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Displacement Current and the Electrotonic State
Frederick David Tombe
Belfast, Northern Ireland, United Kingdom,
sirius184@hotmail.com
11th October 2008
Abstract. When the electromagnetic wave equation is derived in modern
textbooks, Maxwell’s displacement current is used. While investigating the
physical meaning of displacement current, this article will take a closer look at
the magnetic vector potential A, which Maxwell considered to be a momentum
lurking in behind the magnetic field.
Electric Current and Gravity
I. Electric current is simply a flow of the primary substance that fills all
of space. This electric fluid is also known as the aether and electric
current is simply aether momentum. The aether should not be confused
with the medium for the propagation of light, the luminiferous medium,
which is a sea of tiny aether whirlpools [1], [5], [6], [7].
In a laboratory electric circuit, current is a pressurized flow of aether
along conducting channels and we normally use the symbol J. It behaves
according to Bernoulli’s principle. The pressure is the electric charge, and
the flow is the kinetic energy. Gravity is an all pervasive radial electric
current which constitutes a rarefied flow of aether that gives rise to a
tension, and hence to a pull force. Positively charged particles are aether
sources and they will be driven along in an electric current. Negatively
charged particles are aether sinks and they will eat their way in the
opposite direction to that of positive particles. Although particles share
the acceleration of the aether due to pressure and tension, the inviscidity
of the aether means that they will not automatically share the aether’s
flow velocity and they will generally move very much slower.
In the special case of Maxwell’s displacement current, ∂D/∂t or
ε∂E/∂t, which is observed experimentally in the case of an electric current
that is induced in a secondary circuit due to the changing magnetic field
of a primary circuit (Faraday’s Law), there is a problem regarding how to
account for its existence in conjunction with electromagnetic radiation in
deep space far from any electrical apparatus. In Part II of his 1861 paper
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“On Physical Lines of Force”, Maxwell introduced the electromagnetic
momentum A, which accounts for Faraday’s electrotonic state [1]. It will
be proposed that this vector A actually is Maxwell’s displacement
current, because when we derive the electromagnetic wave equation, we
are working on the premises that E will equal −∂A/∂t as per Faraday’s
law. The vector A would then simply be a special case of J for the
circumstances that exist in wireless electromagnetic radiation in deep
space. Those circumstances would of course require the existence of an
actual electric current everywhere in space where electromagnetic
radiation exists, which is more or less what Maxwell proposed in his
1861 paper in the form of his sea of molecular vortices. Maxwell’s
proposal regarding the sea of vortices was however rejected, yet
ironically his displacement current has been retained in modern physics
with its meaning altered so as to render it into a virtual current. This
rejection of Maxwell’s sea of molecular vortices will now be shown to be
in error. From Faraday’s law, it follows that,
∂E/∂t = −∂²A/∂t² (1)
and accepting the vector A to be displacement current as per,
A = ε∂E/∂t (Displacement Current) (2)
it then follows from (1) and (2), that in this context,
A = −ε∂²A/∂t² (3)
This is a simple harmonic motion equation in which ε is the inverse of the
elastic constant.
Displacement current can therefore be justified on grounds of the
existence of some kind of oscillatory disturbance in the aether, with the
electric permittivity ε being related to the elasticity. It further follows that
since,
∇×A = B (Maxwell’s Second Equation) (4)
and since,
∇×B = μA (Ampère’s Circuital Law) (5)
that we are dealing with interlocking solenoidal lines of electric current
and magnetic force at every point in space. This state of affairs could only
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come about if the aether exists and were to be rendered into a state of tiny
vortices.
Modern textbooks always attempt to justify the existence of
Maxwell’s displacement current in connection with capacitors, and worse
still, in connection with conservation of charge. But from the above
considerations we can conclude that capacitors have been a red herring as
regards the understanding of Maxwell’s displacement current if it is
indeed actually a fine-grained vortex flow of aether which can occur in
deep space. In fact, without a sea of tiny aethereal vortices, it is
impossible to justify Maxwell’s displacement current at all. The articles
“Displacement Current” [2], and “Maxwell’s Original Equations” [3],
explain how the modern textbook derivations are heavily flawed.
The Electromagnetic Wave Equation
II. In order to confirm that the magnetic vector potential A is a special
case of current density J more generally, we will treat it as such and
derive the electromagnetic wave equation accordingly. Combining
equations (3), (4), and (5), we obtain,
∇×∇×A = −με∂²A/∂t² (6)
This expands to,
(∇∙A) − ²A = −με∂²A/∂t² (7)
If we take the divergence of A to be zero†, this will reduce to a wave
equation for disturbances in the aether such that the propagation speed
will be exactly equal to the speed of light [4]. This would be the situation
that would occur when we are considering a fine-grained vortex flow
through a sea of tiny aether whirlpools. In such a case, the motion of the
aether would be tangential to the vortices, and hence the divergence of
the aether momentum (or the divergence of the displacement current A)
would always be zero.
†
∇
∙A = 0 is known as the Coulomb gauge
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Conclusion
III. Wireless electromagnetic radiation can exist in deep space far from
any electrical apparatus, and so Maxwell’s displacement current has got
nothing to do with capacitors or linear polarization. The linkage between
displacement current and capacitors in modern physics has been a red
herring of enormous proportions. It’s true though that Maxwell first
introduced displacement current in Part III of his 1861 paper [1] as a
special kind of transient electric current that occurs when an external
electric field is applied across a non-conducting solid, and where the
elasticity of the solid causes the induced current to quickly grind to a halt.
Maxwell however failed to make it explicitly clear that when the
displacement current is used with Ampère’s Circuital Law when deriving
the electromagnetic wave equation, that cause and effect have been
reversed, in that rather than the elasticity impeding the current, the
elasticity is actually causing the current as per Faraday’s Law of
electromagnetic induction. This omission led to the erroneous belief that
a changing electric field causes a magnetic field.
Maxwell’s displacement current is in fact none other than the
magnetic vector potential A itself, which is a circulating aether
momentum giving rise to a magnetic moment. Wireless radiation should
not be confused with the transverse electric waves which propagate in the
space between the two wires of a transmission line. Linear polarization
between the two wires will impede the flow of aether across the gap, and
so as the aether flows sideways between the wires, it will be advancing
parallel to them in order to circumvent the induced impedance. Cable
transmissions do not constitute electromagnetic radiation as is often
wrongly believed.
There are some who reject Maxwell’s displacement current outright
on the grounds that it doesn’t correctly fit with capacitor and transmission
line theory, or that it can’t possibly exist in empty space, and that there is
no experimental evidence for its existence either in deep space or
between the plates of a capacitor. These arguments are all correct as
regards the displacement current associated with wireless electromagnetic
radiation. But then they go further and deny the mathematical argument
that displacement current is necessary for the symmetry of the
electromagnetic equations and the derivation of the electromagnetic wave
equation, while claiming that all of modern electromagnetic theory is
wrong.
Maxwell’s sea of molecular vortices solves all of these problems, but
if this idea is rejected, then the only alternative is indeed to do away with
displacement current altogether. There is however too much experimental
evidence confirming all the other equations of electromagnetism,
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including experimental evidence of displacement current being induced
on the large scale in a secondary electric circuit due to the changing
magnetic field of a primary. The most likely inference is therefore that
Maxwell was correct about the sea of molecular vortices. Nikola Tesla,
John Bernoulli the Younger, and Sir Oliver Lodge, have all independently
supported a similar approach [5], [6], [7].
References
[1] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical
Magazine, Volume XXI, Fourth Series, London, (1861)
http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf
[2] Tombe, F.D., “Displacement Current” (2008)
http://gsjournal.net/Science-Journals/Research%20Papers-
Mechanics%20/%20Electrodynamics/Download/227
[3] Tombe, F.D., “Maxwell’s Original Equations” (2011)
http://gsjournal.net/Science-Journals/Essays-Mechanics%20/%20Electrodynamics/Download/3889
[4] Tombe, F.D., “The Speed of Light” (2014)
http://gsjournal.net/Science-Journals/Research%20Papers-
Mechanics%20/%20Electrodynamics/Download/5373
[5] O’Neill, John J., “PRODIGAL GENIUS, Biography of Nikola Tesla”, Freeport, Long Island, New
York, (15th July 1944)
Quoting Tesla from an unpublished paper entitled “Man’s Greatest Achievement”
“Long ago he (mankind) recognized that all perceptible matter comes from a primary substance, or
tenuity beyond conception, filling all space, the Akasha or luminiferous ether, 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
[6] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, Chapter 4, pages 100-102,
(1910)
“ - - - All space, according to the young [John] 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 - - -”.
[7] Lodge, Sir Oliver J., “Ether (in Physics)”, Encyclopaedia Britannica, Fourteenth Edition, Volume
XIII, Pages 751-755, (1937)
It says in the section entitled, “POSSIBLE STRUCTURE.__ The question arises as to what that velocity
can be due to. 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 order of magnitude as the vortex or
circulation speed - - - -”
http://gsjournal.net/Science-Journals/Historical%20Papers-
%20Mechanics%20/%20Electrodynamics/Download/4105
26th October 2018 Amendment
