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Revisiting the Ether Approaches Ⅱ: Physics free from Relativity
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20210427

Revisiting the Ether Approaches Ⅱ: Physics free from Relativity

Masanori Sato
Honda Electronics Co., Ltd., 20 Oyamazuka, Oiwa-cho, Toyohashi, Aichi 441-3193 Japan msato@honda-el.co.jp

This paper visualizes the problems of relativity: Relativity cannot explain the aberration, especially water-filled telescope experiment by Airy. Then, the alternative theory of relativity, ether theory, is presented. We propose physics free from relativity which refutes the principle of relativity, invariant light speed with regard to the observer, mass energy equivalence, Lorentz transformation, and spacetime symmetry. Maxwell equations are Galilean invariant. Schrödinger equation is not Lorentz invariant. Quantum mechanics is also free from relativity; Lévy-Leblond [“Nonrelativistic Particles and Wave Equations,” Commun. math. Phys. 6, 286, (1967)] showed that spin is not relativistic effect. Furthermore, the curvature of spacetime and the accelerating universe are refuted. Gravitational wave is not disturbances in the curvature of spacetime but acoustic wave in the ether. I propose experiment aboard the ISS: the measurement of the permittivity 0 and permeability 0 of free space in 9% small gravity with weightlessness condition. It is time to discuss physics free from relativity and back to the ether theory.
I think that the idea of the aether should be taught to students as a pedagogical device, because I find that there are lots of problems which are solved more easily by imagining the existence of an aether.
J. S. Bell, 1993
Key words: Principle of relativity, mass energy equivalence, Lorentz transformation, space time symmetry, ether

1. Introduction The theory of special relativity relies on the principle of relativity, the theory of general relativity does on the equivalence principle of gravitation and acceleration. The theory of special relativity will be denied by Phipps’s counterexample1,2 of the Principle of Relativity. Phipps1 noted the global positioning system (GPS) evidence for clock rate asymmetry; that is, only the GPS clocks suffer time dilation. In the GPS satellites, gravitation is cancelled to be weightless by centrifugal acceleration. However, Ashby3 reported that there are 45.7 s time gains every day by gravitational potential difference. Gravitational time dilation at the height 20,000 km of GPS orbit is not cancelled. Weight is cancelled but time dilation is not. Therefore, acceleration can be distinguished from a real gravitational field due to mass. It was noted that Newton's ideas of time and space were discarded prematurely. Newton's law of universal gravitation should be reviewed; Newton's gravitational lensing generates Newton's gravitational ring (see section 10.2).
An alternative theory of relativity is the ether theory. Bell, who is known as Bell’s inequality, stated in the interview with Davies4 that “Well, what is not sufficiently emphasized in textbooks, in my opinion, is that the preEinstein position of Lorentz and Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and

these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view.” Thereafter, “Well, on the grounds of philosophy; that what is unobservable does not exist. And also on grounds of simplicity, because Einstein found that the theory was both more elegant and simpler when we left out the idea of the aether. I think that the idea of the aether should be taught to students as a pedagogical device, because I find that there are lots of problems which are solved more easily by imagining the existence of an aether. But that's another story. The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now, if all Lorentz frames are equivalent, that also means that things can go backward in time.” Bell4 first pointed out the relation between the ether and entanglement.
Bell4 pointed out that the ether theory is not inconsistent with relativity theory. Therefore, in this article, we show that aberration cannot be explained by relativity theory (see section 6.) Rafelski5 noted “However, it is important that students and scholar of Special Relativity recognize Einstein’s evolution to acceptance of non-material realistically invariant aether.” In 1920, Einstein6 first represented the evolving view of the ether noting that “we may say that according to the general theory of relativity space is

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endowed with physical qualities; in this sense, therefore, there exists an ether.”
In this article, both the special and general relativity theories are refuted. Thereafter, physics free from relativity is proposed. It is time to reexamine the property of ether.
2. Physical meaning of relativity
The purpose of this article is a critical examination of relativity. Therefore, it is useful to clarify the physical meaning of relativity. For example, there are two interpretations of the Lorentz length contraction; one is “a change of coordinates” by Lord7, and the other is “a moving length contracts” by Rafelski5, and Günther and Müller8. In this report, we do not accept Lorentz length contraction.

mathematically represented to satisfy x2 + y2 + z2 - (ct)2 = k2 (k is constant); that is, some sort of union of space and time shall preserve independence. Physical meaning is the length and time vary to make the speed of light c constant.
Lévy-Leblond9 showed criticism of the emphasis put on the invariance of the speed of light in standard derivations of the Lorentz transformation, thereafter showed another derivation.
Phipps13 denied covariance describing that “Covariance masquerades as equivalent to invariance.” We discuss both Maxwell equations and Dirac equation are invariant under Galilean transformations. Relativity is not supported by Lorentz covariance; that is, the Lorentz covariance of Maxwell and Dirac equations does not support relativity. (See sections 5 and 7.)

2.1 De Broglie wave and relativity9

The kinetic energy of moving object is represented by a

de Broglie wave9 which is represented by (γ − 1)m𝑐2 ,

where m is the rest mass, 𝛾

=

1 √1−(𝑣𝑐)2

is the Lorentz factor,

v is the velocity defined in the ECI coordinate system, and

c is the speed of light. In the theory of relativity, the limit

v/c → 0 is Newtonian limit. Where the wave energy is

represented by Newtonian formalism as (𝛾 − 1)𝑚𝑐2 =

1 2

𝑚𝑣

2.

2.2 Physical meaning of the relativistic mass Let us make the relativistic mass clear9. The relativistic
mass is represented as γ𝑚, which is the summation of the rest mass m and the mass of de Broglie wave (γ − 1)𝑚. Where, (γ − 1)𝑚 is the real mass of photon that is radiated as synchrotron radiation. Therefore, the relativistic mass is considered to be the rest mass adding an adhered photon
mass.

2.3 Physical meaning of the Lorentz factor The Lorentz factor is represented by the interaction
interval of photon actions, thus depends on the path length of a travelling photon which transfers the force acting on the object. Therefore, the Lorentz factor is represented using square root of v and c.
The Lorentz factor relates to time dilation not length contraction10.

2.4 Physical meaning of Lorentz covariance
In this paper, covariance is equivalent to form invariance; that is, the laws of physics take on the same form. Minkowski11,12 introduced covariant form of time and length to satisfy the constancy of the speed of light. the Lorentz length contraction and Lorentz time dilation is

2.5 Lorentz transformation

Engelhardt9 noted that “The Lorentz Transformation,

which is considered as constitutive for the Special

Relativity Theory, was invented by Voigt in 1887, adopted

by Lorentz in 1904, and baptized by Poincaré in 1906.

Einstein probably picked it up from Voigt directly.” From

Wikipedia, it is noted that “In 1887 Voigt formulated a

form of the Lorentz transformation between a rest frame of

reference and a frame moving with speed v in the x

direction.”

Voigt's transformation9 is represented:

𝑥′

=

x

−

vt,

𝑦′

=

𝑦 𝛾

,

z′

=

𝑧 𝛾

t′ = t − 𝑣𝑐𝑥2.

(a)

Lorentz transformation is represented:

𝑥′ = γ(x − vt), 𝑦′ = y, z′ = z,

t′ = γ(t − 𝑣𝑐𝑥2).

(b)

Gift9 showed that relative simultaneity does not exist and

refuted the Lorentz transformation using the GPS data. He

proposed to replace by the Selleri transformations18:

𝑥′ = γ(x − vt), 𝑦′ = y, z′ = z

t′ = 𝑡.

(c)

𝛾

At length contraction, we do not agree with Selleri and

Gift. We proposed Galilean transformation with Lorentz

time dilation9:

𝑥′ = 𝑥 − 𝑣𝑡, 𝑦′ = y, z′ = z

t′ = 𝛾𝑡.

(d)

For the measured time and reference time, in time

transformation  appears in denominator or numerator. In

equation (c) and (d), it is the measured time t' runs slow.

We can rewrite using the reference time t’ dilates:

𝑥′ = 𝑥 − 𝑣𝑡, 𝑦′ = y, z′ = z

t′ = γt.

(e)

Phipps13 proposed using corrective time in which

excludes not only velocity but also gravitational effects,

that is, equivalent to Galilean transformation:

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𝑥′ = 𝑥 − 𝑣𝑡, 𝑦′ = y, z′ = z

t′ = t.

(f)

In this transformation, clock is not light but quantum clock.

3 Counterexample of the principle of relativity
3.1 The principle of relativity
Einstein19 noted the principle of relativity that “The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.” (English translation)
If things go slowly in a system, the principle of relativity will be denied.

3.2 Counterexample of the principle of relativity
Van Flandern20 noted that “the Global Positioning System (GPS) showed the remarkable fact that all atomic clocks on board orbiting satellites moving at high speeds in different directions could be simultaneously and continuously synchronized with each other and with all ground clocks.” Although Van Flandern20 did not clearly mention, however this statement is considered to be the refutation of the principle of relativity.

70, we represent all GPS satellites using K'. The systems

of coordinates represented as K' have the relative velocity

with regard to the earth. The velocity of the GPS satellite

vG is 4 km/s. All clocks in every GPS satellite run 1/ times

slower,

where

𝛾

=

1 √1−(𝑣𝑐)2

is the Lorentz factor, v is the

velocity defined in the ECI coordinate system, and c is the

speed of light. Asymmetry in clock progress appears

between the earth and the GPS satellites. The experimental

data of the GPS shows that the clocks in the GPS satellites

tick off time more slowly (7.1 s every day) by the velocity.

There are no asymmetries among the GPS satellites. That

is, times are equal in every GPS satellites.

Einstein6 noted between two systems K and K' which is

moving in uniform translation relatively to K as shown in

Fig. 2 that “Now comes the anxious question: - Why must

I in the theory distinguish the K system above all K'

systems, which are physically equivalent to it in all

respects, by assuming that the ether is at rest relatively to

the K system?” The answer to this question was given by

Phipps1: The K system can be distinguished above all K'

systems.

Feynman’s22 light clocks are also shown. Time dilation is

only caused by the velocity vG = 4 km/s. There are

relativistic Doppler shifts observed between the earth and

the GPS satellites.

In 2016, Phipps1 first showed a counterexample of the Principle of Relativity noting that “Thus we see that in the real world the relativity principle cannot be valid for timekeeping. Proper time clocks having different accelerational histories really do run at different rates and yield different measurement results when at rest in different inertial systems.” Phipps noted the global positioning system (GPS) evidence for clock rate asymmetry; that is, only the GPS clocks suffer time dilation. That is, in the earth-centered locally inertial (ECI) coordinate system, the Principle of Relativity was denied using the experimental data of the GPS. Proper time clocks are atomic clocks. Moving atomic clocks tick off time more slowly than that of stationary. This is a counterexample of the Principle of Relativity. A paradigm shift in relativity has begun.

Solar system
vG = 4 km/s ECI coordinate system

vd = 30 km/s

For readers’ convenience, let us illustrate the counterexample of the Principle of Relativity2. Figure 1 shows the hierarchy structure of the reference frames, that is, the GPS satellite moves (vG = 4 km/s) in the ECI coordinate system which is moving in the solar system at vd = 30 km/s. A hierarchy structure21 of locally inertial coordinate systems is the ECI coordinate system moving in the solar system.
Figure 2 shows a counterexample between two frames in the ECI coordinate system. A system of coordinates K is set on the earth, another system of coordinate K' is set in the GPS satellite. The number of GPS satellites is around

Fig. 1 Hierarchy structure21 of reference frames: the solar system, the ECI coordinate system and the GPS satellite
Lord7 noted that “A Lorentz transformation is a relationship between "inertial frames" chosen by two "inertial observers" who are in uniform motion relative to each other. It is merely a change of coordinates.” “It does not "contract lengths" or "dilate time";” Günther and Müller8 noted that “With respect to this system a moving clock loses time and a moving length contracts.” They consider that both time dilation and length contraction are

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real physical phenomena. We do not consider it is the case, length contraction is a change of coordinates, time dilation is a real physical phenomenon. The Principle of Relativity critically depends whether time dilation is a change of coordinates or a real physical phenomenon. We consider that time dilation does not have any relation to the Lorentz coordinate transformation, that is, time dilation is a real physical phenomenon; Feynman22 used a light clock to visualize time dilation by motion. Therefore, the Principle of Relativity is denied by Phipps’s1 counterexample.

vG = 4 km/s Plane wave

GPS satellite

3.3 Distinguishability of stationary and moving systems
Günther and Müller8 discussed the indistinguishability of inertial systems. Let us discuss the distinguishability of two systems. The GPS uses Newtonian absolute time; this is Phipps’s collective time14 in which not only gravitational effects but also velocity effects are eliminated. All clocks in the travelling GPS satellites and clocks on earth are synchronized in advance. The GPS satellite obtains the data of collective time and finds time dilation of the clock on board; therefore, distinguishes that the GPS satellite is moving. A system where time advances slowly is moving faster.
Figure 3 shows the thought experiment of distinguishability of two systems. To make the discussion simple, the stations on the earth are assumed twodimensional array antenna to generate plane wave parallel to the GPS satellite orbit. The clock in the GPS satellite suffers time dilation. We cannot say that the earth is moving.
z

x z'

K: The earth

y

Relativistic Doppler shift

vG = 4 km/s

x'

y'

K': GPS satellite

Fig. 2 Counterexample of the principle of relativity

Two-dimensional array antenna on the earth to generate plane wave
Fig. 3 Thought experiment of the distinguishability of two systems.
4. The speed of light is observer-dependent
4.1 The constancy of the speed of light
Einstein noted the constancy of the speed of light that “Any ray of light moves in the “stationary'' system of coordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.” (English translation) In the later part of his paper, Einstein noted that “The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible.” (English translation) This indicates that the velocity of electromagnetic wave is observed as invariance independent of the observer’s velocity.
Many researchers have already denied the constancy of the speed of light using the experimental data of Sagnac effect and Doppler shift. These two phenomena are physically equivalent.
Wang23 et al. reported that “Our finding is that there is a travel-time difference Δt = 2vΔl/c2 in a fiber segment of length Δl moving with the source and detector at a speed v, whether the segment is moving uniformly or circularly.” Suleiman24 noted that “the circular Sagnac effect is fully explainable in the framework of inertial systems,” the Sagnac effect can be discussed over a one-way path.
Gift25 showed that Doppler shift reveals light speed variation. The merit of discussion using Doppler shift is that the discussion can be carried out in inertial frame.

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For readers’ convenience, let us show that the speed of

light is observer-dependent using Doppler shift. Figure 4

shows the Doppler shift of the carrier and modulated waves.

The wave form in (a) shows the modulated wave observed

by a stationary observer, the wave form in (b) is the

modulated wave observed by a moving observer. The

modulated wave as well as the carrier wave suffers the

Doppler shift. Stationary observer detects the speed of light

𝐿 ∆𝑡𝑠

=𝑐

.

Moving

observer

toward

the

source

does

𝐿 ∆𝑡𝑚

.

Therefore,

𝐿 =𝑐
∆𝑡𝑠

<

𝐿 ∆𝑡𝑚

.

That

is,

the

speed

of

light

is

observer-dependent. In this discussion, for simplicity,

Lorentz

factor

𝛾

=

1 √1−(𝑣𝑐)2

is neglected; this is because, at

v=0.47 km/s, Lorentz factor (-1= 1.23 × 10-12) is 10-6

compering with v/c=1.57×10-6, therefore negligible.

L
Modulated wave: group velocity = c

Source

Detector 1 Detector 2

Observer’s velocity: v
Observed wave by Detector 1
Observed wave by Detector 2

contraction is suitable to explain the Michelson-Morley's experimental results. Although Michelson-Morley's experiment is considered to compare photon’s arrival times in two arms, MichelsonMorley's experiment is interferometer experiment; let us consider a single photon Michelson-Morley's experiment27 as shown in Fig. 5. In interferometer experiment, null results mean that there is no length change of the arm. Therefore, the Michelson-Morley's experimental results do not show length contraction.
Mirror 2

Path 2 Photon source

Half mirror Photon

Path 1

Detector

Mirror 1

Fig. 5 Single-photon Michelson-Morley experiment27 There is only a single photon in the Michelson interferometer: in spite of the single photon, interference is observed. This experiment does not show the simultaneous arrival of two photons.

ts (a) Modulated wave observed by a stationary observer
tm
(b) Modulated wave observed by a moving observer Fig. 4 Doppler shift of carrier and modulated waves reveals that the speed of light is observer-dependent.

5.2 Lagrangian and Eulerian descriptions28 Today’s Maxwell equations are Eulerian description. Original Maxwell equations used Lagrangian description. Lagrangian description is material description and Eulerian description is spatial description; that is, the Lagrangian description (𝑑/𝑑𝑡) is fixed to the drifting material. Figure 6 shows the Lagrangian description (𝑑/𝑑𝑡) and the Eulerian description (𝜕⁄𝜕𝑡) in two dimensions. If we observe a drifting object from a drifting boat which is fixed to the drifting material, then we use the Lagrangian description (𝑑/𝑑𝑡); if we observe a drifting object from a bridge which is spatially fixed, then we use the Eulerian description (𝜕⁄𝜕𝑡).

5. Refutation of the Lorentz transformation

5.1 Refutation of the Lorentz contraction Lorentz contraction was proposed to explain the
experimental results of Michelson-Morley. Let us look back the conclusion of Michelson-Morley26 paper in 1887; that was “the ether is at rest with regard to the earth's surface.” Therefore, we do not consider that the Lorentz

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Bridge 𝜕⁄𝜕𝑡

Drift velocity 𝑣⃗⃗⃗⃗𝑑 Object
Boat 𝑑/𝑑𝑡

River

Fig. 6 Lagrangian description (𝑑/𝑑𝑡) and Eulerian description (𝜕⁄𝜕𝑡) in two dimensions: According to
Hertz, we consider that drift velocity 𝑣⃗⃗⃗⃗𝑑 represents that of the ether.

bodies. The HERTZian forms must be given up, for it has

appeared that they are contrary to many experimental

results.” (English translation)

Minkowski did not accept Hertzian form, thus introduced

covariant form of time and length to satisfy the constancy

of the speed of light. As was pointed out by Minkowski12,

in a laboratory scale experiment by Eichenwald and

Wilson31, rotation ∇ × (𝑣⃗⃗⃗⃗𝑑 ×) did not generate any magnetic field. However, this experimental result does not

rule out Hertzian form. Let us use the convective derivative

excluding ∇ × (𝑣⃗⃗⃗⃗𝑑 ×) from equation (2),

𝑑𝜕

𝑑𝑡 = 𝜕𝑡 + 𝑣⃗⃗⃗⃗𝑑(∇ ∙)

(3)

Thus, original Maxwell equations are not shown to be

spacetime symmetry. That is, 𝑑 is not symmetry with 𝜕 .

𝑑𝑡

𝜕𝑥

5.3 Maxwell equations are Galilean invariant

In the late 19th century, almost all scientists believed in

the ether, they considered that Maxwell equations are

Galilean invariant, since the Galilean transformation is the

only one in those days. This is the premise. Hertz's29

Galilean invariant form of Maxwell equations was simple

and intuitive. Phipps14 summarized Hertz's works.

Today’s Maxwell equations look symmetric in space and

time, thus looks Lorentz covariant.

Hertz's Galilean invariant form of Maxwell equations are

represented as,

∇

×

𝐸⃗

=

−

𝑑𝐵⃗ 𝑑𝑡 ,

∇

×

𝐻⃗

=

𝑗

+

𝑑𝐷⃗ 𝑑𝑡

∇ × 𝐷⃗ = 𝜌, ∇ ∙ 𝐵⃗ = 0

(1)

The convective derivative is defined from standard

traditional field theory as,

𝑑𝜕

𝑑𝑡 = 𝜕𝑡 − ∇ × (𝑣⃗⃗⃗⃗𝑑 ×) + 𝑣⃗⃗⃗⃗𝑑(∇ ∙)

(2)

where, 𝑣⃗⃗⃗⃗𝑑 is the drift velocity of the ether combine with

matter. Phipps noted that equation (1) is invariant under the

Galilean transformation. Hertz used the standard

traditional field theory, thus assumed the ether drift. Phipps

did not assume the ether, and therefore noted that Hertz’s

assumption of ether drift velocity 𝑣⃗⃗⃗⃗𝑑 was a fatal mistake.
We do not think it is the case, Hertz was correct; 𝑣⃗⃗⃗⃗𝑑 is the drift velocity of ether30.

5.4 Refutation of the spacetime symmetry Minkowski11 proposed the idea of spacetime that
“Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence.” (English translation) We consider that this was the starting point of spacetime symmetry. Minkowski12 noted that “At the present time, different opinions are being held about the fundamental equations of Electrodynamics for moving

5.5 Derivation of today’s Maxwell equations by Hertz

Hertz had known the results of the Michelson-Morley
experiment that the ether is at rest with regard to the earth's surface, and thus, at the earth's surface, he set vd = 0 .
This is today’s Maxwell equations.

∇ × 𝐸⃗ = − 𝜕𝐵⃗ , ∇ × 𝐻⃗ = 𝑗 + 𝜕𝐷⃗ (4)

𝜕𝑡

𝜕𝑡

Although Hertz derived equation (4) for the surface of the

earth where the ether is at rest; however, in the early of the

20th century, this equation was walking alone as the

equation

for

universal

condition.

Again,

𝑑 𝑑𝑡

is

symmetry

with

𝜕 𝜕𝑥

at

the

surface

of

the

earth

where

the

ether

is

at

rest.

6. GPS clocks variation

GPS clocks variation28 in the solar system cannot be

explained by the theory of relativity. Figure 7 shows that

the summation of the velocity of the earth vd and the

velocity of the GPS satellite vG in the solar system is

periodically changed every 6 hours. The reference time tG

is calculated using equation (3) from the Lorentz

transformation by setting vd= 30 km/s and vG= 4 km/s,

𝑡𝐺

=

𝑡0 √1−(𝑣𝑑+𝑐 𝑣𝐺)2

(5)

The reference time t0 is the time of the stationary state in

the solar system eliminating the gravitational effect.

Equation (5) shows that there is a periodic deviation

depending on the velocity (vd+vG)2. The maximum

deviation of the reference time tG is calculated as tG=±1.3×10-9. The deviation tG is periodic, which causes

a deviation in distance of around 0.28 km. However, the

earth-centered locally inertial (ECI) coordinate system

operates well by the GPS satellites, meaning no periodic

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distance deviation is observed. Therefore, GPS clocks cannot be explained by the theory of relativity.
GPS satellite vd = 30 km/s
vG = 4 km/s, around 12 hours in one rotation
Fig. 7 GPS clocks in the solar system
7. Aberration: Water-filled telescope experiment by Airy
7.1 Aberration cannot be explained by the relative velocity
If the observer moves, the optical aberration is observed. Here, we will discuss the 20 arc seconds annual aberration discovered by Bradley. Both the Sun and Mercury show the aberration angle of 20 arc seconds, although the Sun and Mercury have deferent relative velocities with regard to the earth as shown in Fig. 8. The relative velocities of Mercury become from 17 km/s to 77 km/s. Venus also shows 20 arc seconds aberration. Therefore, the relative velocity cannot explain aberration; the revolution velocity of the earth 30 km/s looks to decide the aberration of 20 arc seconds.
Let us consider the relativity of aberration angle seen from the earth and Mercury. If we are on Mercury and see the earth, we will observe around 31 arc seconds aberration; relativity will not be satisfied between the earth and Mercury, this is another counterexample of the principle of relativity. It was pointed out that the moon shows 0.7 not 20 arc seconds aberration; therefore, the revolution velocity cannot explain aberration. We show the explanation of aberration in section 7.3.

7.2 Water-filled telescope experiment by Airy We consider that the water-filled telescope experiment by Airy can give a judgement for relativity28. We do not consider that relativity give a solution for the experimental results. Figure 9 provides an explanation of the aberration by Bradley: The Earth’s revolution velocity (30km/s) makes the stellar light from the top seem as if it comes from the front. The dotted line is considered to be the apparent direction of the light. Figure 10 presents the water-filled telescope experiment by Airy: The direction of the light was unchanged. To satisfy the experiments in Figs.9 and 10, the dotted line was considered not to be the apparent but rather the true direction of the light.
vd = 30 km/s
Fig.9 Explanation of the aberration by Bradley: The earth’s revolution velocity (30 km/s) makes the stellar light from the top seem as if it comes from the front. The dotted line was considered to be the apparent direction of the light.
vd = 30 km/s

Fig. 10 Water-filled telescope experiment by Airy: The direction of the light was not changed. The dotted line was considered to be not the apparent but the true direction of the light.

Mercury

Sun

47 km/s

Venus 35 km/s

Moon

Earth 30 km/s
Fig. 8 Aberration is decided by the revolution velocity of the earth 30 km/s, not the relative velocity between Mercury and the earth. Moon does not show aberration.

7.3 Explanation of aberration Figure 1128 explains the aberration using the Stokes’s ether model in the distance scale of the earth and the moon (the radius of the ether sphere is more than 380,000km). Both the particle model and the wave model, at the surface of the dragged ether sphere, the particle and the wave refract according to 𝑠𝑖𝑛𝛼~𝛼~ 𝑣𝑐, photons hit the front of the ether sphere; thus, we see the photons at an angle  according to Huygens’s principle which shows the front surface becomes a new source of light. The aberration is

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caused by the refraction by moving ether sphere. The wave front changes its direction to enclose the dragged ether sphere. The height of the dragged ether sphere from the ground is more than 380,000km, which is the distance from the earth to the moon. The minimum distance of 380,000km is estimated from the experimental evidence that there is little aberration of the moon light32.
Let us consider the moon’s aberration. Van Flandern32 estimated around 0.7 arc seconds by the relative velocity of 1 km/s. However, as pointed out by Van Flandern32, aberration depends on the velocity of the observer not the relative velocity. The barycenter is in the earth, that is, the earth is assumed to be stationary in the gravitational field of the earth. Therefore, there is little aberration of the moon.
We consider the explanation of the aberration by the Stokes’s ether dragging hypothesis is simple. As shown in Fig. 10, the photons represent the true direction of the light with respect to the ECI coordinate system.

Solar system

Wave front


vd = 30 km/s

wave includes the rest mass, but the Schrödinger equation does not. If the rest mass is excluded, de Broglie waves become free from relativity.
In 1928, Dirac33 derived Dirac equation from KleinGordon equation which has dispersion relation including rest mass energy mc2. Therefore, Klein-Gordon as well as Dirac equations were considered to be relativistic. Dirac equation derived spins; thus, it was believed that spin is relativistic phenomena. I do not consider it is the case.

8.2 Lévy-Leblond’s paper

Schrödinger equation was derived using the

nonrelativistic dispersion relation of equation (6), at this

stage without potential energy.

𝐸 = 𝑝2

(6)

2𝑚

∴

𝑖ℏ

𝜕𝜑 𝜕𝑡

=

−

ℏ2 2𝑚

𝜕2𝜑 𝜕𝑥2

(7)

Lévy-Leblond34 made linearization of the Schrödinger

equation describing that “We shall now derive such a wave

equation, which will turn out to describe spin 1/2 particles,

using the heuristic idea that DIRAC applied so successfully

in RQM;” where, linearization means transforming the

second order space differential equation into a first order

space differential equation using matrix. Lévy-Leblond

noted that “A complete nonrelativistic theory predicts the

correct value for the intrinsic magnetic moment of a spin

1/2 particle.”

In this section, we showed from spin derivation by Lévy-

Leblond that spin is not the relativistic effect. Therefore,

quantum mechanics cannot support relativity.

ECI coordinate system
Fig. 11 Explanation of the aberration by Stokes’ ether dragging model28
8. Quantum physics free from relativity It is considered that relativity is compatible with Lorentz invariance. Thus, Lorentz invariance is used to support relativity in quantum physics. I do not consider it is the case. Physics should not be restricted by relativity; that is, physics does not need to be Lorentz invariant. As was shown in section 5.1, Maxwell equation is not Lorentz invariant. Let us discuss quantum physics.

8.3 Refutation of the mass energy equivalence 𝐸 = 𝑚𝑐2 relates to quantum mechanics rather than the theory of special relativity35. Using the quantum mechanical momentum conservation law between massive particle and photon, the discussion does not need to carry out using the theory of special relativity. From quantum mechanics, we obtain for the energy of photon 𝜀 = 𝑐𝜇. Assuming a photon transfers the invariant mass ∆𝑚 at the speed of light c, the momentum of photon is 𝜇 = ∆𝑚 × 𝑐 , therefore, 𝜀 = 𝑐𝜇 = ∆𝑚𝑐2 . This represents the energy of photon, not the equivalence of the mass and energy. Nuclear fission and fusion are release of photons from atom with energy and mass; it does not show the
equivalence of the mass and energy. This relates to the light bending by gravity (see section 9).

8.1 De Broglie waves and Schrödinger equation Schrödinger equation is not Lorentz invariant. This tells
everything; that is, quantum physics is free from relativity. We showed that the difference between de Broglie waves and Schrödinger equation is the rest mass9. The de Broglie

9. Refutation of the curvature of spacetime Gravitational lensing is not caused by the curvature of spacetime but by the property of photon itself.
9.1 Space, time and gravitation by Eddington36

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In his book, Eddington36 discussed the mass and inertia of

light, he might be already aware of light bending by

Newtonian mechanics. That is, the magnification of

Newton gravitational lensing is half. Therefore, Newton

gravitational lensing should be used E=mc2 instead of 𝐸 =

1 2

𝑚𝑣2

for

photons.

Light bending by gravity is two times greater than that of

ordinary particles. Eddington36 calculated the light bending

by the sun to be 1.75″ using the theory of general relativity;

that of Newtonian mechanics was 0.87″. In 1801, using

Newtonian mechanics Soldner37 calculated to be 0.84″.

The light bending by gravity becomes 2 times greater

without assumption of the curvature of spacetime.

Einstein’s gravitational ring is equivalent to Newton's

gravitational ring38.

9.2 Schwarzschild radius for a photon

In the theory of relativity, the limit v/c → 0 is Newtonian

limit; however, the theory of relativity does not degenerate

to Newtonian mechanics in the limit r → ∞. (Where v is

the velocity, c is the speed of light, r is the distance from

the

mass.)

Schwarzschild

radius

𝑟𝑆

=

2𝐺𝑀 𝑐2

was

calculated

under the assumption of degeneration to Newtonian

mechanics in the limit r → ∞. However, this assumption

was not correct; that is the light bending by the gravity is

two times greater in weak gravitational fields.

Schwarzschild radius for a photon r’s is represented as

𝑟′𝑆

=

𝐺𝑀 𝑐2

in

Newtonian

mechanics

using

E=

𝑚𝑐2

instead

of E = 1 𝑚𝑣2. That is, Schwarzschild radius for a photon

2

is half.

Light bending by gravity is caused by the property of

photon not the curvature of spacetime38. We should get

back to space and time from spacetime.

distribution as an exponential function 𝑦 = 𝑒−1𝑟, as shown

in Fig. 1239. This form, proposed by Hatch40, is chosen

because

satisfies

𝑑𝑦 𝑑𝑟

=

1 𝑟2

𝑦.

y

1 0.8 0.6 0.4 0.2
0 0 1 2 3 4 5 6 7 8 9 10 11 r
Fig. 12 Illustration of the equation 𝑦 = 𝑒−1𝑟, which is used to model the distribution of the ether density from a point mass

10.2 Exclusion of the gravitational singularity

In

Fig.

13,

the

solid

line

corresponds

to

𝑑𝑦 𝑑𝑟

=

1 𝑟2

𝑒 −1𝑟

and

the

dotted

line

corresponds

to

𝑑𝑦 𝑑𝑟

=

1 𝑟2

.

Two

lines

are

asymptotic, at the same time, the solid line excludes the

gravitational singularity at r=0.

8 6 4

dy/dr

10. Equivalence principle The equivalence principle of gravitational and inertial
masses was experimentally confirmed. However, there is a question about the equivalence principle of gravitation and acceleration.
10.1 Gravitational and inertial masses The resistance (i.e., the impedance) from accelerated
motion in the ether is considered to be inertia. Inertia is an eddy making resistance generated by the accelerated motion of a massive particle in the ether. The resistance in the ether is isotropic; thus, the inertial mass is equivalent to the gravitational mass39.
We consider that ether originates from mass. The gradient in the ether density results from the mass distribution.
At the same time, the equivalence of the inertial and gravitational masses leads us to represent the ether density

2
0 0 1 2 3 4 5 6 7 8 9 10 11 r

Fig. 13 Plot of equations: the solid line corresponds to

𝑑𝑦 𝑑𝑟

=

1 𝑟2

𝑒 −1𝑟

and

the

dotted

line

corresponds

to

𝑑𝑦 𝑑𝑟

= 𝑟12.

10.3 A possible solution of galaxy rotation problem: refutation of dark matter The equivalence of the inertial and gravitational masses may show a solution of galaxy rotation problem. The gravitational mass decreases according to the distance from the supermassive black hole, therefore inertial mass decreases. The momentum conservation makes to increase the velocity according to the decrease of inertial mass. The

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decrease of the inertial and gravitational masses may cause flat rotation curve (solid line) as shown in Fig. 14 without dark matter.

The sun

Velocity

vE= 30 km/s Orbit P
GPS satellite

Gravity eclipse

Distance

Fig. 14 Flat rotation curve
10.4 Absence of the Noon-Midnight redshift It is known that two clocks fixed on the Earth’s surface,
when compared to each other, do not display a frequency difference due to external masses (Sun, Moon). Absence of the Noon-Midnight redshift was discussed by Hoffmann41 noting that Noon-Midnight redshift is cancelled by the relativistic Doppler effect.
Hoffmann’s arguments were criticized by Ashby and Weiss42 using the effect of acceleration cannot be distinguished from a real gravitational field due to mass. Figure 15 shows two explanations of absence of the NoonMidnight redshift; one is the cancellation by the relativistic Doppler effect41,43, and the other is the cancellation of gravitation by acceleration42,44. Montenbruck45 et al. reported GPS satellite clock variations of orbit dependency. At low angle (the sun is in the GPS orbital plane), the deviations of the GPS clocks were observed.
We consider that the ether sphere is deformed to cancel the effects due to external masses.
10.5 Question about the equivalence principle of gravitation and acceleration
Ashby and Weiss42 noted a freely falling elevator in earth’s gravity field cancels the real gravitational field strength, resulting in weightlessness within the elevator.
In the International Space Station (ISS), the gravity becomes around 9 % smaller comparing to the Earth. Therefore, according to the equivalence principle of the gravitational and inertial masses, the inertial mass also becomes 9 % smaller. The mass moves 9 % easier in the ISS than on the earth. That is the inertia is not cancelled in the ISS. On the moon, both weight and inertia become 1/6.
We do not consider that a freely falling elevator in earth’s gravity field cancels the real gravitational field.

Fig. 15 Gravity eclipse by the earth (shadowed area): GPS satellite on orbit P is eclipsed by the earth. The clocks on the GPS satellites show periodic variations. Not the velocity but the eclipse by the earth affects the reference times of the GPS satellites.
11. Gravity Maxwell46 noted that “Newton himself, however, endeavored to account for gravitation by differences of pressure in an aether, but he did not publish his theory.” We assume the idea by Newton that the gradient of the ether density causes the gravitation: 𝑔 ∝ − 𝜕𝜌𝐸. It is also
𝜕𝑥
assumed that the gravitation is action at a distance (i.e., entanglement). The speed of gravitational wave is the speed of light (see section 12).
11.1 The speed of gravity by Van Flandern Van Flandern16 noted that “Why do total eclipses of the Sun by the Moon reach maximum eclipse about 40 seconds before the Sun and Moon’s gravitational forces align?” Figure 16 shows the illustration of notation by Van Flandern. Angle  is not on scale; 20 arc seconds are around 1% of the apparent diameter of the Moon. From the deference between total eclipses of the Sun and the Sun and Moon’s gravitational forces align, Van Flandern16 estimated that the speed of gravity is at least 20 times greater than that of the light c. After 38 ± 1.9 seconds from total eclipse, the Sun and Moon’s gravitational forces align occurs as shown in Fig. 17. At 38 seconds, the speed of gravity is infinite, at 1.9 seconds later, the speed of gravity is  ÷ 1.9 = 20 times greater than that of light c; this was explained by Van Flandern20. Although Fig. 16 shows that the gravity is interaction between the sun and the earth but light is propagation from the sun to the earth. Thus, it may explain that the aberration occurs only on light propagation; however, the speed of gravity is not assumed by equation 𝑠𝑖𝑛𝛼~𝛼~ 𝑣𝑐.

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Gravity

 Sun light

Moon

Earth Eclipse

vd = 30 km/s

Fig. 16 Total eclipses of the Sun by the Moon and the Sun and Moon’s gravitational forces align explained by Van Flandern20. (Angle  is not on scale.)
Sun
Gravity

Buoy
Chain
Ripples
Anchor
Fig. 18 Anchor-buoy model by Van Flandern and Viger47
11.3 Gravity entanglement48 Gravity entanglement is similar to the anchor-buoy model. The distribution of the ether density from a point mass simultaneously moves with the point mass as shown in Fig.19; this is gravity entanglement. We assume that point mass deceleration causes not only Bremsstrahlung but also gravitational waves (acoustic waves in the ether). Bremsstrahlung is the radiation of adhered photons of point mass. The motion of point mass generates a compressional fluctuation of ether density which travels at the speed of light, this is gravitational waves.

Moon

Earth

vd = 30 km/s

Fig. 17 After 38 ± 1.9 seconds from total eclipse, the Sun and Moon’s gravitational forces align occurs.
11.2 Gravitational force and gravitational waves Van Flandern and Viger47 explained gravitational force
and gravitational waves by anchor-buoy model as shown in Fig. 18. Gravitational force is anchor and chain pulling on buoy, and gravitational waves are water ripples emerging form buoy.

Fig.19 Ether density distribution from point mass simultaneously moves with the point mass. At the same time, the fluctuation travels at the speed of light c, as gravitational waves.

Let us assume the elastic modulus of the ether is KE, the density of the ether is E, the speed of gravitational wave is c, and the distance from the point mass is r. Therefore,

√𝐾𝜌𝐸𝐸 = 𝑐(𝑟) = √𝜀10𝜇0.

(8)

Thus, we obtain,

𝜌𝐸(𝑟) = 𝐾𝐸𝜀0𝜇0.

(9)

Gravity g is caused by the gradient of the distribution of the ether density E as,

𝑔

=

𝑀

𝜕𝜌𝐸 𝜕𝑟

.

(10)

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Where M is the mass of the earth. The ether density distribution, as shown in Fig. 19, is assumed to be an exponential function6,

𝜌𝐸(𝑟) = 𝐺(1 − 𝑒−1𝑟).

(11)

Substitute equation (11) into equation (10), thus, we obtain,

𝑔

=

𝑀

𝑑𝜌𝐸 𝑑𝑟

=

−𝐺𝑀

𝑑 𝑑𝑟

𝑒 −1𝑟

=

𝐺𝑀 𝑟2

𝑒 −1𝑟 .

(12)

Equation

(12)

shows

that

gravity

g

approaches

to

𝐺𝑀 𝑟2

at

r≫0, furthermore excludes the gravitational singularity at

r = 0; that is, g = 0 not ∞ at r = 0. Figure 20 shows gravity

from the point mass calculated using equation (12).

The distribution of the ether density simultaneously moves with the point mass as shown in Fig. 19. The distribution overlaps over that of another point mass to cause attraction at a distance; this is gravity entanglement6. We assume that point mass deceleration causes not only Bremsstrahlung but also gravitational waves7. The motion of point mass generates a compressional fluctuation of ether density which travels at the speed of light, this is gravitational waves.
Quantum entanglement is accepted because it does not transfer any information, therefore, gravity entanglement has a possibility of acceptance because there is no information transmission.

Quantum entanglement disappears with interaction of another system. We discussed the continuity of quantum entanglement49. Gravity entanglement is considered to permanently continue.

momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observations if the speed is at all comparable with that of light. The argument is fallacious, because the effect of propagation will not necessarily be that S is attracted in the direction towards J’. Indeed it is found that if S and J are two electric charges, S will be attracted very approximately towards J (not J’) in spite of the electric influence being propagated with the velocity of light." It is considered that Eddington36 was already aware that the gravity is an entanglement. Using the discussion by Eddington36, Van Flandern and Viger47 first proposed the idea of gravity entanglement. Van Flandern20 noted that “Yet, anyone with a computer and orbit computation or numerical integration software can verify the consequences of introducing a delay into gravitational interactions. The effect on computed orbits is usually disastrous because conservation of angular momentum is destroyed.” Van Flandern20 wrote that Eddington36 was already aware of the mostly equivalent “refracting medium” explanation for general relativistic (GR) features, which retains Euclidean space and time in the same mathematical formalism. “In essence, the bending of light, gravitational redshift, Mercury perihelion advance, and radar time delay can all be consequences of electromagnetic wave motion through an underlying refracting medium that is made denser in proportion to the nearness of a source of gravity.” And “The principal objection to this conceptually simpler refraction interpretation of GR is that a faster-than-light propagation speed for gravity itself is required.”

J

S'

J'

S

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Fig. 20 Gravity from the point mass

Fig. 21 Copy from Eddington’s36 book (P. 84, FIG. 13) J

Eddington36 discussed the motion of the Sun and Jupiter

as shown in Fig. 21 noting that "If the Sun attracts Jupiter

towards its present position S, and Jupiter attracts the Sun

towards its present position J, the two forces are in the

same line and balance. But if the Sun attracts Jupiter

S

toward its previous position S', and Jupiter attracts the Sun

towards its previous position J', when the force of attraction

started out to cross the gulf, then the two forces give a

couple. This couple will tend to increase the angular Fig. 22 Newton’s gravity entanglement model

(r)

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Quantum entanglement started from the conservation of spin. Thus, gravity entanglement started from the conservation of angular momentum. The Sun and Jupiter rotate around the barycenter satisfying the conservation of angular momentum. We consider that the conservation of angular momentum derives gravity entanglement. We consider Newton’s gravity entanglement model in Fig. 22 is correct.

𝑝𝑔 𝜌𝐸

=

𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

(15)

Equations (13) ~ (15) define the acoustic waves in the

ether. This is the gravitational waves. For linearization,

separate the parameters to the constants and variances. The

subscript 0 shows constant, and that of 1 shows variance;

thus subscript 1 indicates the fluctuation of the

gravitational wave.

𝜌𝐸 = 𝜌0 + 𝜌1 , 𝑣 = 𝑣0 + 𝑣1 , 𝑝𝑔 = 𝑝0 + 𝑝1

And assuming 𝜌0 ≫ 𝜌1, 𝑝0 ≫ 𝑝1 to linearize equations (13) ~ (15), we obtain,

12. Gravitational wave From Wikipedia it is noted that “Gravitational waves are
disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light.” We consider that the gravitational wave is an acoustic wave in the ether50.

12.1 Refutation of the disturbances in the curvature of spacetime
Perlmutter51 noted that “the cosmic expansion stretches not only the distances between galaxy clusters but also the very wavelengths of the photons en route.” I do not consider that this notation is right. However, if it is right, in the Michelson interferometer experiment of the Laser Interferometer Gravitational-Wave Observatory (LIGO), we cannot observe a curvature of spacetime. This is because wavelengths are changed to cancel the disturbances in the curvature of spacetime.

12.2 Gravitational wave derived from fluid mechanics

In this section we introduce an idea that gravitational

wave is an acoustic wave in the ether50. Let us assume the

elastic modulus of the ether is KE, the density of the ether

is E, and the speed of gravitational wave is c. Therefore,

√𝐾𝜌𝐸𝐸

=

𝑐(𝑥)

=

1.
√𝜀0𝜇0

Thus,

we

obtain

𝜌𝐸(𝑥) = 𝐾𝐸𝜀0𝜇0.

The gravitational wave is the fluctuation of the ether

density E. Let us derive the gravitational wave. To simplify the

discussion, it is carried out with one dimension. According

to the analogy of acoustic wave, let us use three equations;

equation (13) shows the Euler’s equation of motion, in

which the gradient of gravity causes ether motion toward

the high ether density region, where pg is the pressure of gravity. Equation (14) is the equation of continuity of the

ether and equation (15) is that of adiabatic processes

(Boyle’s law). The fluctuation of gravity is proportional to

that of the ether.

𝜌𝐸

𝜕𝑣 ( 𝜕𝑡

+

𝑣

𝜕𝑣 𝜕𝑥)

=

𝜕𝑝𝑔 𝜕𝑥

𝜕𝜌𝐸 𝜕𝑡

+

𝜕 𝜕𝑥

(𝜌𝐸𝑣)

=

0

(13) (14)

𝜌0

(𝜕𝜕𝑣𝑡1

+

𝑣0

𝜕𝜕𝑣𝑥1)

=

𝜕𝑝1 𝜕𝑥

(16)

𝜕𝜌1 𝜕𝑡

+

𝜌0

𝜕𝑣1 𝜕𝑥

+

𝑣0

𝜕𝜌1 𝜕𝑥

=

0

𝑝1 𝜌1

=

−

𝐾𝐸 𝜌0

(17) (18)

Equation (18) is purposely assumed to make the phase

velocity becomes the speed of light c.

Let us assume that the fluctuations vibrate according to

equation (19),

𝑣1 = 𝑣̃1𝑒𝑥𝑝𝑖(𝑘𝑥 − 𝜔𝑡) 𝑝1 = 𝑝̃1𝑒𝑥𝑝𝑖(𝑘𝑥 − 𝜔𝑡 + ∅1) (19) 𝜌1 = 𝜌̃1𝑒𝑥𝑝𝑖(𝑘𝑥 − 𝜔𝑡 + ∅2)

where, 𝜔 = 2𝜋𝑓 (f: frequency) is the angular frequency,

𝑘

=

2𝜋 𝜆

(:

wavelength)

is

the

wave

number,

and



is

the

phase. Inserting equation (19) into equations (16) to (18),

we obtain,

−𝑖𝜔𝜌0𝑣1 + 𝑖𝑘𝜌0𝑣0𝑣1 = 𝑖𝑘𝑝1 −𝑝1𝑖𝜔=𝜌−1 +𝐾𝐸𝑖𝑘𝜌𝜌10𝜌0𝑣1 + 𝑖𝑘𝑣0𝜌1 = 0
Thereafter, arranging these equations into matrix,

𝑖𝜔𝜌0 − 𝑖𝑘𝜌0𝑣0 𝑖𝑘𝜌0
0 (

𝑖𝑘 0
1

0

−𝑖𝜔 + 𝑖𝑘𝑣0

−

𝐾𝐸 𝜌0

)

𝑣1
(𝑝1) 𝜌1

=

0 (0)
0

At the condition that the system of linear equations has non-zero solutions set of v1, p1, and , it will propagate as a gravitational wave. This condition is derived from the determinant of coefficients set 0; this shows the dispersion relation of the gravitational wave as,

𝜔 𝑘

=

𝑣0

±

√𝐾𝜌𝐸0

=

𝑣0

±

𝑐

Where, v0 is the drift velocity of the ether. Let us set v0 = 0, thus, the phase velocity of gravitational wave is the speed of light c; this is because we purposely assume equation (18) for adiabatic processes.

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Not only transverse waves (electromagnetic waves) but also longitudinal waves (acoustic waves) have the phase velocity of the speed of light c. The LIGO can observe the acoustic waves in the ether rather than the curvature of spacetime.
13. Refutation of the big bang There are many arguments against the big bang. Van
Flandern52 presented a list of problems with the Big Bang. Selleri53 refuted the big bang model noting that “The
model is built on the four dimensional space of general relativity, in turn based on the Minkowski space of special relativity which is entirely dependent on the Lorentz transformation of time.” We refuted relativity, Minkowski’s spacetime and Lorentz transformation.
In the next sections using experimental results of supernova and quasar, we refute the big bang.
13.1 Hubble’s discovery Hubble initially accepted a finite expanding universe, but
later on, he turned to an infinite stationary universe and a new principle of nature to explain the redshifts.
Perlmutter53 noted that “In Edwin Hubble’s discovery of the cosmic expansion in the 1920s, he used entire galaxies as standard candles.” However, Hubble, contrary to the statements of many modern authors, did not accept the expanding universe theory. Expansion is a theoretical idea of the de Sitter model. Hubble’s observations are not necessarily proof of an expanding universe. Hubble remained cautiously against the big bang.

Redshift and width

Ia supernovae (magnitude 20 to 25) in linear scale, which shows w=1+z. The universe has not expanded in the last 1.3 billion years.
13.3 Tired light by Zwicky We propose Zwicky’s tired light mechanism to explain the redshift. In 1929, Zwicky58, 59 explained the redshift of spectral lines through interstellar space using the “tired light” model, which is a class of hypothetical redshift mechanisms proposed as an explanation for the redshiftdistance relationship. Zwicky58 proposed that a gravitational “drag” acts on light—that is, a light quantum loses its energy in the gravitational fields of nebulae, causing its frequency to decrease. Zwicky58 noted that “It should be expected, therefore, that a quantum h passing a mass M will not only be deflected but not it will also transfer momentum and energy to the M and to mass make it recoil.”
1
0.1
0.01 14 15 16 17 18 19 20 mB(peak)

13.2 An alternative interpretation of the accelerating universe: refutation of dark energy
In this section, we refute expanding universe. Let us look back redshift and light curve width relations. In the expanding universe, it is considered that redshift z and light curve width w are proportional. This is explained that space expansion stretches both wavelength and distances of photons en route. Distances between photons are stretched, that is, the light curve widths w increase. However, wavelengths are not stretched but are velocity redshifted.
Let us show magnitude redshift and light curve width relations of type Ia supernovae using the experimental data by Perlmutter54 et al. and Goldhaber55 et al. In this figure, as Hubble did, we consider the magnitude to correspond to the distance from the earth. (Hubble56, p. 169, FIG. 14) Figure 2357 shows that at magnitudes of approximately 14~20 the light curve widths do not show the effects of time dilation. These data do not appear to show the accelerating universe. The upper figure shows low-z only, where widths decrease with increasing magnitude (mB). The lower figure shows all supernovae, and in this case light curve width slowing appears. Figure 24 shows magnitude-redshift and light curve width relation of type
14

Redshift and width

10

w

1

z

0.1

0.01 14

16 18 20 22 24 Magnitude mB (peak)

Fig. 23 Magnitude-redshift and light curve width relation of type Ia e using the experimental data by Perlmutter54 et al. and Goldhaber55 et al.

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Redshift z and width w Redshift z

2.5
2
1.5
1
0.5
0 20 21 22 23 24 25 mB (peak)
Fig. 24 Magnitude-redshift and light curve width relation of type Ia supernovae (magnitude 20 to 25) using the experimental data by Perlmutter53 et al. and Goldhaber54 et al.
13.4 Refutation of the expanding universe Hawkins60 reported on “over 800 quasars monitored on
timescales from 50 days to 28 years to construct Fourier power spectra for high and low redshift samples,” and concluded that “quasar light curves do not show the effects of time dilation.” He noted that “there is however surprisingly little direct evidence that the Universe is expanding.” He also noted that “the large body of observations of quasar host galaxies seems to rule out the possibility that quasars are nearby and that as a result time dilation would be negligible.”
Magnitude-redshift and light curve width relation of type Ia supernovae (magnitude 14 to 20) do not show that the Universe is expanding. At magnitude 20 to 25, the Universe looks expanding. From experimental date of time dilation in quasar light curves, the Universe is not expanding. That is, at 𝑧 > 1, the Universe is not expanding.
Figure 25 shows a magnitude-redshift relation of type Ia supernovae using the experimental data by Hicken61 et al. which shows the fluctuation of supernovae. There was a sparse period of supernovae density at approximately z = 0.08 to 0.2, mB = 19 to 21. Figures 23 shows that at low z (< 0.1), the light curve width w is constant. At high z (> 0.1), the light curve width w is proportional to 1+z. The sparse period of supernovae appears to be a point where the inclination of light curve width changes in Fig. 23.

1

0.1

0.01 14 16 18 20 22 24 26 28 Magnitude mB
Fig. 25 Magnitude-redshift relation of type Ia supernovae using the experimental data (tables 1 and 2) by Hicken61 et al. The fluctuation of supernovae appears.
13.5 Refutation of the big bang As shown in section 13.2, at mB = 14~20 (𝑧 < 0.1) there is no expansion. At mB = 20~25 (0.2 < 𝑧 < 0.9), there is expansion. In section 13.3, experimental results showed that at 𝑧 > 1, the Universe is not expanding. Therefore, we conclude that the big bang is refuted.

14. Alternative theory and experimental proposal

14.1 An alternative theory of relativity Physics, especially cosmology should be free from relativity. An alternative theory of relativity is the ether theory that was discussed at least in the early 20th century. Dirac62 described in 1951 that “Physical knowledge has been advanced very much since 1905, notably by the arrival of quantum mechanics, and the situation has again changed. If one reexamines the question in the light of present-day knowledge, one finds that the aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an aether.” Fiennes63 summarized the ether and the history of the ether.
The property of ether is the permittivity 0, and the
permeability 0. It is time to study the ether.

14. 2 Proposal of experiments in the International Space

Station

Equation (13) shows the Coulomb's law.

𝐹

=

𝑞1𝑞2 4𝜋𝜀𝑜𝑟2

.

(20)

The CODATA value in 2019 of the permittivity64 of free space is ε0 = 8.8541878128(13) × 10−12 F⋅m−1 (farads per meter).

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I will try to propose an experiment aboard the ISS: the measurement of the permittivity and permeability of free space in 9% small gravity with weightlessness condition.
15. Summary Table 1 summarizes refuted terms in the theory of
relativity. Table 2 shows unexplained phenomena by the theory of relativity.

Table 1 Refuted terms in the theory of relativity

Refuted terms

References

1 The principle of relativity Phipps1, Sato2

2 The constancy of

Gift25, Sato28

the speed of light

3 Lorentz transformation

Gift17

4 Relative simultaneity

Gift17

5 Support from

Hertz29, Phipps14

Maxwell equations

6 Support from

Lévy-Leblond34

quantum mechanics

Table 2 Unexplained phenomena by the theory of

relativity

Unexplained phenomena References

1 GPS clocks variation

Sato28

2 Aberration

Van Flandern32, Sato27

16. Conclusion The ether theories were revisited. The ether theory covers
relativity theory; one of exception is aberration. We showed that aberration cannot be explained by relativity theory, however, the ether theory can. Both the special and general relativity theories were refuted from the viewpoints of physics and mathematics. Physics should be free from relativity and back to the ether theory. It is time to reexamine the property of ether; the permittivity and permeability of free space should be examined.

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