The Coriolis Force in Maxwell's Equations (The Compound Centrifugal Force)

Abstract

The Coriolis force is a consequence of Newton's first law of motion and it can be observed in a radial force field as a transverse deflection of the radial component of the motion by an amount required to conserve angular momentum. It is a physical reality most commonly associated with atmospheric cyclones, but it can also be observed deflecting the effect of gravity on a comet or causing a pivoted gyroscope to defy gravity. In a paper which he wrote in 1835 in connection with water wheels, French scientist Gaspard-Gustave Coriolis referred to its mathematical formula 2mv×ω as the "compound centrifugal force". This is an interesting choice of name which suggests that it is the sum of two centrifugal forces, yet without giving any indication as to how this might be. The physical origins of the Coriolis force will now be traced to differential centrifugal pressure in the dense background sea of tiny aethereal vortices which serves as the medium for the propagation of light.

Full text

The Coriolis Force in Maxwell’s Equations
(The Compound Centrifugal Force)
Frederick David Tombe,
Belfast, Northern Ireland, United Kingdom,
sirius184@hotmail.com
7th December 2010
Abstract. The Coriolis force is a consequence of Newton’s first law of motion and it
can be observed in a radial force field as a transverse deflection of the radial
component of the motion by an amount required to conserve angular momentum. It
is a physical reality most commonly associated with atmospheric cyclones, but it can
also be observed deflecting the effect of gravity on a comet or causing a pivoted
gyroscope to defy gravity. In a paper which he wrote in 1835 in connection with
water wheels, French scientist Gaspard-Gustave Coriolis referred to its
mathematical formula 2mv×ω as the “compound centrifugal force”. This is an
interesting choice of name which suggests that it is the sum of two centrifugal forces,
yet without giving any indication as to how this might be. The physical origins of the
Coriolis force will now be traced to differential centrifugal pressure in the dense
background sea of tiny aethereal vortices which serves as the medium for the
propagation of light.
The Magnetic Field
I. James Clerk Maxwell explained the magnetic field in terms of a sea of
tiny aethereal vortices that press against each other with centrifugal force
while striving to dilate. These vortices self align with their mutual rotation
axes tracing out magnetic lines of force. A tension along these lines of force
accounts for magnetic attraction between unlike poles, with centrifugal
repulsion acting sideways from the lines of force causing magnetic repulsion
between like poles. Maxwell went on to explain the sideways force acting on
an electric current that is moving at right angles through a magnetic field.
The explanation is based on the principle that all the vortices within the
immediate vicinity are spinning in the same direction, therefore an electric
current passing through will not experience the same speed relative to the
vortex circulation on one side as it will on the other. The combined effect

will be a compound centrifugal force causing a sideways deflection of the
current. Compound centrifugal force will likewise explain the centripetal
force which causes a charged particle that is moving in a magnetic field to
follow a helical path. This compound centrifugal force appeared in
Maxwell’s original equations in the form μv×H [1].
The Double Helix
II. The quantity μ in μv×H is related to the density of the sea of tiny
aethereal vortices. If we consider these vortices to be dipolar, comprised of a
sink (an electron) and a source (a positron), then the vorticity or magnetic
field strength H is equal to 2ω, where ω is the angular velocity of the
rotating electron-positron dipoles. When this compound centrifugal force
appears in the form 2μv×ω, it becomes identifiable as the familiar Coriolis
force F = 2mv×ω [2].
Fig. 1. Close-up view of a single magnetic line of force. The electrons are shown in
red and the positrons are shown in black. The double helix is rotating about its axis
with a circumferential speed in the order of the speed of light, and the rotation axis
represents the magnetic field vector H. [3]
The Gyroscopic Force
III. The electron-positron sea passes right through the interstitial spaces
within rotating atomic and molecular matter as like water passing through a
basket, and so when studying gyroscopes, we need to examine the situation
at the molecular level and consider the individual molecules themselves to
be miniature gyroscopes. When a gyroscope is spinning, the electron-
positron sea which permeates the space between its molecules will be like an
electric wind circulating inside it. If we extrapolate Ampère's Circuital Law
to the molecular scale, the spinning gyroscope will become comprised of
many tiny gyroscopes all aligned with their mutual rotation axes tracing out
solenoidal rings around its rotation axis. If we then subject the spinning
gyroscope to a forced precession, this will alter the angle of attack of the

electric wind and this will induce the equivalent of the aerodynamic P-factor
on the molecules. For example if the applied torque causes a tilt in the
molecules relative to the wind on an axis joining 3 O’clock to 9 O’clock,
then the wind will act differently at 3 O’clock than it will at 9 O’clock,
hence inducing a torque about the 6 O’clock/12 O’clock axis at right angles
to the applied torque. The induced torque is therefore a compound
centrifugal force (Coriolis force). When a pivoted spinning gyroscope
topples under the force of gravity, the induced Coriolis force will deflect the
gyroscope sideways. This sideways deflection will not be merely a
superimposition on top of the downward motion [4]. Mathematically it will
be, but physically it will have curled the effect of gravity. It will be like as if
the tiny vortices of the electron-positron sea have introduced a vorticity into
the gravitational field. And unless there were such a physical presence as this
all-pervading electron-positron sea, there could be nothing for the toppling
gyroscope to push against in order to stop it from falling freely.
Cyclones and Comets
IV. In a radial force field such as an atmospheric cyclone or a gravitational
field, a Coriolis force arises when an object undergoes both radial and
transverse motion at the same time. Eccentric planetary orbits are a good
example. The Coriolis Force has the effect of changing the speed of the
transverse motion. This means that in the transverse direction, the pressure
coming from the tiny vortices in front of the motion is different from the
pressure coming from the vortices behind the motion. This is therefore a
compound centrifugal force. Such asymmetry does not arise when the
motion is purely transverse, such as in a circular orbit, or when the motion is
purely radial such as in the case of a falling apple. Geometry alone is
responsible for the conservation of angular momentum. The apparent equal
and opposite force to the Coriolis force, that shows up in the polar
coordinate formulation, should not be confused with the fine-grained
centrifugal pressure on that same side of the motion and which forms part of
the physical cause of the Coriolis force itself.
Conclusion
V. It’s a common error to believe that the Coriolis force is merely an illusion

that arises when making observations from a rotating frame of reference. In
fact it’s nothing of the sort. The illusion observed from a rotating frame of
reference is never a Coriolis force. The Coriolis force is a physically real
inertial force sourced in Newton’s first law of motion and measured relative
to a polar origin. It physically manifests itself in radial force fields by virtue
of changing the speed of transverse motion when radial motion is also
occurring. It takes on the mathematical form F = 2mv×ω and it has a
physical explanation which lies in the tiny aethereal vortices that comprise
the medium for the propagation of light, and it also accounts for the
electromagnetic force F = qv×B. It is caused by the centrifugal pressure
within the all-pervading background of electron-positron dipolar vortices
which fills all of space. It acts at right angles to the direction of motion due
to differential centrifugal pressure on either side of the moving object when
an asymmetry is introduced into the field. The term “Compound Centrifugal
Force” originally used for this force back in 1835 by Gaspard-Gustave
Coriolis himself was most appropriate, even though it would seem that he
had no idea about the underlying physical cause that justified his choice of
name.
Unlike in the case of the simple radial centrifugal force, there is no
intuitive way of explaining Coriolis force to the public at large. In its most
commonly associated context, that being atmospheric cyclones, we might
say that as the wind moves into the centre of the cyclone, and where angular
momentum already exists due to the rotation of the Earth, a Coriolis force
causes the wind to be increasingly deflected sideways in order to conserve
angular momentum relative to the centre of the cyclone. More generally we
might say that the Coriolis force is an inertial force that maintains
conservation of angular momentum in a radial force field, or which causes a
centripetal force to act on a charged particle that is moving in a solenoidal
(magnetic) force field.
Ultimately, the Coriolis force is tied up with vortex behaviour at the
most fundamental aethereal level and the effect transmits itself through all
scales of activity.
References
[1] Clerk-Maxwell, J., “On Physical Lines of Force”, Part II, equation (77),
Philosophical Magazine, Volume 21, (1861)
http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf
[2] Coriolis, Gaspard-Gustave, “Sur les équations du mouvement relatif des systèmes de
corps”, J. de L’Ecole Royale Polytechnique, 24th cahier, p142 (1835)

[3] Tombe, F.D., “The Double Helix Theory of the Magnetic Field” (2006)
http://gsjournal.net/Science-Journals/Research%20Papers-Mathematical%20Physics/Download/6371
Galilean Electrodynamics, Volume 24, Number 2, p.34, (March/April 2013)
[4] Tombe. F.D., “Magnetic Repulsion and the Gyroscopic Force” (2015)
https://www.researchgate.net/publication/
283225757_Magnetic_Repulsion_and_the_Gyroscopic_Force
15 th
February 2020 Amendment