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Einstein’s Big Mistake

Frederick David Tombe,

Belfast, Northern Ireland,

United Kingdom,

sirius184@hotmail.com

7th October 2020

Introduction

I. Einstein overlooked the fact that the speed of light, as it occurs in the

Lorentz transformation equations, is determined by the density and

elasticity of a physical medium which pervades all of space, and which

acts as the medium for the propagation of light waves [1]. This fact had

already been established by Scottish physicist James Clerk Maxwell,

(1831-1879), who happened to die in the same year that Einstein was

born. The physical medium in question was known to Maxwell as

the luminiferous medium although Einstein later referred to it as a

Lichtäthers (luminiferous aether). Maxwell provided us with a reasonably

clear picture of what the physical structure of this medium would need to

be. He proposed that all of space is filled with a sea of molecular vortices

comprised of tiny aethereal whirlpools, each surrounded by electric

particles [2]. This was an idea, which according to Tesla in 1907 [3], had in

essence, long been known to men of old.

Long ago he (mankind) recognized that all perceptible matter comes from

a primary substance, of a tenuity beyond conception and filling all space

- the Akasha or luminiferous ether - which is acted upon by the life-giving

Prana or creative force, calling into existence, in never ending cycles, all

things and phenomena. The primary substance, thrown into infinitesimal

whirls of prodigious velocity, becomes gross matter; the force subsiding,

the motion ceases and matter disappears, reverting to the primary

substance. Nikola Tesla, 1907

It was certainly known to John Bernoulli the Younger in the eighteenth

century [4].

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The Special Theory of Relativity

II. Einstein's Special Theory of Relativity first appeared in German in a

paper entitled "Zur Elektrodynamik bewegter Körper" which was

received for publication in Bern, Switzerland, on 30th June 1905 [5]. The

Lorentz transformation equations appeared in this paper, although they

had already been broadly established by Hendrik Lorentz and Sir Joseph

Larmor in the previous decade [6], [7], in conjunction with a luminiferous

medium! See Appendix A. Einstein was inspired by the symmetry

inherent in electromagnetic theory which is observed in the case where an

electric current is induced in a conducting coil when a bar magnet is

moved into it. The result is exactly the same whether the magnet moves

into the coil, or the coil moves over the magnet. In order to rationalize

with this observation, Einstein considered two of Maxwell's equations

which happen to exhibit a perfect duality when expressed in Gaussian

units. This perfect duality comes in conjunction with an overt expression

of the speed of light ‘c’, but it is totally unrelated to the symmetry

mentioned above. The two equations in question,

∇×B = (1/c)∂E/∂t (1)

∇×E= −(1/c)∂B/∂t (2)

are respectively the differential (curl) version of Ampère’s Circuital

Law, with Maxwell's displacement current, and the Maxwell-Faraday

Law of Induction (time-varying case), also a differential (curl) equation.

Einstein found a way to maintain the mathematical form of these two

equations under a Lorentz transformation, although this wasn't able to be

demonstrated correctly until Poincaré published his Palermo paper [8]. See

Appendix B. This paper was received on 23 July 1905 and published in

1906. Henri Poincaré's Palermo paper introduced the concept of four-

vectors, an ingenious mathematical tool which is essential to the analysis,

and which exposes the existence of what we now know as four-

dimensional space-time. The four-vector invention was in some respects

the modification to Sir William Rowan Hamilton's quaternions, that was

needed to make them fully useful in electromagnetic theory. Maxwell

missed out on this tool, although in his 1873 treatise, he did inadvertently

demonstrate the futility of quaternions within the context of

electromagnetism. Hamilton, in 1843, had in effect substituted the

imaginary part of a complex number with a three-vector. It is as if

Poincaré then puts the imaginary part back in again, but this time in place

of the scalar component. The term imaginary is somewhat misleading in

the context. It simply refers to the use of the square root of minus-one as

an algebraic tool. All physical concepts involved are real.

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Einstein’s Folly

III. The symmetry inherent in his 1905 Special Theory of Relativity arises

from Einstein’s belief that no physical medium is required for the

propagation of light waves. He therefore used one absurdity to justify

another absurdity. Firstly, it is absurd to suggest that light, being a wave,

doesn't require a physical medium of propagation. A wave is by

definition, a propagated oscillation in a physical medium. Secondly, it's

the symmetry in Einstein’s special relativity which leads to the absurd

implication that two clocks in relative motion would each be ticking

slower than the other. None of these absurdities would exist if the Lorentz

transformation equations where to be applied in conjunction with the

luminiferous aether, as they were originally intended to apply. The

Lorentz transformation equations are mathematically identical to

Einstein's special theory of relativity, but when applied as originally

intended by Larmor and Lorentz, in conjunction with the luminiferous

medium, the physical implications are no longer absurd. Many of the

experiments which are claimed today as evidence of Einstein's theories of

relativity are in fact merely evidence of aether wind theory, in

conjunction with Maxwell's sea of molecular vortices. The important

difference though, is that the aether provides an absolute physical rest

frame, entrained within the Earth's gravitational field, and this means that

there are no paradoxes associated with time. The time variable in the

Lorentz transformation equations simply refers to the frequency of the

physical processes within the molecular structure of a moving body.

So, when motion through the luminiferous medium causes GPS

satellite clocks in orbit to tick slower than the ground clocks, this is

simply due to a physical interaction between the caesium atoms within

the mechanism of the atomic clocks and the luminiferous medium itself,

and we are in no doubt that it is the satellite clocks, and not the ground

clocks, which will be the ones to tick slower as a consequence of this

motion [9]. In actual fact, the satellite clocks tick faster than the ground

clocks, but this is because of an additional dominant effect related to the

Earth's gravitational field strength. Time dilation, within the context of

aether wind theory, will not however involve a slowing down of actual

time, and it will not involve any clock paradox since there will be no

symmetry. The motion of ponderable matter through Maxwell's sea of

molecular vortices will cause a shear interaction that results in an increase

in the internal aether pressure, which will in turn cause all the atomic and

molecular processes to slow down. This is just Dan Bernoulli’s Principle.

The frequency change in the atomic clocks is not the same thing as the

actual time dilation that is inferred by Einstein's special relativity after he

foolishly overturned centuries of wisdom by casting out the aether. The

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Earth will still complete an orbit of the Sun, relative to the background

stars, in a time period defined as one year, and this standard of time will

apply equally to all observers throughout the universe, no matter how fast

they are moving. Their own individual motion cannot alter the Earth’s

orbital period around the Sun, and so it cannot alter the measurement of

actual time.

Had Einstein performed the exact same mathematical analysis that he

performed in the kinematical part of his 1905 paper, but instead retained

the luminiferous aether, he would have obtained the exact same results,

because the analysis takes place over a return path. But by removing the

luminiferous aether, that being the very physical medium within which

light waves propagate, Einstein opened the door to the absurd idea that

light is always measured to have the same speed, irrespective of the speed

of the receiver.

The Back-Pedalling

IV. In 1920, when Einstein re-introduced the aether during an address at

the University of Leiden, it was only a half-baked aether, more aimed at

explaining gravity than explaining electromagnetic induction. In fact, it

explained neither. Einstein proposed no structural details, and it certainly

wasn't Maxwell's aether. Ten years later in 1930, Paul Dirac proposed

that all space is pervaded by a sea of electrons and positrons. Things were

getting back on track again, but unfortunately the Dirac Sea was never

applied to electromagnetic wave theory, where it should have been

applied [10], [11], [12], [13].

Maxwell and Einstein

V. We often hear it said that Einstein’s special theory of relativity follows

on naturally from Maxwell’s theory. This statement is simply not true. It

could however be argued that the Lorentz transformations do follow from

Maxwell’s equations, but only once we have introduced the concept of an

aether wind. Following the death of Maxwell in 1879, attention soon

swung towards the physical detection of the luminiferous medium by

virtue of the Earth’s motion through space. In 1887, the famous

Michelson-Morley experiment was conducted in an attempt to detect this

motion, and the ensuing null result caused much confusion. While it was

interpreted by some, such as George Stokes, to mean that there is no

aether wind in the immediate vicinity of the Earth [14], others such as

Lorentz were nevertheless convinced that the aether wind was having an

effect on the Michelson interferometer such as to undermine the expected

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fringe shift. In 1889, Oliver Heaviside wrote a paper in which he

introduced the concept of a convection current, which in effect amounted

to an aether wind [15]. It was in connection with an aether wind that the

concept of the Lorentz transformations evolved, and the first equation

resembling these transformation equations, and applying in this context,

appeared as equation (27) in Heaviside’s 1889 paper († see note on

Woldemar Voigt at the end of the reference section). This equation, in

conjunction with the title of Heaviside’s paper [15], suggested that

electromagnetic forces are affected by motion through a dielectric aether.

Later that same year, in part based on Heaviside’s work, his friend

George Francis Fitzgerald proposed the idea that the arm of the

Michelson interferometer contracts along its direction of motion through

the aether, owing to the fact that the constituent atoms are bonded

together by electromagnetic forces [16]. Maxwell had already provided the

nuts and bolts of the luminiferous medium. He saw this aether as a

dielectric sea of tiny vortices, and he explained how it all linked up to the

electromagnetic induction process. It was now just a matter of

extrapolating his theory in order to take into account the effects of an

aether wind. Had Maxwell still been around during the investigation of

the aether wind, it is hardly likely that he would have disregarded the

physical substance of the wind itself, the structure of which he had

devoted so much time and energy into exposing.

Einstein’s special theory of relativity is a counterfeit theory

exhibiting an outward form of the Lorentz transformation equations, but

with all the vital ingredients relating to electromagnetism having been

excised. Far from contributing anything useful to the Lorentz

transformation debate, Einstein actually engaged in one of the greatest

acts of academic vandalism in the history of science, by virtue of

disregarding the physical essence underlying the equations that fronted

his theory. Einstein’s special theory of relativity is a hollow shell of a

theory which merely mimics the more substantial Lorentz aether wind

approach which went immediately before it. The Lorentz transformation

is simply an extension of Maxwell’s theory which takes into account the

asymptotic nature of the elastic interaction between Maxwell’s

luminiferous medium and matter in motion. This asymptotic effect

becomes significant at speeds approaching c. Unlike in the case of the

speed of sound, where the sound barrier can be broken, it seems that no

amount of energy can actually accelerate an object to c, and that as the

speed increases, more and more of the input energy gets absorbed into the

inertial mass and the surrounding magnetic field, rather than going into

further increasing the speed. The symbol c in the Lorentz transformation

equations, although usually close to the speed of light, is actually a

variable which depends on the physical context in question.

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Ironically, although Hendrik Lorentz envisaged the aether wind to be

due to the Earth’s orbital motion around the Sun, the weight of evidence

arising from the GPS system is that the aether is actually entrained within

the Earth’s gravitational and magnetic fields, and that hence no aether

wind blows at the surface of the Earth as a result of the Earth’s orbital

motion. This does not however mean that the Lorentz aether theory is

wrong in principle. Aether winds are involved in atomic clocks as the

GPS satellites orbit around the Earth, but Fitzgerald and Lorentz may not

have been correct in their belief that length contraction solves the

Michelson-Morley problem.

Appendix A

(The Lorentz Transformations)

In 1897, Ulster physicist Sir Joseph Larmor presented equations in a paper which was

published in Philosophical Transactions of the Royal Society [17]. On page 229,

Larmor wrote x1 = xЄ½, where the more familiar gamma factor, γ, appears in the form

Є½. He probably meant to write, x1 = xꞌЄ½, where xꞌ = (x – vt). He also wrote dt1 =

dtꞌЄ−½, where tꞌ = t – vx/c2. These equations approximate to what we know today as

the Lorentz transformations. Then in the year 1900, on page 174 in his article entitled

“Aether and Matter” [7], Larmor transformed x1, y1, z1, and t1 into Є½xꞌ, yꞌ, zꞌ, and

Є−½tꞌ − (v/c2) Є½xꞌ.

Whatever the finer details are, because they are not always very clear, Lorentz

and Larmor were the two pioneers who first worked on the problem throughout the

1890s. They achieved what they believed to be justification for length contraction, but

as regards their twin aim of finding a transformation that would make Maxwell’s

equations invariant, this wasn’t possible until Henri Poincaré invented four-vectors in

1905. In that same year, Einstein re-derived the Lorentz transformations in the form

below, which is unequivocally that which is used in modern textbooks,

xꞌ = γ(x – vt) (1A)

yꞌ = y (2A)

zꞌ = z (3A)

tꞌ = γ(t – vx/c2) (4A)

Appendix B

(The Advent of Four-Vectors)

On page 907 of his 1905 Bern paper [5], Einstein purported to subject Ampère’s

Circuital Law and Faraday’s Law to a Lorentz transformation. He wrote these two

curl equations out in a perfectly dual format, using Gaussian units, which expose the

speed of light, and he expanded them into their three Cartesian components, hence

resulting in six equations in total. The primed versions were then displayed on pages

907-908 as seen below, with the solutions shown within the curved brackets.

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1/c.∂Ex/∂tꞌ = ∂/∂yꞌ[γ(Bz – v/c.Ey)] − ∂/∂zꞌ[γ(By + v/c.Ez)]

1/c.∂/∂tꞌ[γ(Ey – v/c.Bz)] = ∂Bx/∂zꞌ − ∂/∂xꞌ[γ(Bz – v/c.Ey)]

1/c.∂/∂tꞌ[γ(Ez + v/c.By)] = ∂/∂xꞌ[γ(By + v/c.Ez)] − ∂Bx/∂yꞌ

1/c.∂Bx/∂tꞌ = ∂/∂zꞌ[γ(Ey – v/c.Bz)] − ∂/∂yꞌ[γ(Ez + v/c.By)]

1/c.∂/∂tꞌ[γ(By + v/c.Ez)] = ∂/∂xꞌ[γ(Ez + v/c.By)] − ∂Ex/∂zꞌ

1/c.∂/∂tꞌ[γ(Bz – v/c.Ey)] = ∂Ex/∂yꞌ − ∂/∂xꞌ[γ(Ey – v/c.Bz)]

This would not have been possible using the kinematical Lorentz transformations

which he had derived on page 902. He would not have been able to introduce the beta

factor, v/c, so symmetrically.

References

[1] Tombe, F.D., “The 1855 Weber-Kohlrausch Experiment” (2019)

http://gsjournal.net/Science-

Journals/Research%20PapersMechanics%20/%20Electrodynamics/Download/7711

[2] Maxwell, J.C., “On Physical Lines of Force”, Philosophical Magazine, Volume

XXI, Fourth Series, London, (1861)

http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf

[3] O’Neill, John J., “PRODIGAL GENIUS, Biography of Nikola Tesla”, Long

Island, New York, 15th July 1944, quoting Tesla from his 1907 paper “Man’s

Greatest Achievement” which was published in 1930 in the Milwaukee Sentinel.

http://www.rastko.rs/istorija/tesla/oniell-tesla.html

http://www.ascension-research.org/tesla.html

[4] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, Chapter

4, pp. 100-102, (1910)

“All space, according to the younger Bernoulli, is permeated by a fluid aether,

containing an immense number of excessively small whirlpools. The elasticity which

the aether appears to possess, and in virtue of which it is able to transmit vibrations,

is really due to the presence of these whirlpools; for, owing to centrifugal force, each

whirlpool is continually striving to dilate, and so presses against the neighbouring

whirlpools.”

[5] Einstein, Albert, “Zur Elektrodynamik bewegter Körper”, Annalen der Physik

322 (10) pp. 891-921, Bern, (1905)

http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf

https://en.wikisource.org/wiki/Translation:On_the_Electrodynamics_of_Moving_Bod

ies

[6] Lorentz, H.A., “La théorie électromagnétique de Maxwell et son application aux

corps mouvants”, E.J. Brill, Leiden (1892)

8

[7] Larmor, J. “Aether and Matter”, p. 174 (1900)

https://en.wikisource.org/wiki/Aether_and_Matter

[8] Poincaré, Henri, “Sur la dynamique de l'électron”, Rendiconti del Circolo

Matematico di Palermo 21, pp. 129-175 (1-47), received on 23 July 1905, (1906)

[9] Tombe, F.D., “Atomic Clocks and Gravitational Field Strength” (2017)

https://www.researchgate.net/publication/319366888_Atomic_Clocks_and_Gravitatio

nal_Field_Strength

[10] Tombe, F.D., “The Positronium Orbit in the Electron-Positron Sea” (2020)

https://www.researchgate.net/publication/338816847_The_Positronium_Orbit_in_the

_Electron-Positron_Sea

[11] Tombe, F.D., “The Double Helix Theory of the Magnetic Field” (2006)

Galilean Electrodynamics, Volume 24, Number 2, p.34, (March/April 2013)

https://www.researchgate.net/publication/295010637_The_Double_Helix_Theory_of

_the_Magnetic_Field

[12] Tombe, F.D., “The Double Helix and the Electron-Positron Aether” (2017)

https://www.researchgate.net/publication/319914395_The_Double_Helix_and_the_El

ectron-Positron_Aether

[13] Lodge, Sir Oliver, “Ether (in physics)”, Encyclopaedia Britannica,

Fourteenth Edition, Volume 8, pp. 751-755, (1937)

http://gsjournal.net/Science-

Journals/Historical%20PapersMechanics%20/%20Electrodynamics/Download/4105

In relation to the speed of light, “The most probable surmise or guess at present is

that the ether is a perfectly incompressible continuous fluid, in a state of fine-

grained vortex motion, circulating with that same enormous speed. For it has been

partly, though as yet incompletely, shown that such a vortex fluid would transmit

waves of the same general nature as light waves— i.e., periodic disturbances across

the line of propagation—and would transmit them at a rate of the same order of

magnitude as the vortex or circulation speed”

[14] Stokes, George Gabriel, “On the Aberration of Light” Philosophical Magazine

27, pp. 9–15 (1845)

[15] Heaviside, O., “On the Electromagnetic Effects due to the Motion of

Electrification through a Dielectric”, Philosophical Magazine, series 5, 27, pp. 324-

339 (1889)

https://en.wikisource.org/wiki/Motion_of_Electrification_through_a_Dielectric

[16] Fitzgerald, G.F., “The Ether and the Earth’s Atmosphere” Science, Volume

XIII page 390 https://archive.org/details/science131889mich/page/390/mode/2up

https://en.wikisource.org/wiki/The_Ether_and_the_Earth%27s_Atmosphere

9

[17] Larmor, J., “Dynamical Theory of the Electric and Luminiferous Medium”,

Philosophical Transactions of the Royal Society, Part III, p.229 (1897)

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1897.0020

https://en.wikisource.org/wiki/Dynamical_Theory_of_the_Electric_and_Luminiferous

_Medium_III

† In 1887, Woldemar Voigt formulated equations which bore a striking resemblance

to the Lorentz transformations, but these applied in the context of the Doppler effect,

which is a concept that is not entirely unrelated to the distortion of electromagnetic

fields in an aether wind.