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Analogue Of Gravitoelectromagnetism And Consciousness
Sam Henry Larsen
New Hampshire, USA | arche-effect.com
Keywords:
Electrokinetic field
Magnetodielectric field
Electric field
Magnetic field
Gravitation field
Cogravitation field
Quantum effects
Field geometry
Visualization
Ferrofluid nanoparticles
Superparamagnetism
Fluid dynamics
James-Lange theory
Consciousness
Highlights:
• Gravitoelectromagnetism
summary
• Diamagnetism and
permanent magnets
• Ferrofluid nanoparticles
and ferrocell observation
• Introductory fluid
dynamics analogue
• Golden section summary
• James-Lange theory
summary and analogue
ABSTRACT
Dr. Oleg Jefimenko’s theory of gravitoelectromagnetism consists of a set of analogous equations
between electromagnetism and gravity (excluding nonlinear gravitational effects). Jefimenko
stated the expression “magnetic force” is a misnomer since the magnetic field has no causal link
with the force. Likewise, he stated “electromagnetic induction” is also a misnomer. Magnetic
fields do no cause electric fields and electric fields do not cause magnetic fields. The electric and
magnetic fields have the same causative source: a changing electric current.
Jefimenko’s theory of gravitoelectromagnetism is summarized in the first chapter, however, this
chapter will exclude his equations for nonlinear gravitational effects and some of the examples
given for the application of his equations. Observational phenomena is assessed in the second
chapter in accordance with Jefimenko’s model. The James-Lange theory is summarized in the
third chapter, drawing causative comparisons between arousal and emotion to the theory of
gravitoelectromagnetism.
The goal is to create an analogue between the James-Lange theory and gravitoelectromagnetism.
The conclusions of the summarized and compared theories indicate there are seamless analogues
between many branches of science. These analogues are important to point out, since they may
give predictable insight into unknown phenomenon.
ANALOGUE OF GRAVITOELECTROMAGNETISM AND CONSCIOUSNESS
ii
TABLE OF CONTENTS
1. Theory of Gravitoelectromagnetism
1
1.1 The Lorentz Force ·········································································································· 1
1.2 Electromagnetic Induction and Electrokinetic Fields ···················································· 2
1.3 Gravitational Induction and Gravikinetic Fields ···························································· 5
1.4 Generalized Newtonian Theory for Time-Dependent Systems ····································· 5
1.5 Gravitation and Antigravitation ······················································································ 7
1.6 The Five Forces of Gravity ···························································································· 9
1.7 Gravitoelectromagnetic Equations ··············································································· 11
2. Observational Discussion
15
2.1 Diamagnetism ··············································································································· 15
2.2 Permanent Magnets ······································································································ 15
2.3 Ferrofluid and Ferrocell ································································································ 16
2.4 Fluid Dynamics Analogue ···························································································· 17
2.5 The Golden Section ······································································································ 18
3. Psychology Analogue
20
3.1 James-Lange Theory ···································································································· 20
4. Conclusions
22
4.1 The Difference Between Gravity and Electromagnetism ············································· 22
4.2 Unified Theory of Physics and Consciousness ····························································· 22
1
THEORY OF GRAVITOELECTROMAGNETISM
1.1 The Lorentz Force
There are multiple orientations of the hand rule. With the thumb and first two
figures oriented as 3D coordinate axes, the index finger is the direction of the
The Lorentz force, commonly known as the electromagnetic force, is the
magnetic field, the middle finger is the direction of electric current, and the
combining measurement of electric and magnetic force on a point charge due
thumb is the direction of thrust or force [Fig. 1.1-1]. The curl right-hand rule
to electromagnetic fields. This electromagnetic force and its associated hand
is another orientation where the fingers are curled around two axes and the
rules are fundamental in the foundation for understanding electromagnetic
thumb is in the direction of the third axis. As the electric current occurs along
phenomena. A particle of charge q moving with a velocity v in relation to an
a straight wire, the magnetic field occurs in a helix formation 90° to the electric
electric field E and a magnetic field B experiences a force of F=qE+qv×B,
current. Coiled wires will produce an altered state of this phenomenon. When
where the electromagnetic force on a charge q is a combining measurement of
the electric current occurs along a coiled helix wire, the magnetic field is 90°
a force in the direction of the electric field E proportional to the magnitude of
to the coil direction along the axis of the coil [Fig. 1.1-2].
the field and the quantity of charge, and a force at right angles to the magnetic
field B and velocity of charge, proportional to the magnitude of the field, the
charge, and the velocity. Variations of this basic expression describe the
magnetic force on a current-carrying wire (sometimes called the Laplace
force), the electromotive force in a wire loop moving through a magnetic field,
and the force on a moving charged particle. Historians suggest that the law is
implicit in a paper published by James Clerk Maxwell in 1865. Hendrik
Lorentz arrived at a complete derivation in 1895, identifying the contribution
of electric force a few years after Oliver Heaviside correctly identified the
contribution of the magnetic force.
MAGNETIC FIELD
ELECTRIC CURRENT
F=B×I
FORCE
Fig. 1.1-2
It should be noted for later understanding that the magnetic field of a timevarying propagation is actually a magnetodielectric field, whereas the
magnetic field of constant current is a magnetostatic field. It should also be
MAGNETIC FIELD
noted for later understanding that the directional axis of the current is the
electrokinetic field. For an increasing current, the electrokinetic field is
opposite to the inducing current, and for a decreasing current, the
electrokinetic field is in the same direction as the inducing current. For gravity,
ELECTRIC CURRENT
Lenz’s law is opposite to electromagnetism, where for an increasing mass
current, the gravikinetic field is in the same direction as the inducing mass
current, and for a decreasing mass current, the gravikinetic field is opposite to
the inducing mass current.
Fig. 1.1-1
In mathematics and physics, the hand rules are a common mnemonic for
understanding orientation of axes in three-dimensional space. Left-hand and
right-hand rules arise when dealing with coordinate axes. These hand rules can
be used to find the direction of the magnetic field, rotation, spirals,
electromagnetic fields, mirror images, and enantiomers.
THEORY OF GRAVITOELECTROMAGNETISM
1.2 Electromagnetic Induction and Electrokinetic Fields
2
Faraday had discovered two basic effects of electromagnetic induction: the
induction of electric current in a circuit due to a changing current of the
Electromagnetic induction is one of the most important physical phenomenon.
inducing circuit, and the induction of a current in a circuit due to a relative
Its induction is commonly explained as a phenomenon in which a changing
motion of this circuit with respect to a current-carrying circuit or magnet (he
magnetic field produces an electric field (“Faraday induction”) and a changing
also discovered “self-induction” of current in a single circuit). Although
electric field produces a magnetic field (“Maxwell induction”). However,
Faraday was the originator of the concept of the magnetic field (which he
according to Jefimenko’s analysis of Maxwell’s equations, there is no causal
described in terms of the “magnetic curves”), he never suggested that the
relation between electric and magnetic fields.
induced currents were a result of changing magnetic fields. On the contrary, he
clearly associated the phenomenon of electromagnetic induction with
The causal equations given by Jefimenko for electric and magnetic fields in a
changing electric currents, even when the induction was caused by a motion
vacuum are
of a permanent magnet (reference to Ampère in the letter to Phillips).
E=
[ρ]
1 ∂J
1
1 ∂[ρ]
1
+
r dv′ −
dv′
4πϵ0 ∫ { r 2
rc ∂t } u
4πϵ0c2 ∫ r [ ∂t ]
(1.2-1)
[J]
1
1 ∂[J]
+
× rudv′
4π ∫ { r 2
rc ∂t }
(1.2-2)
and
H=
The mathematical formulation of the phenomenon of electromagnetic
induction was due to Maxwell. In Chapter III entitled “On the Induction of
Electric Currents” of Vol. 2 of his famous Treatise on Electricity and
Magnetism he wrote: “It was perhaps for the advantage of science that
Faraday, though thoroughly conscious of the fundamental forms of space,
According to these equations, for time-variation systems electric and magnetic
time, and force, was not a professed mathematician… He was thus left at
fields are always created simultaneously since they have a common causative
leisure to do his proper work, to coordinate his ideas with the facts, and to
source: the changing electric current [last term of Eq. 1.2-1 and the last term
express them in natural, untechnical language. It is mainly with the hope of
in the integral of Eq. 1.2-2]. Once created, the two fields coexist without any
making these ideas the basis of a mathematical method that I have undertaken
effect upon each other. Therefore, electromagnetic induction as a phenomenon
this treatise.” Maxwell then reviewed Faraday’s observations in four sections
in which one of the fields creates the other is an illusion. The illusion of the
entitled “Induction by Variation of the Primary Current,” “Induction by
“mutual creation” arises from the facts that in time-dependent systems, the two
Motion of the Secondary Circuit,” and “Induction by the Relative Motion of a
fields always appear prominently together, while their causative sources
Magnet and the Secondary Circuit.” Next he analyzed Faraday’s concept of
remain in the background. If the two fields are created simultaneously and
the electrotonic state. Finally he formulated his law of electromagnetic
coexist from then on as a dual entity, then the concept of electromagnetic
induction: “The number of lines of force which at any instant pass through the
induction requires a thorough reexamination.
circuit is mathematically equivalent to Faraday’s earlier conception of the
electrotonic state of that circuit… It is only since the definitions of
In 1820, Oersted discovered the fundamental electromagnetic phenomenon,
electromotive force… and its measurement have been made more precise, that
the fact that an electric current was accompanied by a magnetic field
we can enunciate completely the true law of magneto-electric induction in the
encircling that current. In the same year, Ampère discovered that current-
following terms: The total electromotive force acting round a circuit at any
carrying conductors attracted each other if the currents were in the same
instant is measured by the rate of decrease of the number of lines of magnetic
direction, and repelled each other if they were in opposite directions. He
force which pass through it… Instead of speaking of the number of lines of
named these forces between the current-carrying conductors as “electro-
magnetic force, we may speak of the magnetic induction through the circuit,
dynamic” forces. Later he identified these forces as magnetic and suggested
or the surface-integral of magnetic induction extended over any surface
that magnetism was really an electrical phenomenon, where magnetized
bounded by the circuit.” As written by Maxwell, like Faraday, considered the
bodies owed their magnetic effects to circular electric currents within the
electromagnetic induction as a phenomenon in which a current (or
bodies. Also in 1820, Biot and Savart provided a mathematical description of
electromotive force) is induced in a circuit, but not as a phenomenon in which
Oersted’s discovery, and Davy discovered that a current-carrying wire
a changing magnetic field causes an electric field. Maxwell clearly said that
attracted iron filings to itself. These theories inspired Faraday to start his
the induced electromotive force is measured by, not caused by, the changing
popular researches in electricity and magnetism.
magnetic field. Just as Faraday, Maxwell made no allusion to any causal link
between magnetic and electric fields.
Michael Faraday was first mainly interested in finding answers for two
questions: can a current induce a secondary current in neighboring bodies, and
The expression “Maxwell induction” is of a relatively recent origin. The
can magnetism be converted into electricity? By 1831, Faraday had the
expression refers to an alleged phenomenon where a magnetic field is created
answers to both questions. A detailed account of the various and numerous
by a changing electric field. Its theoretical basis is presumed to be in the fourth
experiments that had led Faraday to his discovery and to the study of
Maxwell’s equation, specifically in the last term of this equation: the time-
electromagnetic induction was communicated to the Royal Society and was
variable displacement current density ∂D/∂t. The reality of this phenomenon
published in Philosophical Transactions and later his famous Experimental
has never been demonstrated experimentally. There is one frequently used
Researches in Electricity. The experiments that he conducted in 1831
“theoretical” illustration of Maxwell induction: the computation of the
comprised the first 75 pages of the first volume of Experimental Researches.
magnetic field between the plates of a thin parallel-plate capacitor with
3
THEORY OF GRAVITOELECTROMAGNETISM
circular plates in a circuit, with a slowly varying current. However, this
move parallel to the convection current, rather than toward or away from the
illustration actually demonstrates the utility of the displacement current
charges forming the convection current [the total electric force is given by all
concept and does not really manifest an induction phenomenon. More
three terms of Eq. 1.2-1]. The electric field created by time-variable currents
intriguing, it has been repeatedly shown that the same result can be obtained
is very different from all other fields encountered in electromagnetic
from the Biot-Savart law applied to the conduction current in the lead wires
phenomena. Therefore a special name should be given to it. Taking into
and in the capacitor plates, without using the displacement current at all.
account that the cause of this field is a motion of electric charges (current), it
Attempts have been made by some investigators to observe displacement
may be called the electrokinetic field, and the force which this field exerts on
current experimentally, however, according to the investigators, these attempts
an electric charge the electrokinetic force. The electrokinetic field is
were futile. The concept of the displacement current was introduced in the
designated by the vector Ek. From Eq. 1.2-1 there is
electromagnetic theory by Maxwell. In Chapter I of Vol. 1 of his Treatise,
Ek = −
Maxwell concluded displacement current was not a changing electric field, as
we interpret it today, but a displacement of actual electric charges residing
1 ∂J
1
dv′
4πε0c2 ∫ r [ ∂t ]
(1.2-3)
inside dielectric media. In this respect, it should be noted that in Maxwell’s
The electrokinetic field provides a precise and clear explanation of one of the
times it was believed that all space was occupied by ether, a dielectric medium.
most remarkable properties of electromagnetic induction: the Lenz’s law.
It is therefore completely baseless to associate Maxwell’s name with the idea
Consider a straight carrying conductor parallel to another conductor.
that a changing electric field can cause a magnetic field. Since this idea is
According to Lenz’s law, the current induced in the second conductor is
without any experimental or theoretical support, it must be completely
opposite to the inducing current in the first conductor when the inducing
discarded. Faraday induction, as a phenomena where an electric current is
current is increasing, and is in the same direction as the inducing current when
generated in a conductor by a changing electric current in another (or in the
the inducing current is decreasing. In the past no convincing explanation of
same) conductor, is a true physical effect. “Maxwell induction,” on the other
this effect was known. But the electrokinetic field provides the definitive
hand is an inappropriately named illusion.
explanation of Lenz’s law: by Eq. 1.2-3, the sign (direction) of the
electrokinetic field is opposite to the sign of the time derivative of the inducing
It must be emphasized that there is only one phenomenon that can be called
current. When the derivative is positive, the electrokinetic field is opposite to
electromagnetic induction in systems at rest. Since as we have seen, electric
the inducing current, when the derivative is negative, the electrokinetic field is
and magnetic fields cannot cause one another, the only electromagnetic
in the same direction as the inducing current. Since the induced current is
induction in systems at rest is Faraday induction of an electric current in a
caused by the electrokinetic field, the direction of the electrokinetic field
conductor due to a changing electric current in some other (or the same)
determines the direction of the induced current: opposite direction to the
conductor. As far as the electromagnetic induction in conductors moving with
inducing current when the inducing current increases (positive derivative), and
respect to other conductors (or magnets) is concerned, this induction is
the same direction as the inducing current when the inducing current decreases
reducible to the induction in systems at rest, and, as an alternative can be
(negative derivative). Since the direction of the inducing current varies from
considered in terms of Lorentz’z fields and forces without invoking any
point to point in space, the ultimate direction of the electrokinetic field and of
induction effect at all.
the current that it produces is determined by the combined effect of all the
current elements of the inducing current in the integral of Eq. 1.2-3.
The true nature of electromagnetic induction is quite simple. According to Eq.
1.2-1, a time-variable electric current creates an electric field parallel to that
The electrokinetic field also gives a simple explanation of the fact (first noted
current [last term of Eq. 1.2-1]. This field exerts an electric force on the
by Faraday) that the strongest induced current is produced between parallel
charges in nearby conductors thereby creating induced electric currents in
conductors, whereas no induction takes place between conductors at right
them. Thus, the term “electromagnetic induction” is actually a misnomer,
angles to each other. This phenomenon is now easily understood from the fact
since no magnetic effect is involved in the phenomenon, and since the induced
that the electrokinetic field due to a straight conductor carrying an inducing
current is caused solely by the time-variable electric current and by the electric
current is always parallel to the conductor. If Eq. 1.2-3 is compared with the
field produced by that current. Observe that the electric field produced by a
expression for the retarded magnetic vector potential A* produced by
time-variable current differs in two important respects from the ordinary
a current J,
electric field produced by electric charges at rest: the field is directed along the
current rather than along a radius vector, and it exists only as long as the
current is changing in time. Therefore, the electric force caused by this field is
A∙=
μ0 [J]
dv′
4π ∫ r
(1.2-4)
also different from the ordinary electric (electrostatic) force: it is directed
it is recognized that the electrokinetic field is equal to the negative time
along the current and it lasts only as long as the current is changing. Unlike the
derivative of A* (observe that µ0=1/ɛ0c2):
electrostatic force, which is always an attraction or repulsion between electric
charges, the electric force due to a time-variable current is a dragging force: it
causes electric charges to move parallel (or antiparallel) relative to the
direction of the current. If the time-variable current is a convection current,
then the force that this current exerts on neighboring charges causes them to
Ek = −
∂A ∙
∂t
(1.2-5)
4
THEORY OF GRAVITOELECTROMAGNETISM
It is interesting to note that Eq. 1.2-5 points out a possibility of a new
The calculation of electrokinetic fields, calculations of electrokinetic forces,
definition and interpretation of the magnetic vector potential. By integrating
and calculation of currents and voltages induced by electrokinetic fields, can
Eq. 1.2-5 gives
be presented using examples requiring very simply calculations. The purpose
A ∙ = − Ekdt + const.
∫
is to provide an unambiguous demonstration of the effects and actions of
(1.2-6)
electrokinetic fields, which can be best achieved with uncomplicated
examples. As far as the induced voltages are concerned, the purpose of the
The time integral of Ek will be called the electrokinetic impulse. It is true then
calculations will be merely to demonstrate that conventional result can be
that the magnetic vector potential created by a current at a point in space is
obtained solely by using electrokinetic fields, without invoking any causal
equal to the negative of the electrokinetic impulse produced by this current at
linkage between electric and magnetic fields. For simplicity, the calculations
that point when the current is switched on. Since the electrokinetic impulse is
will be limited to relatively small systems and relatively slow variations of
a measurable quantity, we therefore have an operational definition and a
electric quantities. In such systems, retardation effects are negligible so that
physical interpretation of the magnetic vector potential. It is useful to note,
Eq. 1.2-3 can be written without brackets as
although Eq. 1.2-5 and 1.2-6 correlate the electrokinetic field with the
Ek = −
magnetic vector potential, there is no causal link between the two: the
correlation merely reflects the fact that both the electrokinetic field and the
μ0 1 ∂J
dv′
4π ∫ r ∂t
(1.2-7)
magnetic vector potential are simultaneously caused by the same electric
where 1/c2 is replaced by µ0ɛ0 and have cancelled ɛ0. If the current is confined
current. Important as it is, the electrokinetic field has not been studied or even
to a filament (wire), Eq. 1.2-7 can be given as
recognized as a special force field until Jefimenko’s theory, although the fact
Ek = −
that the time derivative of the retarded vector potential is associated with an
electric field has been known for a long time.
∂I μ0 d l′
∂t 4π ∫ r
(1.2-8)
where I is the current of the filament and dl’ is a length element of the filament
Like any electric field, the electrokinetic field of a moving charge exerts forces
in the direction of the current. Finally, if the retardation is neglected, the
on electric charges located in this field. However, a moving electric current can
electrokinetic field of a current J can be found according to 1.2-5 from
create not only an electrokinetic field, but also an “ordinary” electric field
Ek = −
given by the first integral of Eq. 1.2-1. This is because a current-carrying
conductor moving in the direction of the current or in the direction opposite to
∂A
∂t
(1.2-9)
the current appears to acquire additional electric charges in consequences of
where A is the ordinary (not retarded) magnetic vector potential associated
its motion. This is erroneously considered to be a relativistic effect. Actually,
with J. When an electrokinetic force acts on a charge distribution ρ, it changes
however, this effect is a consequence of retardation and is explainable on the
the mechanical momentum P of the charge distribution in accordance with
basis of Eq. 1.2-1. “Electromagnetic induction” by a moving current, just as
ΔP = Fdt =
ρE dv′dt
∫
∫∫ k
the induction by a stationary current, is a result of the creation of an
(1.2-10)
electrokinetic field (with the creation of an additional “ordinary” electric field)
by this current. However, also in this case the induction has no causal link with
If Ek is a function of time only, the momentum change is
any magnetic field. Its cause is not a changing magnetic field, rather the
ΔP = q Ekdt = − qΔA
∫
electric field (or fields) produced by the moving electric current. As far as it is
presently known, all magnetic fields are created by electric currents.
(1.2-11)
Therefore, a moving magnet may be represented by moving microscopic
where q is the total charge of the distribution, and ΔA is the change in the
electric currents forming elementary magnetic dipoles.
vector potential during the time interval under consideration. If a circular
electrokinetic force acts on a charge distribution restricted to a circular motion,
As discussed early in this chapter, a moving charge generates not only an
the angular momentum of the charge distribution changes. For a charge
electrokinetic field, but also an “ordinary” electric field. The “ordinary” field
distribution and electrokinetic field of circular symmetry, the change in the
generated by a current constituting a moving magnetic dipole is an electric
angular momentum ΔL is
dipole field. The electrokinetic field itself also creates an “ordinary” electric
field. This additional electric field has closed loops analogous to the magnetic
field of a propagation and is called the magnetodielectric field by Eric Dollard.
ΔL =
∫∫
r × Ekdqdt = − r × Adq
∫
(1.2-12)
The expression “force exerted by a moving magnet” is actually a misnomer,
As already mentioned, these are ordinary vector potentials for simplicity. For
since this force has no causal link with the magnetic field of the magnet. The
exact calculations the retarded vector potential must be used in Eqs. 1.2-9,
phenomenon of “induced electric force” or “induced current” by a moving
1.2-10, 1.2-11, and 1.2-12. It should be pointed out that an association between
magnet is simply the effect of the electric field caused by the collective
the momentum change of a charged body and the change of the magnetic
translational motion of microscopic currents participating in the motion of the
vector potential at the location of the body has been noted before, however,
magnet.
up until the present this association was erroneously interpreted as an
electromagnetic effect rather than as a consequence of the fact that both an
5
THEORY OF GRAVITOELECTROMAGNETISM
electrokinetic force and a time-variable magnetic field (and its time-variable
1.4 Generalized Newtonian Theory for Time-Dependent Systems
vector potential) are simultaneously created by a time-variable current. It was
generally not recognized that the actual phenomenon involved the retarded
Dr. Oleg Jefimenko generalized Newton’s theory of universal gravitation to
vector potential rather than the ordinary one. As it is known, a magnetic vector
time-dependent systems. Jefimenko thought there to be no reason to abandon
potential may contain an arbitrary additive function of zero curl (“gauge
Newton’s theory since it had not been completed. Newton’s theory of
calibration”). However, only the vector potential given by Eq. 1.2-4 and by its
gravitation is based on his gravitational law
unretarded version can be used for the calculation of the electrokinetic field.
F/m = − G
An explanatory note is required concerning calculations of forces and torques
M
r2
ru
(1.4-1)
exerted on charge distributions by electrokinetic fields and concerning
calculations of induced currents and voltages. The force experienced by a
where F is the force exerted on the point mass m by the point mass M, G is the
charge distribution is determined by the total electric field given by Eq. 1.2-1,
constant of gravitation, r is the distance between the two masses, and ru is the
not just by the electrokinetic field, Eqs. 1.2-3, 1.2-7, or 1.2-8. Therefore, a
unit vector directed from M to m. This law is limited to time-independent
force calculated from the electrokinetic field alone may not be the true force
systems. To begin this generalization, we will first reconcile Newton’s law of
experienced by the charge distribution under consideration. In contrast, only
gravitation with the law of conservation of momentum. The base of the
the electrokinetic force has an effect on the torque experienced by ringers of
derivations will not be Eq. 1.4-1 directly, but on the two equations that
charge and by similar objects. This is because the torque in such systems is
formulate Newton’s theory as a force-field theory in terms of the gravitational
determined by a closed line integral of the electric field, and only the
field vector g. These equations are
electrokinetic field gives a non-vanishing contribution to such integrals [the
∇×g=0
(1.4-2)
∇ ⋅ g = − 4πGρ
(1.4-3)
first term of Eq. 1.2-1, being a function of r in the direction of r, has zero curl
and therefore cannot contribute to closed line integrals]. Closed line integrals
of electric fields are also involved in the calculations of induced voltages.
and
Therefore induced voltages are also determined by electrokinetic fields alone.
The gravitational field vector g is defined as
1.3 Gravitational Induction and Gravikinetic Fields
g = F/m
Gravitational induction and the gravikinetic field exist analogously to
electromagnetic induction and the electrokinetic field. By replacing the
symbols of the equations in the previous section on electromagnetic induction
and electrokinetic fields with their counterpart symbols provided in the next
where F is the force exerted by the gravitational field on a test mass m, which
is at rest relative to an inertial reference frame (“laboratory”). In Eq. 1.4-3, ρ
is the mass density defined as
section, the calculation of gravitational induction and gravikinetic fields can
ρ = dm /dv
be observed. Basic examples are given as followed, where
Ek = −
1 ∂J
1
dv′
4πε0c2 ∫ r [ ∂t ]
(1.3-1)
1 ∂J
gk = 2
dv′
c ∫ r [ ∂t ]
where dm is a mass element contained in the volume element dv. Let us
consider two mass distributions ρ1 and ρ2 producing gravitational fields
force exerted by ρ1 upon ρ2 is ∫ ρ2g1dv. If applied to the fields g1 and g2 vector
(1.3-2)
identity
is the corresponding gravikinetic expression. These two expressions are
∫
analogous to each other by their calculations, their only differences being the
constants and symbols. The induction and electrokinetic calculations
discussed in the previous section may now be now converted into gravitational
expressions using the corresponding gravitational constants and symbols from
Table 1.7-1 (Section 1.7). It can be now understood that a changing mass
current induces a secondary mass current in the neighboring bodies. The effect
is similar to electromagnetic induction, except that in contrast, the direction of
the induced current is the same as the original current if the original current
increases, and is direction of the induced current is opposite to the original
current if the original current decreases. Hence the sign of the “gravitational
Lenz’s law” is opposite to the electromagnetic Lenz’s law.
(1.4-5)
respectively g1 and g2. The force exerted by ρ2 upon ρ1 is then ∫ ρ1g2dv, and the
is the electrokinetic expression and
G
(1.4-4)
∮
(A ⋅ B)dS −
∮
B(A ⋅ dS) −
∮
A(B ⋅ dS) =
(1.4-V)
[A × ( ∇ × B) + B × ( ∇ × A) − A( ∇ ⋅ B) − B( ∇ ⋅ A)]dv
obtains
∫
ρ1g2dv = − ρ2g1dv
∫
(1.4-6)
Therefore, according to Newton’s theory of gravitation, the forces of action
and reaction are always equal. But, the law of action and reaction cannot
possibly hold for time-dependent gravitational interactions (unless gravitation
propagates instantaneously, which cannot be accepted). As a result, the
derivation of Eq. 1.4-6 shows that at least one of the two basic field laws of
Newton’s theory of gravitation, Eqs. 1.4-2 and 1.4-3, is incompatible with the
6
THEORY OF GRAVITOELECTROMAGNETISM
law of conservation of momentum. There are only three possibilities for
The similarity of Eqs. 1.4-7 and 1.4-3 with Maxwell’s third and first equations
modifying the Newtonian theory so that it does not conflict with the law of
suggests that electromagnetic phenomena should have its gravitational
conservation of momentum: (1) to make ∇×g ≠ 0, (2) to modify ∇⋅g, or (3) to
counterparts. In particular, it appears gravitational waves exist analogously to
modify both ∇×g and ∇⋅g. The theory can be made compatible with the law of
electromagnetic waves. To confirm this analogous wave phenomena, let us
conservation of momentum by making ∇×g ≠ 0. Taking into account that ∇×g
take the curl of Eq. 1.4-7. We have
must reduce to ∇×g = 0 for time-independent systems, it will be assumed that
∂K
∇×g=−
∂t
(1.4-7)
∇×K=−
repeat the derivation used for obtaining Eq. 1.4-6 and use Eq. 1-4.7 instead of
4πG
∂K1
∂K2
1
1
g ×
dv = − ρ2g1dv +
g ×
dv (1.4-8)
∫
4πG ∫ 2
∂t
4πG ∫ 1
∂t
J+
c2
Eq. 1-4.2, the derivation yields
∫
(1.4-12)
This equation can be transformed into a wave equation by assuming that
where K is some function of space and time (later to be discussed). If we
ρ1g2dv −
∂
∇×K
∂t
∇×∇×g=−
1 ∂g
c2 ∂t
(1.4-13)
where J is some function of space and time (later to be discussed). We then
obtain
2
∇×∇×g+
where K1 is associated with the field g1, and K2 with the field g2. The two
integrals containing the time derivatives can be interpreted as the rates of
1 ∂g
c ∂t 2
2
=
4πG ∂J
c2 ∂t
(1.4-14)
change of the field momentum, and Eq. 1.4-8 can be interpreted as the
which is an equation for a g wave propagating in space with velocity c. As can
statement of the conservation of momentum for gravitational interactions.
be seen from Eqs. 1.4-13 and 1.4-7, the field vector K satisfies a similar
According to this interpretation, the gravitational field is a repository of
equation
momentum given by
2
1
G=
K × gdv
4πG ∫
∇×∇×K+
(1.4-9)
1 ∂K
c2 ∂t 2
=−
4πG
c2
∇×J
(1.4-15)
which is an equation for a K wave propagating in space with velocity c.
and the field can exchange momentum with the bodies located in it (although
there is not yet enough information to determine whether the sign in front of
The significance of function J must be assessed. If we determine the
the integral of Eq. 1.4-9 should be + or −, it will be presently be seen that Eq.
divergence of Eq. 1.4-13, taking into account that the divergence of a curl is
1.4-9 is correct as written). Therefore, if we amend Newton’s theory by
zero, we obtain
accepting Eq. 1-4.7 as a basic law, the theory becomes fully compatible with
0=−
the law of conservation of momentum.
The function K that was previously introduced constitutes a vector field. As
4πG
c2
∇⋅J+
1 ∂( ∇ ⋅ g)
∂t
(1.4-16)
c2
which, with Eq. 1.4-3, becomes
can be seen by comparing Eq. 1.4-7 with the third Maxwell’s equation, K is
∇⋅J=−
associated with the gravitational field g just like the magnetic field B is
associated with the electric field E. Let us call K the cogravitional field.
∂ρ
∂t
(1.4-17)
By analogue with electromagnetism, it could then be assumed that the
Equation 1.4-17 is a “continuity” equation stating that J is a mass current (and
cogravitational field represents a force field acting on moving masses. If
therefore also an energy current) coming out of a mass accumulation
Newton’s gravitational force, Eq. 1.4-1, obeys the force transformation
whenever this accumulation diminishes with time; that is, Eq. 1.4-17 is a
equations of special relativity, then the existence of the cogravitational field is
statement of the conservation of mass for time-dependent gravitational
demanded by these equations. The force exerted by K on a mass moving with
systems. By analogue with the electric convection current, the mass current
velocity u is then
created by a beam of mass particles of density ρ moving with a velocity v is
F = m(u × K)
J = ρv
(1.4-10)
(1.4-18)
This equation can be considered to be the definition of K [the order of vectors
We are now ready to complete the generalization of Newton’s theory of
in the cross product reflects the fact that the gravitational force given by Eq.
gravitation to time-dependent systems. The solution of Eq. 1.4-14 is
1.4-1 is always attractive]. As it is known from Helmholtz’s theorem of vector
analysis, a vector field requires for its complete specification, a definition of
its divergence and its curl. It will be assumed that
g=−
1 [
4π ∫
∇′( ∇′ ⋅ g) −
r
4πG ∂J
c 2 ∂t ]
dv′
(1.4-19)
Square brackets are used as the retardation symbol to indicate that the
∇⋅K=0
(1.4-11)
quantities between the brackets are to be evaluated for t’ = t − r/c, where t is
the time for which g is evaluated, r is the distance between the field point
7
THEORY OF GRAVITOELECTROMAGNETISM
(point for which g is evaluated) and the source point (volume element dv’), c
brackets denote retarded values. For a point mass moving without acceleration,
is the propagation velocity of gravitation, and ∇’ is the operator del operating
Eq. 1.4-24 can be expressed in terms of the present position vector r0 as
on the source-point coordinates. Substituting ∇⋅g from Eq. 1.4-3, we can write
2
g=−G
Eq. 1.4-19 as
g=G
∫
[
∇′ρ +
1 ∂J
c 2 ∂t ]
r
(1.4-20)
dv′
K=−
[ ∇′ × J]
dv′
r
G
c2 ∫
(1.4-21)
2
r0 [1 − (v /c sin θ ]3/ 2
2
2
r0
(1.4-27)
where θ is the angle between v and r0, and Eq. 1.4-26 can be expressed as
K=
The solution of Eq. 1.4-15 is, similarly,
2
m(1 − v /c )
3
v×g
c2
(1.4-28)
This essentially completes the generalization of Newton’s theory of universal
gravitation to time-dependent systems.
where we have taken into account that, according to Eq. 1.4-11, ∇⋅K = 0.
These two equations can be transformed into equations not containing spatial
derivatives. We then obtain
1.5 Gravitation and Antigravitation
1 ∂[ρ]
G 1 ∂J
g=−G
+
r dv′ + 2
dv′
∫ { r2
rc ∂t } u
c ∫ r [ ∂t ]
[ρ]
(1.4-22)
According to Einstein’s mass-energy relation, any energy has a certain mass.
But mass is the source of gravitation. Therefore any energy, including
and
gravitational energy, should be a source of gravitation. Dr. Oleg Jefimenko
1 ∂[J]
K=− 2
+
× rudv′
rc ∂t }
c ∫ { r2
G
[J]
(1.4-23)
Equations 1.4-22 and 1.4-23 are the fundamental causal equations of the
Newton’s gravitational theory generalized to time-dependent systems.
Although we have derived them with the help of several assumptions and
definitions, they should preferably be considered as postulates, and their
validity should be judged not by the method by which they have been
obtained, but by the agreement (or disagreement) with experimental data and
with other laws and theories of proven validity. It is important to emphasize
that if Eqs. 1.4-22 and 1.4-23 are regarded as postulates, then Eqs. 1.4-2, 1.4-3,
1.4-7, 1.4-11, 1.4-13, 1.4-14, 1.4-15, and 1.4-17 can be derived directly from
them.
outlines gravitational energy as a source of gravitation, examples of nonlinear
gravitational fields, and properties of gravitational fields in free space. His
conclusions state there are both attractive gravitational fields and also
repulsive antigravitational fields. The field outside a uniform spherical mass
distribution depends not only on the magnitude of this distribution but also on
its internal field, so that such a mass distribution cannot be replaced by an
equal point mass at its center, as it can be done in the conventional Newtonian
theory. The most interesting aspect of the effect of the gravitational energy on
gravitational fields is the possibility of the existence of mass distributions
creating antigravitational fields in free space. Naturally, if such mass
distributions are to be stable under gravitational forces alone, the internal
gravitational field of the mass distributions must be attractive anywhere within
the distributions. There can be no spherically symmetric antigravitational field
Equations 1.4-22 and 1.4-23 make it possible to calculate gravitational and
cogravitational fields produced by continuous mass distributions. The can be
transformed, however, into equations for fields of moving point masses. For a
point mass m moving with velocity v and acceleration a, the resulting
equations are
outside a mass distribution if the field within the distribution is everywhere
attractive. Consequently, a spherical antigravitational body must be held
together by some nongravitational forces in addition to the gravitational ones.
There is a widespread belief that the general relativity theory is the definitive
theory of gravitation. However, the generalized Newton’s theory of gravitation
g=−G
m
s3
2
v
1
R 1 − 2 + 2 [r] × (R × [a])
[
c ] c
(1.4-24)
outlined by Dr. Oleg Jefimenko points out a path for an unquestionably viable
new inquiry into the nature and properties of gravitational fields and
interactions. The generalized Newton’s theory is based to a large extent on the
and
idea that the gravitational-cogravitational field is a seat of momentum and
K=−G
m
c2 s3
2
v
1
[r] × (R × [a])
[v] 1 − 2 −
[
c ] c[r]
× [r]
(1.4-25)
energy. One of the consequences of this idea is the assumption that gravitation
is caused not only by a true mass but also by the equivalent mass of the
gravitational field energy. This assumption is contrary to the general relativity
with
theory. Even the existence of gravitational field energy is contrary to the
K=
[r] × g
c[r]
(1.4-26)
where [r] is the retarded position vector of the moving point mass given by
t’= t − [r]/c and directed from the mass to the point of observation; R = [r − rv/c]
is the “projected” present position vector of the point mass (also directed
toward the point of observation); s = [r − r⋅v/c]; and where the square
general relativity theory. It is important to therefore clarify the reasons why
the general relativity theory denies the existence of gravitational field energy
and it is important to examine the validity of theses reasons.
8
THEORY OF GRAVITOELECTROMAGNETISM
The basic gravitational equation of the general relativity theory is the
an accelerated reference frame does not prove the nonexistence of
Einstein’s gravitational field equation
nonlocalizability of gravitational field energy, and hence the equivalence
Rik −
1
8π
Rg = − G 4 Tik
2 ik
c
principle does not forbid its appearance as a source term in Einstein’s
(1.5-1)
gravitational field equation. Therefore, the exclusion of the gravitational
energy as a source of gravitation in the general relativity theory is merely a
The sources of gravitation appear in this equation in the form of energy-
matter of practical necessity (since no tensor has been found for it). Hence,
momentum tensor Tik. This tensor includes all types of mass densities and all
stated by Dr. Oleg Jefimenko, all presently known results of the general
types of energy densities (electric, magnetic, thermal, etc.) except for the
relativity theory based on Einstein’s field equation cannot be considered as
energy density of the gravitational field itself. The determining reason for this
reliable when these results involve gravitational fields whose gravitational-
is quite simple: in spite of many effects, no energy-momentum tensor has been
energy mass is comparable with the true mass of the system. The fact that the
found for the gravitational energy (only a “pseudotensor” has been obtained).
results obtained by Jefimenko are in conflict with the general relativity theory
Various plausibility arguments have therefore been suggested to justify the
does in no way indicate that these results are wrong. The conflict cannot be
absence of the gravitational energy as a source of gravitation in Einstein’s field
resolved by plausibility arguments. Only reliable observational data can truly
equation. Since it would be difficult (if not impossible) to accept the existence
resolve it.
of gravitational field energy without accepting this energy as a source of
gravitation, these arguments are also the arguments against the presence of
The theory of nonlinear gravitational fields by Dr. Oleg Jefimenko indicate:
gravitational energy in the gravitational field.
The two strongest plausibility arguments for excluding gravitational energy as
(1) The gravitational force acting on a body in a gravitational field is
a source of gravitation are:
determined not only by the mass of the field-producing body, but also by the
gravitational field energy of the field-producing body.
(1) Predications of the general relativity theory obtained with the aid of
Einstein’s field equation without gravitational energy as a source of gravitation
(2) Antigravitational bodies can exist in the universe.
have been found to agree with observations.
(3) The mass of the universe, of a galaxy, or of a stellar object can be much
(2) Einstein’s “equivalence principle” forbids gravitational energy to be a
larger than the present astrophysical measurements indicate, since there can
source of gravitation.
exist objects of negative or of zero apparent mass. The latter objects would
constitute “hidden” masses, as they do not produce or experience gravitational
However, a careful examination of these two arguments shows that neither of
effects.
them is truly convince or compelling according to Jefimenko. The first
argument is easily refuted by the fact that all presently verifiable predictions
(4) “Black holes” cannot exist, and “gravitational collapse” is impossible.
of the general relativity theory are in the domain of weak fields, where the
Indeed, according to the general relativity theory, a sphere creates an
effects of the gravitational energy are hardly noticeable, as stated by
“unescapable” gravitational field and becomes a “black hole” after its radius
Jefimenko in his article Gravitation and Antigravitation.
becomes smaller than the “gravitational radius”
The second argument appears to be much stronger than the first. What it means
rg = G
2m
c2
(1.5-2 )
is that since, according to Einstein, a gravitational field is equivalent to a
certain accelerated frame of reference, and since there apparently is no special
But the radius of the central mass of the mass distribution shown in Fig. 1.5-1
energy in the space defined by the accelerated frame of reference, no energy
is smaller than the gravitational radius, yet the field at this radius is zero rather
should be present in the space containing the gravitational field (this is known
than immensely strong, as is required for black holes.
as the “nonlocalizability” of gravitational energy). An analysis of this
argument shows, however, that it is based on an unprovable premiss and that
(5) Since “gravitational collapse” is impossible, and since antigravitational
it can be refuted by reversing it. Let us suppose that a gravitational field is a
mass formations are possible, the normal state of the universe appears to be an
seat of gravitational energy. The equivalence principle demands then that a
alternating expansion and contraction.
certain energy density would appear in the space defined by the equivalent
reference frame. But how will this energy manifest itself? The only presently
(6) Since a “hidden” mass is an object whose overall rest mass is an object
known way in which it could be detected is by its gravitational effects.
whose overall rest mass is zero, such a mass could conceivably move with a
However, since the equivalent reference frame is flat and boundless, the
velocity equal to (or even larger than) the velocity of light.
“equivalent” energy density, as seen in this frame, must be uniform and must
occupy all space. But, as it is well known, a uniformly distributed mass
It should be noted that the generalized Newton’s theory makes it possible to
(energy) occupying all space produces no gravitational effects. Hence the
obtain transformation equations for gravitational and cogravitational fields
“equivalent” energy is not detectable, or, as an observer in the equivalent
which make the linear theory of gravitation compatible with special relativity
reference frame would say, is “absent.” Thus, the absence of space energy in
theory (see O. D. Jefimenko, Electromagnetic Retardation and Theory of
THEORY OF GRAVITOELECTROMAGNETISM
9
Relativity) However, the nonlinear gravitational equations discussed in
First let us consider Eq. 1.6-1. The field represented by the first integral in this
Jefimenko’s article Gravitation and Antigravitation are not compatible with
equation is the ordinary Newton’s gravitational field created by the mass
the special relativity theory. Jefimenko states, although there is a widespread
distribution ρ corrected for finite speed of the propagation of the field (this is
opinion that all correct physical theories and equations must be compatible
indicated by the square brackets—the retardation symbol—in the numerator).
with the special relativity theory, the incompatibility of the nonlinear
The field represented by the second integral in Eq. 1.6-1 is created by a mass
gravitational equations with this theory does not mean they are wrong. In this
whose density varies with time. Like the ordinary Newton’s gravitational field,
connection it may be noted that there are other examples of perfectly viable
these two fields are directed toward the masses which create them. The field
equations which are incompatible with the special relativity theory. Maxwell’s
represented by the last integral in Eq. 1.6-1 is created by a mass current whose
electromagnetic equations in their vector form present the most prominent
magnitude and/or direction varies with time. The direction of this field is
example of such incompatibility. Furthermore, in the real world, the special
parallel to the direction along which the mass current increases. All three fields
relativity theory is itself only approximately correct. This is because this
in Eq. 1.6-1 act on stationary masses as well as on moving masses.
theory is only applicable to inertial systems, but true inertial systems do not
really exist. In the end, the only reliable criterion of the correctness (or
Consider now Eq. 1.6-2. The first integral in this equation represents the
erroneousness) of Jefimenko’s nonlinear is the agreement (or disagreement) of
cogravitational field created by the mass current. The direction of this field is
these equations with the experimental data.
normal to the mass current vector. The second integral in Eq. 1.6-2 represents
2
the field created by a time-variable mass current. The direction of this field is
3
ga
Gm
ρ
4πa
3m
2
normal to the direction along which the mass current increases. Both fields in
Eq. 1.6-2 act on moving masses only.
If the mass under consideration does not move and does not change with time,
ρ
then there is no retardation and no mass current. In this case both integrals in
1
0
Eq. 1.6-2 vanish and only the first integral remains in Eq. 1.6-1. As a
g
result, one simply obtains the integral representing the ordinary Newton’s
gravitational field. Therefore, the ordinary Newton’s gravitational theory is a
1
2
3
4
5
6
7
r /a
special case of the generalized theory, as it should be.
As far as the interactions between two masses is concerned, the meaning of the
five integrals discussed above can be explained with the help of Fig. 1.6-1. The
1
upper part of Fig. 1.6-1 shows the force which the mass m1 experience under
the action of the mass m2 according to the ordinary Newton’s theory. The
lower part of Fig. 1.6-1 shows five forces which the same mass m1 experiences
Fig. 1.5-1 An example of an antigravitational field and of
the corresponding mass distribution. The scale for the field is
twice as large as the scale for the mass density.
under the action of the mass m2 according to the generalized Newton’s theory.
The time for which the positions of the two masses and the force experience
1.6 The Five Forces of Gravity
by m1 are observed is indicated by the letter t. Let us note first of all that,
As was explained by Jefimenko’s generalized Newton’s theory of gravitation
according to the ordinary Newton’s theory, the mass m1 is subjected to one
to time-dependent systems, gravitational interaction between two bodies is
single force directed to the mass m2 at its presented location, that is, to its
described not by one single force, as in the original Newton’s theory, but by an
location at the time t. However, According to the generalized Newton’s theory,
intricate juxtaposition of several different forces. Mathematically, these forces
all forces acting on the mass m1 are associated not with the position of the mass
result from four of Jefimenko’s equations, including Eqs. 1.4-22 and 1.4-23.
m2 at the time of observation, but with the position of m2 at an earlier time
When Eqs. 1.4-22 and 1.4-23 are written as five separate integrals, they
t’ < t. Therefore, the magnitude of the mass m2 and its position and its state of
become
motion at the present time t have no effect at all on the mass m1.
g=−G
and
G 1 ∂J
[ρ]
1 ∂[ρ]
r dv′ − G
r dv′ + 2
dv′
∫ r2 u
∫ rc ∂t u
c ∫ r [ ∂t ]
(1.6-1)
The subscripts identifying the five forces shown in the lower part of Fig. 1.6-1
correspond to the five integrals in the Eqs. 1.6-1 and 1.6-2. The force F1 is
associated simply with the mass m2 and differs from the ordinary Newton’s
1 ∂[J]
K=− 2
× rudv′ − 2
× rudv′
c ∫ r2
c ∫ rc ∂t
G
[J]
G
(1.6-2)
gravitational force only insofar as it is directed not to the mass m2 at its present
position, but to the place where m2 was located at the past time t’. The force F2
Each of these integrals represents a force field. Therefore, according to the
is associated with the variation of the density of the mass m2 with time; the
generalized Newton’s theory, gravitational interactions between two bodies
direction of this force is the same as F1. The force F3 is associated with the
involve at least five different forces. Let us consider the nature of these forces.
time variation of the mass current produced by m2; this force is directed along
the acceleration vector a (or along the velocity vector v2) which the mass m2
THEORY OF GRAVITOELECTROMAGNETISM
had at the time t’. The three forces are produced by the gravitational field g (if
m2 is a point mass moving at a constant velocity, g and the resultant of the three
forces are directed toward the present position of m2. The forces F4 and F5 are
due to the cogravitational field K. The force F4 is associated with the mass
current created by the mass m2 and with the velocity of the mass m1. Its
direction is normal to the velocity vector v2 which the mass m2 had at the time
t’ and normal to the velocity vector v1 which the mass m1 has at the present
time t. The force F5 is associated with the velocity of the mass m1 and with the
variation of the mass current of the mass m2 with time; the direction of this
force is normal to the acceleration vector (or to the velocity vector) that the
mass m2 had at the time t’ and normal to the velocity vector that the mass m1
has at the present time t. Although not shown in Fig. 1.6-1, additional forces
associated with the rotation of m2 and m1 (angular velocities ω2 and ω1) are
generally involved in the interaction between two masses due to the field K.
The forces F2, F3, F4, and F5 are usually much weaker than the force F1
because of the presence of the speed of gravitation c (generally assumed to be
the same as the speed of light) in denominators of the integrals representing
the fields responsible for these four forces. This means that only when the
translational or rotational velocity of m2 or m1 is close to c, the forces F2, F3,
F4, and F5 are significant. Of course, the cumulative effect of these force in
long lasting gravitational systems (such as the Solar system, for example) may
be significant regardless of the velocities of the interacting masses.
t
m2
m1
t
F
a
F4
F3
m1
F1
ω1
t
F5
ω2
F2
t’< t
v2
v1
Fig. 1.6-1
The upper part of this figure shows the force
that mass m1 experiences under the action of the mass m2
according to the ordinary Newton’s theory. The lower part
shows five forces which the same mass m1 experiences under
the action of the mass m2 according to the generalized
Newton’s theory.
t
m2
Fig. 1.6-2 The generalized theory of gravitation provides
a clear explanation of the mechanism of energy exchange
involved in gravitational interactions: the increase of the
kinetic energy of a body m moving under the action of a
gravitational field occurs as a consequence of the influx of
gravitational field energy into the body via the gravitational
Poynting vector.
10
11
THEORY OF GRAVITOELECTROMAGNETISM
1.7 Gravitoelectromagnetic Equations
The gravitoelectromagnetic equations presented by Dr. Oleg Jefimenko are the
analogous equations for both electromagnetic and gravitational theories.
Many new gravitational equations arise that were either unknown or were
ignored in the past.
The electromagnetic equations and gravitational equations can be presented
by two analogous sets of equations, each containing an identical three
categories. These three categories are: (1) basic definition equations, (2) basic
differential equations, and (3) basic causal equations.
The electromagnetic equations are given by:
The gravitational equations are analogously given by:
1. Basic definition of equations for electromagnetic fields
1. Basic definition of equations for gravitational fields
Electric field E
Gravitational field g
E = F/q
(1.7-1)
Magnetic flux density field B
(1.7-2)
Electric charge density ρ
F = m(u × K)
(1.7-12)
ρ = dm /dv
(1.7-13)
J = ρv
(1.7-14)
Mass density ρ
ρ = dq/dv
(1.7-3)
Electric convection current density J
Mass current density J
J = ρv
(1.7-4)
2. Basic differential equations for electromagnetic fields in a vacuum
2. Basic differential equations for gravitational fields
∇ ⋅ E = ρ/ε0
(1.7-5)
∇ ⋅ g = − 4πGρ
(1.7-15)
∇⋅B=0
(1.7-6)
∇⋅K=0
(1.7-16)
∇×E=−
∇ × B = μ0 J +
∂B
∂t
(1.7-7)
1 ∂E
c2 ∂t
(1.7-8)
3. Basic causal equations for electromagnetic fields
∇×g=−
∇×K=−
4πG
c2
∂K
∂t
J+
(1.7-17)
1 ∂g
c2 ∂t
(1.7-18)
3. Basic casual equations for gravitational fields
[ρ]
1 ∂J
1
1 ∂[ρ]
1
+
r dv′ −
dv′
4πϵ0 ∫ { r 2
rc ∂t } u
4πϵ0c2 ∫ r [ ∂t ]
(1.7-9)
μ0
[J]
1 ∂[J]
+
× rudv′
4π ∫ { r 2
rc ∂t }
(1.7-10)
B=
(1.7-11)
Cogravitational field K
F = q(u × B)
E=
g = F/m
g=−G
[ρ]
1 ∂[ρ]
G 1 ∂J
+
r dv′ + 2
dv′
∫ { r2
rc ∂t } u
c ∫ r [ ∂t ]
K=−
c2 ∫ { r 2
G
[J]
+
1 ∂[J]
× rudv′
rc ∂t }
(1.7-19)
(1.7-20)
12
THEORY OF GRAVITOELECTROMAGNETISM
If we compare the electromagnetic equations with the gravitational equations
1. Equations for calculating fields and potentials
listed above, we find that to each electromagnetic equation there corresponds
a gravitational equation. The corresponding equations are identical except for
Basic gravitational laws in integral notation
the symbols and constants occurring in them. The relations between the
∮
corresponding symbols and constants are shown in
∮
(Table. 1.7.1)
∮
Corresponding Electromagnetic and Gravitational
Symbols and Constants
Electrical
g ⋅ dS = − 4πG ρdv
∫
∮
Gravitational
K ⋅ dS = 0
(1.7-22)
∂
K ⋅ dS
∂t ∫
(1.7-23)
1
∂g
4πGJ −
⋅ dS
∂t )
c2 ∫ (
(1.7-24)
g ⋅ dl = −
K ⋅ dl = −
(1.7-21)
Gravitational field of a point mass
q (charge)
-
m (mass)
ρ (volume charge density)
-
ρ (volume mass density)
σ (surface charge density)
-
σ (surface mass density)
λ (line charge density)
-
λ (line mass density)
φ (scalar potential)
-
φ (scalar potential)
A (vector potential)
-
A (vector potential)
J (convection current density)
-
J (mass-current density)
I (electric current)
-
I (mass current)
m (magnetic dipole moment)
-
d (cogravitational moment)
E (electric field)
-
g (gravitational field)
B (magnetic field)
-
K (cogravitational field)
g=−G
m
r2
ru
(1.7-25)
Gravitational field of a mass distribution
g=−G
ρ
r dv′
∫ r2 u
(1.7-26)
Gravitational field in terms of mass inhomogeneities (constant interior mass)
ε0 (permittivity of space)
-
−1/4πG
μ0 (permeability of space)
-
−4πG/c2
−1/4πε0 or −μ0c2/4π
-
G (gravitational constant)
g = − Gρ
dS′
∮ r
(1.7-27)
Gravitational scalar potential (with respect to ∞)
It is clear that all the equations derivable from the basic electromagnetic
φ =−G
ρ
dv′
∫r
(1.7-28)
m
r
(1.7-29)
Gravitational potential of a point mass
equations listed above have their gravitational counterparts, and that
gravitational
equations
can
be
obtained
from
the
corresponding
φ =−G
electromagnetic equations by simply replacing the electromagnetic symbols
and constants by the corresponding gravitational symbols and constants in
Gravitational field in terms of scalar potential
accordance with Table. 1.7-1. Symbols such as force, energy, momentum, etc.,
do not need to be replaced. For electromagnetic equations for fields in a
g = − ∇φ
(1.7-30)
vacuum, replace electromagnetic symbols by the corresponding gravitational
symbols in Table. 1.7-1. In all other cases, the following procedure should be
Gravitational potential in terms of the field
used: (1) If an electromagnetic equation is for fields in the presence of material
media, reduce the equation to fields in a vacuum. (2) If the equations contain
φa =
The following equations are for both electromagnetism and gravitation. These
g ⋅ d l + φc
(1.7-31)
a
field vectors D or H, replace them by E or B, using the relations D = ε0E and
B = μ0H.
∫
c
Poisson’s equations for scalar potential
2
∇ φ = 4πGρ
(1.7-32)
equations will be shown using gravitational symbols, however, the symbols
can be replaced directly by their corresponding electromagnetic symbols in
Gravitational field in terms of vector potential
Table 1.7-1. The equations are arranged in three categories: (1) equations for
calculating fields and potentials, (2) equations for calculating energy and
g = − 4πG∇ × Ag
(1.7-33)
forces, and (3) wave equations.
Cogravitational field of a moving point mass
K=−G
m(v × ru)
c 2r 2
(1.7-34)
13
THEORY OF GRAVITOELECTROMAGNETISM
Cogravitational field of a current distribution
K=−
J × ru
G
c2 ∫
r2
Maxwell’s stress integral for the gravitational field
dv′
F=
(1.7-35)
Cogravitational field in terms of current inhomogeneities (constant mass-
1
1
2
g dS −
g(g ⋅ dS)
8πG ∮
4πG ∮
(1.7-46)
Cogravitational force on a mass current
current density)
K=−
J × dS′
r
c2 ∮
G
F = J × K′dv
∫
(1.7-36)
(1.7-47)
Cogravitational force on a mass-current dipole
Cogravitational vector potential
2
A=−
F=−
J
dv′
c2 ∫ r
G
(1.7-37)
c
(m ⋅ ∇)K′
4πG
(1.7-48)
Cogravitational torque on a mass-current dipole
Cogravitational field in terms of vector potential
2
T=−
K=∇×A
(1.7-38)
c
m × K′
4πG
(1.7-49)
Cogravitational force in terms of vector potential (constant mass-current
Poisson’s equation for cogravitational vector potential
4πG
2
∇ A=
c2
J
density)
Cogravitational field in terms of scalar potential
K=
F=
(1.7-39)
∮
A′ ⋅ JdS
(1.7-50)
Cogravitational force in terms of scalar potential (constant mass-current
density)
4πG
∇φk
c2
(1.7-40)
F=
Cogravitational dipole moment of filamentary mass current I (S’ is righthanded relative to I)
4πG
c2 ∮
φk′J × dS
(1.7-51)
Maxwell’s stress integral for the cogravitational field
m=−
4πG
c
2
2
I S′
(1.7-41)
Cogravitational dipole field
K=
2
c
c
2
K dS −
K(K ⋅ dS)
8πG ∮
4πG ∮
F=
(1.7-52)
Gravitational field energy
m
2πr 3
cosθ ru +
m
4πr 3
sinθ θu
(1.7-42)
U=−
1
2
g dv
8πG ∫
(1.7-53)
Gravitational energy in terms of potential
2. Equations for calculating energy and forces
U=
Gravitational force on a mass distribution
F = ρg′dv
∫
1
φρdv
2∫
(1.7-54)
Energy of a system of point masses
(1.7-43)
U=−
Gravitational force in terms of scalar potential (single mass of constant
density)
mm
G
′ i k + Us
∑ r
2∑
ik
i
k
(1.7-55)
Energy of a mass distribution in an external field
F=−ρ
∮
φ′dS
(1.7-44)
Gravitational force in terms of vector potential (single mass of constant
density)
F = 4πGρ
∮
Ag′ × dS
(1.7-45)
U′ = ρφ′dv
∫
(1.7-56)
Energy of a point mass in an external field
U′ = mφ′
∫
(1.7-57)
THEORY OF GRAVITOELECTROMAGNETISM
Cogravitational field energy
2
U=−
c
2
K dv
8πG ∫
(1.7-58)
Cogravitational energy in terms of vector potential
U=
1
A ⋅ Jdv
2∫
(1.7-59)
Cogravitational energy of a mass current in an external field
U′ = J ⋅ A′dv
∫
(1.7-60)
Gravitational Poynting’s vector
2
c
K×g
4πG
(1.7-61)
1
K × gdv
4πG ∫
(1.7-62)
P=
Gravitational field momentum
G=
Gravitational field angular momentum
L=
1
r × (K × g)dv
4πG ∫
(1.7-63)
3. Wave equations
Direction of field vectors in a plane wave propagating in the z-direction
K=
1
k×g
c
(1.7-64)
Energy density in a gravitational wave
2
Uv = −
1 2
c
2
g =−
K
4πG
4πG
(1.7-65)
Observe that gravitational wave equations are analogous to electromagnetic
wave equations. There is no difference between a gravitational wave and
electromagnetic wave besides the symbols of the equations.
The analogue between electromagnetic and gravitational equations is not
limited to the equations listed above. Any equation representing a solution of
an electromagnetic problem for fields or forces not involving conducting,
dielectric, or magnetic bodies, has its gravitational counterpart. However, if
the propagation velocity of gravitation is not equal to the velocity of light, the
c appearing in the gravitational equations should be the velocity of the
propagation of gravitation rather than the velocity of light.
Until recently it was believed that the analogue between electromagnetic and
gravitational equations did not apply to fast moving systems, because the
electric charge is not affected by velocity, but the mass of a moving body was
thought to vary with velocity. It is now generally accepted that mass does not
depend on velocity.
14
15
OBSERVATIONAL DISCUSSION
2.1 Diamagnetism
(2.2-1a)
(2.2-1b)
(2.2-1c)
Diamagnetism is a weak form of magnetism that is induced by a change in the
orbital torsion of atomic currents due to an applied magnetic field. As stated
by Jefimenko, the magnetic force is a misnomer since the force is electric and
has no causal link with the magnetic field. Therefore, ferromagnetic,
antiferromagnetic, paramagnetic, diamagnetic, superdiamagnetic, and other
forms of magnetism are truly electrical forms. Diamagnetism is found in all
materials; however, because it is so weak it can only be observed in materials
that do not exhibit other forms of magnetism.
Fig. 2.2-1
When an external electrical source such as a permanent magnet is applied to a
diamagnetic material, a negative magnetization is produced and thus the
There is no actual distinction between “magnetism” and “electricity”
susceptibility is negative. This is because diamagnetic materials are composed
considering the magnetic field has no causal link to the forces associated with
of atoms that have no net magnetic moments where all their orbital shells are
magnetism. Magnetic and electric fields cannot cause each other as concluded
filled. This phenomenon of diamagnetic force is due to an atomic level Lorentz
in the first chapter summarizing Jefimenko’s theory. An “electromagnetic”
force, where charges moving in opposite directions repel. As the permanent
propagation is shown in Fig. 2.2-2, where the magnetodielectric field is 90° to
magnet is applied to a diamagnetic material, the diamagnetic material induces
the direction of an electric current. The magnetodielectric field only exists
an opposing electric current, repelling the magnet.
during the change or motion of a magnetic dipole field and with a time-varying
current.
An exception to the weak nature of diamagnetism occurs when materials
become superconducting. Superconductors are ideal diamagnets; when
positioned in an external magnetic field, they repel the field lines from their
interiors (of course this being an electrical repulsion and not magnetic).
Superconducting magnets are the foremost elements of most magnetic
resonance imaging (MRI) systems and are among the most important
applications of diamagnetism. Bismuth displays the strongest diamagnetism in
nature. Material bismuth can be melted down and molded to efficiently capture
any diamagnetic properties. An induced opposing current of any system is an
expansive force. Bismuth is the naturally fastest growing metal in nature.
MAGNETODIELECTRIC FIELD
2.2 Permanent Magnets
TIME-VARYING ELECTRIC CURRENT
Fig. 2.2-2
Permanent magnets are the most common method used to generate electricity
throughout the world. The magnetic field of a stationary permanent magnet is
a magnetostatic field. A moving magnet or changing magnetic field is
accompanied by a magnetodielectric field, the additional electric field created
by the electrokinetic field that has closed loops analogous to the magnetic
field. Therefore, a moving magnetic dipole field is always accompanied by an
analogous secondary electric field. As shown by Eric Dollard, the phenomena
of this magnetodielectric field exists without a charge carrier, always moving
90° across the current direction of a coiled wire. Using a thin piece of glass to
separate two magnets, when a force is applied to the bottom magnet
(Fig. 2.2-1a), the top magnet will rotate as the magnet is moving (Fig. 2.2-1b).
Motion applied to the right creates a counterclockwise spin and motion
applied to the left creates a clockwise spin (this also depends on the dipole
orientation). This is the observation of a circulating magnetic dipole field due
to an “electromagnetic” propagation (Fig. 2.2-1). It is therefore evident fields
are counter-propagating during a time-varying propagation.
Magnets are best understood by their quantum effects. Orbital magnetic fields
are caused by the currents of intermolecular charges in half-filled atomic
shells. These half-filled atomic shells define magnetic atoms of the periodic
table. Although atoms such as chromium are half-filled at the atomic level,
chromium solids align their magnetic fields in an alternating fashion that
cancel out each other. This is the distinction between ferromagnetic and
antiferromagnetic materials.
As stated by Jefimenko, the expression “force exerted by a moving magnet” is
a misnomer, since this fore has no causal link with the magnetic field of the
magnet. The phenomenon of “induced electric force” or “induced current” by
a moving magnet is simply the effect of the electric field caused by the
collective translational motion of microscopic currents participating in the
motion of the magnet. “Magnetic attraction” is also a misnomer, since the
attractive phenomena of a magnet relates to the alignment of microscopic
electric currents. According to the Lorentz force law, two charges moving in
the same direction attract and two charges moving in the opposite direction
16
OBSERVATIONAL DISCUSSION
repel. This is fundamental when understanding the phenomenon of “magnetic
attraction,” however, instead of this force being an electrostatic force with
lines of force ending in matter, this is a magnetodielectric force related to the
closed loop electric field.
There are no dipole ends of a magnet, rather magnetic equipotential regions
separated by a domain wall or Bloch wall. The north and south regions of the
magnetic dipole field are created by the aligned microscopic currents. As
microscopic charges are moving in the same direction of two magnetic
materials they will attract. The materials will repel if the charges are moving
in opposite directions. The compression between charges moving in the same
direction is noticed in neighboring wires of a coil, where the coil windings will
compression as the charge is increased. The term counterspace is defined by
Eric Dollard as the phenomenon of “attraction” or compression between
Fig. 2.3-1
neighboring wires of a coil when the charge is increased (and currents are
aligned). This means a smaller space stores a larger charge, reflecting
electromagnetic waves where decreasing wavelength is increasing frequency.
Similar to the iron filings, the “spiking” of ferrofluid is caused by the dipole
The Casimir effect exists due to the nature of counterspace.
alignment of the material. The attracting “ends” of the dipoles have aligning
microscopic currents whereas the neighboring dipoles repel due to their
Electrets are similar to permanent magnets. These electrets have a permanent
microscopic currents opposing. This creates the “spikes” seen with iron filings
electrostatic field, rather than a permanent magnetostatic field of a magnet.
and in more definition seen with ferrofluid. This could also be interpreted as
Since electrets exhibit an electrostatic force and magnets exhibit a
wave interference, where the alignment of currents is constructive interference
magnetodielectric force, it should be noted the electrostatic force is caused by
and the opposition of currents is destructive interference. When using a
opposing charges (terminal ends of strings) and the magnetodielectric force is
ferrocell, this light geometry is created by a wave interference that is seen
caused by charges moving in the same direction. The nature of counterspace
similarly to the ferrofluid “spike” reaction. A stronger magnetic field displays
applies to both the electrostatic and magnetodielectric forces.
a more frequent and tighter wave interference, whereas a weaker magnetic
field displays a less frequent and wider wave interference. This reflects the
material display of the ferrofluid, where the “spikes” are more frequent and
2.3 Ferrofluid and Ferrocell
tighter with a stronger magnetic field and less frequent and wider with a
weaker magnetic field. It is also interesting to note as ferrofluid droplets are
Ferrofluid is a superparamagnetic nanoparticle fluid used to observe the
quantum effects of a permanent magnet. In accordance with Maxwell-Faraday
equations, accelerating magnets due to the electrical forces of magnetism
creates an temporary time-varying propagation. As the magnetic dipole field
is moving or changing, it is considered a magnetodielectric field. As iron
observed falling downwards towards a magnet, the droplets stretch. The
frontal lobe of the droplet is accelerating faster than the occipital lobe of the
droplet (Fig. 2.3-3). This is due to the magnet’s force pulling harder on the
frontal lobe of the droplet since it is closer to the magnet compared to the
occipital lobe that is farther away from the magnet.
filings are displayed over a permanent magnet they form an electric field
geometry due to the nature of accelerating magnetic fields. It is clearly seen in
Fig. 2.3-1 that the iron filings are ending upon the terminal ends of the magnet,
and not looping analogously with the dipole field of the magnet. As the iron
filings equilibrate their local energy to the external magnetic field (really
aligning electric currents), they clump together forming the illusion of electric
field lines that end upon the terminal ends of the magnet. This is mistakenly
considered “magnetic field lines,” however, there are no magnetic field lines
displayed by the iron filings. The electric field and magnetic field can be
compared in Fig 2.3-2, where the electric field has lines terminating upon the
ends of a conductor and the magnetic field (including the electric field of the
magnetodielectric field) has lines terminating upon themselves as closed loops
surrounding a material.
ELECTROSTATIC FIELD
MAGNETOSTATIC FIELD
Fig. 2.3-2
17
OBSERVATIONAL DISCUSSION
As a magnet is placed against the surface of a thin barrier between itself and
action of electromagnetic radiation.” The photon particle is merely the
the ferrofluid, nanoparticles form a ring surrounding the edge of the dipole end
phenomenon of a longitudinal compression and rarefaction necessitated by
of the magnet. This is identical to iron filings over a large magnet, where the
electric charges and currents. Therefore, there is no moving light particle, only
filings will disperse in a ring formation around the edge of the dipole end of
compressions and rarefactions of an ether perturbation. In accordance with
the magnet. This is due to charge and current existing on the surface
experiments conducted by the Large Hadron Collider (LHC) at CERN, matter
surrounding materials and not in materials. As stated by Charles Proteus
is nothing more than highly concentrated electromagnetic waves (light).
Steinmetz, there is no electric charge or electric current inside the space of a
conductor, rather surrounding the conductor’s surface. The magnet could be
considered a section of a conducting wire, where the dipole axis is in the
direction of the wire. During an equilibration such as iron filings adjusting to
an external magnetic field of a magnet, the iron filings will equilibrate into the
regions where charge and current is induced the most surrounding the magnet.
The light geometry seen upon the ferrocell due to wave interference between
the magnet and ferrofluid will analogously form in the same surrounding
regions of the magnet as the iron filings.
Fig. 2.3-4
It can therefore be concluded that the hypotrochoid geometry observed upon a
ferrocell is the curvature of light due to moving charges and a result of wave
interference. This geometry forms a two-dimensional torus, and from the side
dipole view of a magnet displays a geometry similar to equipotential contours.
This geometry is created purely by an electric phenomenon, having no
magnetic contribution. The geometry could therefore be a visualization of the
boundaries for equipotential domains.
Fig. 2.3-3
2.4 Fluid Dynamics Analogue
The ferrocell is constructed using a pair of optical flat glass planes, ferrofluid,
penetrating oil, and an LED strip. Using thick dark construction paper on the
back of the ferrocell lens will create a clearer image without any visual
pollution. The curvature of light seen through a ferrocell is caused by
microscopic moving charges of the permanent magnet, the light pattern
reflecting the wave interference of the ferrofluid and permanent magnet
(Fig. 2.3-4). The LED light source is highlighting and accommodating this
wave interference, creating the hypotrochoid light geometry upon the ferrocell
lens. This phenomenon is also analogous to the bending of light in a cathode
ray tube by an external magnetic field. Following the Lorentz force, the force
of a permanent magnet will direct the ray upwards or downwards depending
on the orientation of the magnet. It should be noted that in J.J. Thomson’s
announcement on the results of his experiments on cathode rays, he stated the
rays were “corpuscles.” About 1000 corpuscles is considered 1 electron today.
From the views of J.J. Thomson, the coulomb Ψ is the primary unit defining
the ether. Thomson developed the ether atom ideas of Michael Faraday into his
electronic corpuscle. One corpuscle terminates one farad of force, quantified
as one coulomb. With Eric Dollard’s total Planck electrification considered
(Q=Ψ×Φ), Q is the unit of is of the Planck constant unit joule · sec, Ψ is the
unit of the coulomb, and Φ is the unit of the weber. This unit Q can be
accounted for what is conventionally understood as the photon, “the quantum
There are analogues between gravitoelectromagnetism and fluid dynamics,
such as hydrodynamics. Water is a great analogue for describing the ether. It
has been suggested that the vector potential represents some kind of fluid
velocity field. Maxwell was first to suggest that the magnetic vector potential
A behaves like a moving medium that mimics the velocity of a space flow
around a magnetic field line. The Euler force in fluids corresponds with the
Lorentz force in electromagnetism.
Eddies on the surface of water correspond with the behavior of point charges.
They allow energy to be expressed as a disturbance from the water’s flat
equilibrium, but in a more stationary way than transient waves. Just as two
moving charges in opposite directions repel, two surface eddies spinning in the
same direction repel. Two surface eddies spinning in opposite directions
attract, corresponding with two moving charges in the same direction. This can
be seen in Fig 2.4-1, where the opposite spinning eddies have meeting currents
in the same direction. In addition, if counter-rotating vortices meet they
“annihilate”—the angular momentum of one neutralizing that of the other—
and the energy they contained radiates away as waves, closely mimicking the
dynamics of matter and antimatter.
18
OBSERVATIONAL DISCUSSION
This is a Falaco soliton, modon or dipole eddy pairs (Fig. 2.4-2). These paired
vortices seen in Fig 2.4-2 are extraordinarily stable compared to individual
ones. They can persist for minutes at a time rather than the seconds that a
vortex usually lasts. But disrupt the string that joins them, and they’ll dissipate
almost instantly. While two counter-spinning eddies created individually
behave like matter and antimatter, the Falaco soliton lets us see opposite
“charges” interacting in a way that more closely resembles the behavior of
neutrons, or of protons and electrons. Here they balance out and prevent one
another from interacting as strongly with the environment. They create a
“vorticity-neutral” system on the surface, the same way a neutron or a
hydrogen atom is charge-neutral.
2.5 The Golden Section
In Plato’s views on natural science presented in Timaeus, he considered the
golden ratio as the key to the physics of the cosmos and the most biding of all
mathematical relationships. This divided line is visible within the golden
triangle and pentagram (Fig. 2.5-1).
Fig. 2.4-1
1
While canoeing it is likely to create individual eddies on the surface of the
Φ-1
water. As the paddle is pulled back and a small void is created, water ruches in
1
from the sides to fill the void and return the pond to equilibrium, where the
entire surface is at the same height. When a current of this water catches its
Φ
tail, a persistent dimple forms. Before too long, the viscosity of the water saps
away its angular momentum and the vortex dissipates. Imagine we use a plate
rather than a paddle, so that the water rushes in from both sides symmetrically.
Fig. 2.5-1
Done at just the right speed, this process can create a pair of counter-spinning
vortices. Unlike vortices created independently, these ones won’t annihilate
each other due to a special difference: they’re linked and joined by a “string”
of current through the water—the eddies are two ends of a single “topological
defect.”
There is widespread belief that the Fibonacci spiral is the golden spiral. This
also includes an altered version of the spiral that follows a golden ratio
sequence instead of a Fibonacci sequence, but still is constructed as a
Fibonacci spiral. The golden spiral has no direct relation to the Fibonacci
spiral, however, the Fibonacci sequence is of high importance when
constructing the golden spiral. The Fibonacci equation sequence is given by
(Seq. 2.5-1)
phi1 = 0+1⋅phi
phi2 = 1+1⋅phi
phi3 = 1+2⋅phi
phi4 = 2+3⋅phi
phi5 = 3+5⋅phi
where the powers of phi are the product of the double phased Fibonacci
sequence multiplied by the golden ratio. This equation sequence is used
Fig. 2.4-2
to construct the scaling progression of the 108° golden spiral section
(Fig. 2.5 2-3).
19
OBSERVATIONAL DISCUSSION
108º
Φ-1
Φ-4
Φ-2
Φ-5
1
Φ-2
Φ-1
Φ-3
Φ-1
1
1
Φ-1
1
1
1
√5
5
Fig. 2.5-4
Fig. 2.5-2
In relation to the fluid dynamics analogue, the angle of 108° is close to the
molecular bond angle of H-O-H (water). It is also understood that there is a
counter-propagation of wave phenomena which could be related to the golden
section, but more research must be completed.
Φ-1
Φ-4
Φ-3
Φ-5
Φ-2
Fig. 2.5-3
The pentagram is the geometry of the golden ratio and defines the angular
sections of the golden spiral. This golden ratio geometry is the only star
polygon that can solve a square root, specifically the square root of 5. If the
golden isosceles triangle of the pentagram is given a perimeter of √5,
consisting of two legs each of phi-1 and a base of 1, when the perimeter of the
square root of 5 is squared (√52) it extrapolates into the pentagram (Fig. 2.5-4).
The pentagram consists of 5 equal 1 unit lines in this geometric calculation.
Five is predominant in nature, appearing with the five forces of gravity, five
lines or points of the pentagram (golden section star polygon), five fingers of
a hand, and five toes of a foot. We can only see five planets with the naked eye
(Mercury, Venus, Mars, Jupiter, and Saturn). We have five main components
for sensing: eyes, ears, nose, mouth, and skin. The human body has five vital
organs. The pentagram was also known by the Ancient Pythagoreans as good
health (hygē a).
20
PSYCHOLOGY ANALOGUE
3.1 James-Lange Theory
observed due to a physical interaction, its identity is described subjectively
based on the empirical observations. Just like the E and B fields or g and K
The James-Lange theory is a hypothesis on the origin and nature of emotions
fields, subjective emotions have no effect upon charges and currents. As
and is one of the earliest theories of emotion within modern psychology. It was
discussed by Charles Proteus Steinmetz, the medium which surrounds matter
developed independently by two 19th-century scholars, William James and
is the electric charge and electric current, whereas the matter itself is an
Carl Lange. The basic premise of the theory is that physiological arousal
analogous form electricity in which the mass is the “charge” and the
instigates the experience of emotion. Instead of feeling an emotion and
acceleration of the mass is the “current.” Recently it has been observed that
subsequent physiological (bodily) response, the theory proposes that the
masses cannot touch due to the electrical forces between them. However, as
physiological change is primary, and emotion is then experience when the
concluded by Jefimenko, mass exists analogously to electric charge. This
brain reacts to the informations received via the body’s electrical nervous
means that a mass must have a physical interaction analogous to electric
system. It proposes that each specific emotion is attached to a unique and
charge. The reason why touching matter cannot be observed is because the
different pattern of physiological arousal and emotional behavior in reaction
observed matter is simply an emotional expression or concept caused by
due to an exciting stimulus.
physical charges and currents. This ultimately means the person we see in the
mirror is not the true self, rather the identity of a nonphysical emotional
The James-Lange theory was challenged in the 1920s by psychologists such
expression caused by physical charges and currents.
as Walter Cannon and Philip Bard, who developed an alternative theory of
emotion known as Cannon–Bard theory, in which physiological changes
There are two main components in the James-Lange theory (Fig. 3.1-1):
follow emotions. A third theory of emotion is Schachter and Singer's two
arousal and emotion. The arousal is the cause, which corresponds with the
factor theory of emotion. This theory states that cognitions are used to
charge density ρ and current density J. The emotion is the effect, which is the
interpret the meaning of physiological reactions to outside events. This theory
descriptions of matter and corresponds with coexisting nonphysical variables
is different in that emotion is developed from not only cognition, but that
(E, B, g, K). Subjective emotions have no causal link with psychological
combined with a physical reaction. In 2017 Lisa Feldman Barrett reported that
response. Physiological responses of the body are based on physical
the James-Lange theory was created by neither William James nor Carl Lange.
interactions of the electrical nervous system. The induction of electricity (and
It was indeed named by the philosopher John Dewey who would have
gravity) exists analogously to the induction of arousal upon the body.
misrepresented Jame’s ideas on emotion. James never wrote that each
Emotions are embodied as descriptive matter after a physical observation
category of emotion (fear, anger, etc.) has a distinct biological state. He wrote
occurs. Magnetic storage could be analogously compared to the memory of the
that each instance of emotion may have a distinct biological state. Dewey’s
human mind. Recent research has suggested the magnetic storage of
assumed error “represents a 180-degree inversion of Jame’s meaning, as if
information occurs in the human cerebral cortex.
James were claiming the existences of emotion essences, when ironically he
was arguing against them.” Barrett notes that “Dewey’s role in this error is
forgotten.” Lisa Barrett also points out that when testing this theory with
PERCEPTION OF
STIMULUS
PERCEPTION OF
STIMULUS
PERCEPTION OF
STIMULUS
POUNDING HEART
AROUSAL
POUNDING HEART
AROUSAL
POUNDING HEART
AROUSAL
and emotion category. Furthermore, Barrett says that the experience of
emotion is subjective: there is no way to decipher whether a person is feeling
sad, angry, or otherwise without relying on the person’s perception of emotion.
CAUSE
electrical stimulation, there is not a one-to-one response between a behavior
Also, humans do not always exhibit emotions using the same behaviors;
humans may withdraw when angry, or fight out of fear. According to Barrett’s
theory of constructed emotion, a person must make meaning of the physical
response based on context, prior experience, and social cues, before they know
what emotion is attached to the situation. Lisa Barrett and James Gross have
The analogue between consciousness and gravitoelectromagnetism can be
bridged by connecting the key differences between gravitoelectromagnetism
and the components of the James-Lange theory with nondualistic causality.
EFFECT
reviewed a variety of alternative models to the so-called James-Lange theory.
Advaita Vedānta, which means non-duality, strictly follows the principle of
causality. The cause is physical. The effect is illusive.
The charge density ρ and current density J, analogous in both electromagnetic
and gravitational equations, are the processor of the mind. The causative
effects (E and B or g and K) are the emotions of the mind. This effect of
emotion is the nonphysical and subjectivity of imagination. When matter is
Fig. 3.1-1
PSYCHOLOGY ANALOGUE
As an arousal occurs, there is an influx of energy into the body by a causative
source. This influx causes thoughts and opinions directed at the source of the
influx depending on the string geometry of the influx. As a car is approaching
a person they receive an influx of arousal from the moving car, likewise
developing a specific belief and subjective reaction to the oncoming car based
upon the geometry of the influx, the person’s memory, genetics, etc. Arousals
of the James-Lange theory can be considered a mental induction related to the
physical interaction of charges and currents. These arousals stimulate the pure
feeling of ecstasy. The ecstasy is not good nor bad, since it manifests both with
fear and happiness. This is the basic reason why people can enjoy horror
movies or engage in dangerous stunts. If a person is gifted a present the same
type of influx in arousal, however, the overall geometry of the influx is unique
from the oncoming car, hence why the reaction is different. The main key is
that the arousal behind both fear and happiness is the same ecstasy. The
ecstasy of an arousal is a single string, whereas the emotional subjectivity is
based upon a collection of intersecting strings of specific angles and ratios.
Physiological reactions do not depend on emotional opinions or subjectivity
and emotions have no effect upon physical reactions since the emotions occur
after the reaction, sensation, or observation. Focus on emotion can stimulate
physical reactions, however, the focus and its inducing geometry is the driving
factor of this phenomena and not the emotion in focus.
This essentially concludes the analogues relationship between the two main
components of the James-Lange theory and gravitoelectromagnetism. There is
no distinction between physical interactions of physics and physiological
reactions of psychology other than the applications used to describe their
phenomena.
21
CONCLUSIONS
4.1 The Difference Between Gravity and Electromagnetism
22
has its own variables and unique nonlinear gravitational effects. Therefore, the
basic distinction between the two are string count. The electric force is a single
Dr. Oleg Jefimenko has shown gravity and electromagnetism to be analogous
string between charges. The gravitational force is multiple (and intersecting)
in their calculations (excluding nonlinear gravitational effects). Their only
strings between masses. Thus, a body influenced by a gravitational field feels
mathematical difference is the symbols and constants used in the equations, as
a force due to all atomic charges of the body interconnecting with the atomic
shown in the first chapter. Jefimenko has also shown that the magnetic field
charges of the gravitational body. The string geometry of a mass defines the
has no physical meaning, stating that both expressions “electromagnetic
strength of point charges and the distribution of point charges. It is important
induction” and “magnetic force of a magnet” are misnomers considering the
to note that electric currents or field lines cannot cross. The crossing point of
magnetic field has no causal link to the phenomena. The expressions for
strings between masses is a mutual terminal null point (zero charge point), also
“electricity” and “magnetism” are caused by charges and currents. Jefimenko
apparent between attracting magnets when observed using a ferrocell.
strongly supports evidence of “the ether,” as he’s stated “The gravitationalelectromagnetic analogy may be further extended if we allow that the ether
which supports and propagates the gravitational influence can have a
translational motion of its own, thus carrying about and distorting the lines
of force.” Jefimenko suggested the ether was another way to expression the
propagation of gravity. The ether is universal strings that interconnect all
point-like phenomena. The concept of points (whether point particle or point
mass) exist at the end of strings. In natural philosophy, a line is the expansion
of a point and a point cannot exist without a line. Therefore, the strings and
point-like phenomena always exist together as one entity. The charge and
current is the phenomenon of the strings and points. It should be noted
“opposing charges” are really opposite electrical polarities of a string, where
+ and − terminals are each “ending” point of the string. The “end” points of a
string are really always the cross section of strings, since no field line of force
can end in space. These strings and points are expressed in nature as geometry.
Strings account for the phenomenon of volume and points account for the
phenomenon of density, however, density and volume are distinct properties
of a single thing, the ether.
4.2 Unified Theory of Physics and Psychology
With unification given between gravity and electromagnetism, there were also
analogues discussed between the James-Lange theory and physics. The
consciousness is a composite of the two main components of the James-Lange
theory: arousal and emotion. Arousal corresponds with charge density ρ and
current density J. Emotion corresponds with symbols that have no causal link
to charge and current, such as the E and B fields or the g and K fields. It is seen
analogously between electromagnetism and gravity that charges and currents
are physical interactions. This corresponds directly with physiological arousal
of a body. What gives space or definition to this arousal is the resultant effect,
the emotional subjectivity. This creates the phenomenon of imagination which
has no influence upon any physical interaction, entirely nonphysical and
subjective. The concept of causality analogously between components of the
James-Lange theory and gravitoelectromagnetism follow the ideology of
cause and effect in Advaita Vedānta. As shown by Jefimenko, there is
absolutely no such thing as electromagnetic dual or any duality in nature. The
notion of electromagnetic dual is just as illogical as the notion of subjective
emotions manifesting as physical forces. The mechanics of the universe are
constructed by a single simplex physical cause, which has at least one illusive
nonphysical effect. The analogue between physics and psychology paves a
new path towards a unified theory [of everything].
q4
q14
q9
q15
q5
q16
q11
q1
q7
q6
q2
q8
q13
q12
q3
q10
Fig. 4.1-1
Geometry can express the difference between electromagnetism and gravity
precisely (Fig. 4.1-1). The lines of a geometry are the strings of the ether. The
only difference between gravity and electromagnetism is that gravity is a
massive magnitude made up of unaligned dipole domains. This is why gravity
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