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1
The Commonality between Light and Electric Current
Frederick David Tombe,
Northern Ireland, United Kingdom,
sirius184@hotmail.com
1st October 2022
Abstract. In the year 1855, German physicists Wilhelm Eduard Weber and Rudolf
Hermann Arndt Kohlrausch performed an experiment involving the discharge of a
Leyden jar and they established the ratio between electrostatic and electrodynamic
units of charge. This ratio, which became known as Weber’s constant, was measured
numerically to be c√2, where c was very close to the speed of light. Since this experiment
had nothing to do with optics, the question then arises as to whether they had perhaps
actually measured the speed of electric current, which just happens to be close to the
speed of light for the reason that the speed of light is in turn determined by the speed of
electric current within the context of the medium for the propagation of light.
We must establish the physical commonality between light and electric current.
The Speed of Light
I. In the year1855, German physicists Wilhelm Eduard Weber and Rudolf
Hermann Arndt Kohlrausch performed what was perhaps the most historically
significant of all experiments in the fields of optics and electromagnetism, [1],
[2], [3], because it connected the optically measured speed of light to purely
electric and magnetic effects that ostensibly had no connection to optics. The
theory behind the experiment centred on the force law,
F = kq1q2/r2[1 − ṙ2/Cw2 + 2rr/Cw2] (1)
which Weber had already proposed a number of years earlier in the year
1846. This force law contained a constant, Cw, known as Weber’s constant, and
the purpose behind the experiment was to establish a numerical value for Cw.
The experiment involved transferring a quantity of electricity from a
charged Leyden jar over to a 13-inch ball that was coated with tin foil, and then
discharging the remainder through a conducting channel. The electrostatic force
generated by the charged ball was measured using a torsion balance while the
magnetic force induced by the current, due to the discharge of the Leyden jar,
was measured by the deflection of the compass needle in a galvanometer. The
idea behind the experiment was that since the electrostatic force was measured
using electrostatic units of charge, while the magnetic force was measured using
electrodynamic units of charge, then the numerical ratio between the two forces
would yield the value of Cw.
2
The only term of major interest in equation (1) is the middle term on the
right-hand-side. This term, ṙ2/Cw2, is the convective term, where ṙ = Vw. It’s a
magnetic force which is a kind of centrifugal force, [4], because it opposes an
electrostatic force of attraction. Weber considered Vw to be the mutual speed
between two charged particles, q1, and q2, distance r apart, and he saw Cw as a
reducing speed such that when Vw = Cw, then the electrostatic force would be
completely cancelled.
Because the experiment begins with two unknowns, Vw, and Cw, it follows
therefore that there will be a corollary to the discovery of the numerical value of
Cw. This corollary was never noticed though, perhaps due to the conviction that
electric current consisted in the equal and opposite flow of charged particles.
But while that may well be the case, especially when a current is flowing
through an electrolyte, equation (1) above tells us that when the electrostatic
and magnetic forces are equal, then Vw must be equal to Cw, and so something
must be travelling in the discharge wire at speed Cw. Had Weber and
Kohlrausch used electromagnetic units of charge for the magnetic force, instead
of electrodynamics units, they would have concluded that the reducing speed
was in fact very close to the speed of light. Instead, they thought that the
reducing speed was significantly greater than the speed of light.
In 1857, German physicist Gustav Robert Kirchhoff, while studying the
motion of electricity in conducting wires, identified, in German miles, what
appeared to be the speed of light, c, in the relationship Cw = c√2. This is
recorded in a paper which Kirchhoff wrote that year entitled, “On the Motion of
Electricity in Wires”, [5], where he derived a periodic equation in linear charge
density, from which he based his suggestion that electric signals propagate
along a wire in a wave-like manner, at a speed that is close to the speed of light.
Wave Mechanics or Hydrodynamics?
II. While we all know that the electric particles that are involved in an electric
current travel at nowhere remotely near to the speed of light, the implication of
the Weber-Kohlrausch experiment is nevertheless that something much more
subtle must be the fundamental basis of electric current, and that even if
changes in electric current propagate in a wave-like form along a conducting
wire at the speed of light, that this is only because they are carried by the
movement of a fluid which is itself flowing at that same speed. It is therefore
unlikely that electric signals in a conducting wire involve an actual wave. As to
what exactly this flowing fluid is, we should look to the electrostatic field that
surrounds charged particles and consider that the inflowing or outflowing
aethereal electric fluid, that is the physical basis of this field, is the prime
candidate.
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The Electric Fluid
III. Consider the radial electrostatic field lines that surround a charged particle.
It is proposed that this field, ES, has an associated momentum field, A, which
involves a fundamental electric fluid flowing into or out of the particle,
according to whether the particle is negative or positive. This electric fluid
undercurrent is the primary essence of electric current. It is the aether and the
stuff of all matter, [6]. It is further proposed that space is densely packed with
rotating electron-positron dipoles with circumferential speeds which determine
the speed of light, [7], [8]. When these dipoles are induced to angularly accelerate
(or precess), electric current overflows to the immediate neighbour, at this same
speed, causing the neighbour to angularly accelerate too. Electric current in a
conducting wire, flows at roughly this same speed, for the simple reason that
this speed is governed by the flow of aether from positive particles to negative
particles. This is an average speed which determines the order of the speed
associated with both electric current and of wireless electromagnetic waves.
Positively charged particles are pushed along in the flow while negatively
charged particles eat their way in the opposite direction, but due to ohmic
resistance, they are never accelerated to anywhere near the speed of the more
fundamental aethereal undercurrent.
Displacement Current
IV. It is proposed that electric current is hemmed into conducting channels by
the all-pervading sea of rotating electron-positron dipoles, which is equivalent
to a sea of dipolar aether vortices, [9]. The phenomenon of displacement current
occurs when electric fluid leaks from a conductor into this all-pervading
dielectric sea during the transient state, prior to the leak being halted by a back-
EMF. The back-EMF can be electrostatic in nature, such as in connection with a
charging capacitor or in connection with dielectric polarization. The elasticity
involved in this kind of back-EMF is similar in nature to that which is observed
in a mechanical spring. It causes a recoil, and it is associated with the dielectric
nature of the electron-positron sea.
The back-EMF can also be magnetization-based due to the electric field
that is caused by time-varying electromagnetic induction, and the elasticity
involved in this kind of back-EMF is more akin to that observed in the inertial
behaviour of a flywheel. It resists, but it doesn’t induce a recoil. Rather, it
induces a forward kick when the applied EMF is removed, and so it is involved
in the propagation of waves through the sea of tiny vortices.
4
Wireless Electromagnetic Radiation
V. The general picture of the electromagnetic wave propagation mechanism
seems to have already been known by the 1930s. This quote, in relation to the
speed of light, appeared in the 1937 Encyclopaedia Britannica, in the article
entitled, “Ether (in physics)”, [10],
“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”
This picture is fully compatible with the sea of aethereal vortices which
Scottish physicist James Clerk Maxwell proposed in Part I of his 1861 paper,
“On Physical Lines of Force”, [11], in order to account for magnetic force. He
then extended the application to electromagnetic induction in Part II of the same
paper.
In Part III, Maxwell, using Weber’s constant, set out to link the elasticity of
such a sea of aethereal vortices to the speed of light. Maxwell converted the
electrodynamic units of charge inherent in Weber’s constant into
electromagnetic units and he was able to link this to the dielectric constant,
which he had in turn purported to link to the transverse elasticity at equation
(108), although it is uncertain as from where Maxwell obtained the 6 to 5 ratio
of transverse to cubic elasticity. In order to definitively link the elasticity to the
speed of light, Maxwell should have invoked the circumferential speed of his
vortices, but he didn’t.
Such an analysis has however been done in the article entitled, “Radiation
Pressure and E = mc2”, [12]. In this article, the elasticity constant is connected
to the circumferential speed in a rotating electron-positron dipole, and instead of
using Weber’s constant, the speed of light is introduced into the analysis
through the phenomenon of electron-positron pair production and annihilation.
Although Maxwell never explicitly invoked the circumferential speed of his
vortices in the elasticity of the luminiferous medium, he did however transfer
this elasticity into a magnetization-based displacement current in his 1865
paper, “A Dynamical Theory of the Electromagnetic Field”, [13], and this
enabled him to derive a wave equation in the magnetic field. Maxwell first
conceived of displacement current in the preamble of Part III in his 1861 paper,
in connection with dielectric polarization and the electrostatic force, but in order
to obtain a wave equation, a forward propagation mechanism is needed, and
Maxwell found that he had to switch to a magnetization-based version of
5
displacement current, [13], in order to derive a wave equation. But because he
never highlighted this switch, the physical interpretation of magnetization-based
displacement current is never investigated, since the textbooks always associate
displacement current with capacitance or dielectric polarization. This has had
the effect of throwing researchers off the trail when it comes to trying to
establish the physical meaning of the displacement current in wireless
phenomena such as starlight in space.
Meanwhile, in his 1873 Treatise, [14], Maxwell derived the electromagnetic
wave equation again, this time for the magnetic vector potential, A, which he
called the electromagnetic momentum. If we treat this momentum as the
circumferential momentum density of the tiny aethereal vortices, then, since
∇×A = B, and EK = −∂A/∂t in the case of time-varying electromagnetic
induction, it follows that the wave equation in A corresponds exactly to the
picture described above in the 1937 Encyclopaedia Britannica. If A is a
momentum density, then B must be a vorticity density, while EK must be the
circumferential force that drives the wave propagation mechanism within each
vortex. The significance of involving time-varying electromagnetic induction in
the derivation, through the associated magnetization-based displacement
current, is, that unlike in the case of conduction current, which is a pure flow,
wireless electromagnetic waves involve a relay of electric current between
adjacent vortices, in a wave-like manner, by analogy with the transfer of energy
between the two windings of an AC transformer.
Heaviside and the Telegrapher’s Equations
VI. In the 1880s, Oliver Heaviside used capacitance and self-inductance while
deriving his telegrapher’s equations in the context of a single electric circuit, but
there is a question mark hanging over the validity of the derivation. It’s not at
all clear how the capacitive EMF can be equated with the EMF of self-
induction, as is required in Heaviside’s derivation. It appears that liberties have
been taken in the derivation of the telegrapher’s equations, both then and since,
but that these liberties have been camouflaged by the fact that the electric
current in the wire is already flowing at near to the speed of light anyway. This
error can nevertheless be corrected by replacing capacitance and self-inductance
with mutual inductance. This would however change the applicable physical
context from that of uninterrupted electric current in a single circuit, to that of a
relay of electric currents between separate neighbouring closed circuits. The
resulting wave equations would then become Maxwell’s wireless
electromagnetic wave equations for space, providing that space is densely
packed with miniature electric circuits. And this is essentially what Maxwell’s
sea of molecular vortices amounted to, [11].
6
Conclusion
VII. The speed of electric current is what determines the speed of light, because
light itself is a relay of electric current, propagating as fine-grained vortex
circulations through a dense all-pervading sea of tiny rotating dipoles. The 1855
Weber-Kohlrausch experiment was actually measuring the speed of the electric
current in the conducting channel of the discharging Leyden jar, so the question
then remains as to what determines the speed of electric current.
It is proposed that the radial electrostatic field that surrounds a charged
particle has an associated momentum field in connection with the fundamental
aethereal medium with which all matter is comprised. Electric current will
therefore consist in a flow of aether from positive source particles to negative
sink particles, and the average speed will be in the order of the speed of light. In
the case of light itself, the tiny aethereal vortices that fill all of space will
constitute rotating electron-positron dipoles, while electromagnetic radiation
consists in the overflow of aether between the positron of one dipole and the
electron of the immediately neighbouring dipole which occurs when the first
dipole is induced to angularly accelerate. The overflow in turn causes the
second dipole to angularly accelerate and the cycle repeats through the sea of
dipolar vortices in a wave-like manner.
Electromagnetic radiation is Faraday’s law of electromagnetic induction
operating in miniature. The vortices that fill all of space are like tiny electric
circuits. It can be shown that the elasticity constant in the EM wave equation
derives from the circulation speed in a vortex, [10], [12].
References
[1] Weber, W., and Kohlrausch, R., “Elektrodynamische Maassbestimmungen insbesondere
Zurueckfuehrung der Stroemintensitaetsmessungen auf mechanisches Maass”, Treatises
of the Royal Saxon Scientific Society, Volume 5, Leipzig, S. Hirzel, (1856)
See chapters 5, 6, and 7 in this link,
https://www.ifi.unicamp.br/~assis/Weber-in-English-Vol-3.pdf
Prof. A.K.T Assis has written an excellent summary of this work in an article entitled “On
the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and
Rudolf Kohlrausch”.
https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf
Weber and Kohlrausch wrote a short precis of their paper, and this can be found in
Poggendorf’s Annalen, vol. XCIX, pp. 10-25. An English translation of this precis is
presented in the appendix at the end of Prof. Assis’s paper.
[2] Kirchner, F., “American Journal of Physics”, vol. 25, pp. 623-629, (1957)
http://dx.doi.org/10.1119/1.1934570
7
[3] Tombe, F.D., “The 1855 Weber-Kohlrausch Experiment”, (2019)
https://www.researchgate.net/publication/332411168_The_1855_Weber-
Kohlrausch_Experiment_The_Speed_of_Light
[4] Assis, A.K.T., “Centrifugal Electrical Force”, Communications in Theoretical Physics,
18, pages 475-478, (1992)
http://www.ifi.unicamp.br/~assis/Commun-Theor-Phys-V18-p475-478(1992).pdf
[5] Kirchhoff, G.R., “On the Motion of Electricity in Wires”, Philosophical Magazine, vol.
XIII, Fourth Series, pp. 393-412, (1857)
English translation by Professor A.K.T. Assis, vol. 3, chapter 8
https://www.ifi.unicamp.br/~assis/Weber-in-English-Vol-3.pdf
See page 212 for Kirchhoff’s periodic equations in linear charge density and electric current.
Page 213 is where he suggests an analogy between the electric charge equation and the
equation for the propagation of longitudinal waves and see page 214 regarding the connection
between Weber’s constant and the speed of light.
Meanwhile, a summary by Professor A.K.T. Assis can be found on pp. 280-282 in this link,
https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf
[6] O’Neill, John J., “PRODIGAL GENIUS, Biography of Nikola Tesla”, Long Island, New
York, 15th July 1944, Fourth Part, paragraph 23, quoting Tesla from his 1907 paper “Man’s
Greatest Achievement” which was published in 1930 in the Milwaukee Sentinel,
“Long ago he (mankind) recognized that all perceptible matter comes from a primary
substance, of a tenuity beyond conception, filling all space, the Ākāśa 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.”
http://www.rastko.rs/istorija/tesla/oniell-tesla.html
http://www.ascension-research.org/tesla.html
[7] Tombe, F.D., “The Double Helix and the Electron-Positron Aether”, (2017)
https://www.researchgate.net/publication/319914395_The_Double_Helix_and_the_Electron-
Positron_Aether
[8] Tombe, F.D., “The Double Helix Theory of the Magnetic Field”, (2006)
Galilean Electrodynamics, vol. 24, Number 2, p.34, (March/April 2013)
http://gsjournal.net/Science-Journals/Research%20Papers-
Mathematical%20Physics/Download/6371
[9] 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.”
8
[10] Lodge, Sir Oliver, “Ether (in physics)”, Encyclopaedia Britannica, Fourteenth Edition,
vol. 8, pp. 751-755, (1937)
http://gsjournal.net/Science-
Journals/Historical%20PapersMechanics%20/%20Electrodynamics/Download/4105
See pp. 6-7 in the pdf file in the link above, beginning at the paragraph that starts with,
Possible Structure. −, and note that while the quote suggests that the ether is incompressible,
this is almost certainly not the case. The quote in question, in relation to the speed of light,
reads,
“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”
[11] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, vol. XXI,
Fourth Series, London, (1861)
http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf
[12] Tombe, F.D., “Radiation Pressure and E = mc2”, (2018)
Sections I and II
https://www.researchgate.net/publication/325859308_Radiation_Pressure_and_E_mc
[13] Maxwell, J.C., “A Dynamical Theory of the Electromagnetic Field”, Philos. Trans.
Roy. Soc. London 155, pp 459-512, (1865)
Abstract: Proceedings of the Royal Society of London 13, pp. 531-536 (1864)
The derivation of the electromagnetic wave equation in the magnetic field begins on page
497. Note how the electrostatic component of the displacement current is eliminated after
equation (68), hence leaving the elastic displacement mechanism in the wave as an effect that
is connected exclusively with time-varying electromagnetic induction. Maxwell originally
conceived the idea of displacement current in connection with dielectric polarization, and
hence with electrostatics, but in this derivation, it is no longer applicable to polarization, but
instead applies to magnetization. This swap has never been highlighted, and as such,
Maxwell’s displacement current transferred into the early twentieth century literation as a
concept related to capacitors and transmission lines, but in order to derive the electromagnetic
wave equations, we need to use the inductive form that is compatible with Faraday’s law.
VIII. A dynamical theory of the electromagnetic field (royalsocietypublishing.org)
[14] Maxwell, J.C., “A Treatise on Electricity and Magnetism”, vol. II, Chapter XX, ‘Plane
Waves’, section 790, equation (19), pp. 389-390, (1873)
https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Part_IV/Chapter_
XX
4th February 2024 amendment