the Michelson-Morley experiment 
can be solved using the theory of general relativity without the orthodox interpretation. 
5. Conclusion 
The consideration of the ether began because I could not illustrate the expression “the speed, c, is 
a fixed constant in any system of inertial coordinates.” In this study, I found that many great 
scientists believed in the ether. It was surprising for me to read their splendid papers. The ether is 
compatible with the theory of relativity; furthermore, I think the ether is useful for understanding the 
theory of relativity. Although the ether is said to be superfluous, it appears to have a physical reality. 
I believe that searching for the ether opens up possibilities for new physics. For example, the 
quantization of the ether, as pointed out by Dirac, is very attractive. There is a possibility that 
experiments in space physics may obtain new results regarding the ether. Today, we have new 
information from quantum mechanics and the GPS experiments. In the days of these highly valuable 
historic papers, the authors did not have such information. Therefore, it is important to revisit 
historic papers from the viewpoint of modern physics.       
References 
1) A. Einstein, "On the Electrodynamics of Moving Bodies," Annalen der Physik, 17, 891, (1905), 
in English translation; http://www.fourmilab.ch/etexts/einstein/specrel/www/. 
2) A. Michelson, and E. Morley, "On the Relative Motion of the Earth and the Luminiferous Ether", 
American Journal of Science, Third Series, 34, 333, (1887),  
http://www.aip.org/history/gap/PDF/michelson.pdf.  
3) N. Ashby, “Relativity in the Global Positioning System,”  
www.livingreviews.org/Articles/Volume6/2003-1ashby, (2003). 
4) A. Eddington and C. Davidson, "A Determination of the Deflection of Light by the Sun's 
Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919", Phil. Trans. 
Roy. Soc. A 220, 291, (1920). 
5) A. Michelson, F. Pease, and F. Pearson, "Repetition of the Michelson-Morley Experiment", 
Nature, 123, 88, (1929).  
6) A. Michelson, F. Pease, and F. Pearson: "Measurement of the Velocity of Light in a Partial 
Vacuum", Astrophysical J., 82, 26, (1935). 
7) Dorothy Michelson Livingston, "Master of Light: A Biography of Albert A. Michelson," Univ of 
Chicago Pr (Tx), (1979). 
8) A. Michelson, H. Gale, "The Effect of the Earth's Rotation on the Velocity of Light", The 
Astrophysical Journal, 61, 140-145, (1924), http://adsabs.harvard.edu/abs/1925ApJ....61..140M. 
9) D. Allan, M. Weiss, and N. Ashby, “Around-the-World Relativistic Sagnac Experiment”, 
Science, 228, 69–70, (1985). 
10) D. Miller, "The Ether-Drift Experiment and the Determination of the Absolute Motion of the 
Earth", Reviews of Modern Physics, 5, 203, (1933). 
11) R. Shankland, S. McCuskey, F. Leone, and G. Kuerti, "New Analysis of the Interferometer 
Observations of Dayton C. Miller," Rev. Mod. Phys., 27, 167, (1955). 
12) G. Hammar, "The Velocity of Light within a Massive Enclosure," Physical Review 48, 462, 
(1935). 
13) P. Dirac "Is there an ether?" Nature, 168, 906, (1951). 
14) P. Dirac "Is there an ether?" Nature, 169, 702, (1952). 
15) P. Dirac, "General Theory of Relativity", (Princeton Landmarks in Mathematics and Physics), 
(1975). 
16) C. Misner, K. Thorne, J. Wheeler, “Gravitation”, Freeman, (1973). 
Appendix: Sagnac effect on the group velocity  
Let us discuss the group velocity change depending on the observer’s velocity. Sagnac effect is 
observed as the distance change between the light source and the observer by the motion of the 
observer. Let us consider two observers on the equator. The two observers 1 and 2 are combined by a 
rigid rod of length L as shown in Fig. A. Not only observer 1 but also observer 2 observes the 
Sagnac effect. That is, observer 2 moves during the flight time of light between observers 1 and 2. 
Thus, observer 2 also detects Sagnac effect of 61057.1 −× ; which indicates that a light reaches 
earlier to the observers than in the stationary state.  
Considering the Lorentz transformation, the group velocity is calculated as, 
.                                              (A-1) 
Where, γ is the Lorentz factor, t1 is the time when a light reaches observer 1, t2 is the time when a 
light reaches observer 2, and 12 tttS −=∆ . Let the differential time of stationary observers to set 
0t∆ , thus we obtain,  
The Lorentz factor appears both in length and time; therefore it is cancelled as shown in equation 
(2).  
Figure B shows the Sagnac effect between observers 1 and 2; after observer 1 detects the coded 
wave, observer 2 moves towards the GPS satellite. At the time t2, observer 2 moves vtS ×∆ . From 
Fig. B we obtain,  
vtLct SS ×∆−=×∆ .                                                        (A-2) 
=∆∴ .                                                              (A-3) 
G +=⎟
.                                              (A-5) 
The Sagnac effect in GPS data shows group velocity change due to the motion of the observer. 
Fig. A Sagnac effect on the group velocity measurement 
using GPS: pulse coded signal is detected by observers 1 
and 2. The detected times t1 and t2 suffer the Sagnac 
effect. Thus, the differential time 12 tttS −=∆  
becomes smaller than 0t∆  in which observers 1 and 2 
are in the stationary states.  
Observer 2    Observer 1 
GPS satellite 
Coded wave: group velocity c 
t2     t1 
    L 
Observer’s velocity v 
vtS ×∆  ctS ×∆
Fig. B Derivation of the equation of Sagnac effect: after 
observer 1 detects the coded wave, observer 2 moves 
towards the GPS satellite. At the time t2, when the coded 
wave reaches at observer 2, which moves vtS ×∆ . 
Thus, we obtain vtLct SS ×∆−=×∆ . 
           t2                             t1 
Observer 2                            Observer 1
