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Unravelling the potentials puzzle and corresponding case for the scalar longitudinal electrodynamic wave



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Journal of Physics: Conference Series
Unravelling the potentials puzzle and corresponding case for the scalar
longitudinal electrodynamic wave
To cite this article: Donald Reed 2019 J. Phys.: Conf. Ser. 1251 012043
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Unravelling the potentials puzzle and corresponding case for
the scalar longitudinal electrodynamic wave
Donald Reed
State University of New York
SUNY at Buffalo
12 Capen Hall, Buffalo, New York 14260-1660
Abstract This paper will attempt to demonstrate, through a wide range of recent empirical
evidence and theoretical considerations, the viability of the scalar longitudinal wave (SLW)
concept as presenting a new challenge to the science of classical electrodynamics (CED).
Contributing developments underl ying the existence of this field effect are introduced
underscoring the many principal exhibits of the curl-free (irrotational) vector potential, especially
in regards to the compelling Maxwell-Lodge effect, certifying the long-debated physical
significance of the potentials in CED. This will naturally lead to the novel concept of “gradient-
driven” current, a key feature of the 2016 L.M. Hively US Patent 9,306,527, providing the
missing element in standard CED resulting in a consistent understanding of this discipline. In
accordance with these imperatives, institution of a full gauge-free electrodynamics model will
be postulated implying the complete independence of scalar and magnetic vector potentials.
Through these directives, the SLW is then revealed. Due to the unique characteristic of its
minimal attenuation the SLW is then shown to be a potential harbinger of new technology, and
a forerunner of future possible paradigm revolutions.
1. Introduction
For more than a century and a half Maxwell’s equations have served as a bastion for classical
electrodynamics. These four vectoral wave equations have stood the test of time, not only in regards
their principal utility, representing the scaffolding from which has emerged the vast electromagnetic
technological infrastructure of our current world power grid, but their veracity in correctly and
accurately predicting field effects in uncountable numbers of experimental test protocols. Indeed, our
knowledge of the properties and dynamics of electrodynamic systems is believed to be the most solid
and firmly established in all of classical physics.
By its extension, the application of quantum electrodynamics, describing the interaction of light and
matter at sub-atomic realms, has produced the most successful scientific theory yet produced to date,
agreeing with corresponding empirical findings to astounding levels of precision. With such a longevity
of success, it is no wonder that mainstream physics considers that standard classical electrodynamics is
complete and that it is virtually a closed subject.
However, these facts have understandably, albeit unfortunately, lulled contemporary physics into
the false security of the perceived notion that the theoretical structure of modern classical
electrodynamics is now written in stone and there is no compelling reason, empirical or theoretical, for
considering the possible need for its re-evaluation or alteration. These beliefs have even reached the
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levels of a religious fervor on the part of many contemporary physicists, who are wont to summarily
dismiss any claims to the contrary, to the extent of branding those suggesting possible missing elements
as heretics.
Nevertheless, as we hope to demonstrate through forthcoming argument in this paper, there is a key
missing dimension of electrodynamics that can be attributed to the failure to include what can be termed
the electro-scalar force in its structural edifice. Now, as an offshoot to this process, we also wish to
transcend and dispel the derision this subject has engendered over the years by mainstream physics,
having associated it with cultish groups of researchers/hobbyists who for many years have unfortunately
been unable to present much solid evidence of the dynamics of this field structure in electrodynamics,
instead relying principally on mostly unfounded anecdotal evidence to support these claims.
However, we will present cogent arguments, both from theoretical first-principle considerations as
well as compelling recent empirical findings, examining the embodiments of various patented
technology, which will be shown to warrant a thorough re-evaluation of the current structure of classical
electrodynamics both in regards to model consistency and completeness.
The paper is arranged in the following manner – section 2 covers the historical developments in
connection with the origin of the magnetic vector potential from the fertile mind of Faraday coupled
with the mathematical expertise/ingenuity of Maxwell. The controversy surrounding the role of the
vector potential is discussed, with special attention given to the physical significance of the so-called
curl-free vector potential, apart from as well as including its usual quantum context associated with the
celebrated Aharonov-Bohm effect. Accordingly, the case will be built with the aim of putting to rest the
worldview by physicists which, unlike the electric and magnetic field intensities, assigns a purely
secondary mathematical utility for the magnetic vector potential in classical electrodynamics, and not a
primary physical status. Thus, appreciation of the phenomenological import of the curl-free vector
potential in many experimental protocols in classical physics, will then naturally lead to two
interdependent imperatives: the promotion of the potentials to their full birthright physical status in CED,
and the corresponding novel theoretical prescription of the total (manifest) independence of the
potentials (electric and magnetic), culminating in a completely gauge-free model for CED, which is
given the appellation Extended Electrodynamics (EED). Through the advancement of these directives,
as a natural progression as will be shown in section 3, subsequently will be ascertained the disclosure of
the scalar longitudinal field, and its hitherto unsuspected role in classical electrodynamics. Central to
this view will be an examination of the recent patent granted to physicist Lee M. Hively, demonstrating
how the novel concept of gradient-driven electrical current, as a natural implication of the curl-free
vector potential, not only sets the stage for the scalar longitudinal wave (SLW) dynamics, but provides
the missing element in standard Maxwellian electrodynamics which will establish the basis for a
consistent understanding of this discipline. The unique feature of the lack of attenuation of the SLW, as
not being subject to the “skin effect”, will round off our investigation in section 4, revealing the vast
potential applications of scalar wave dynamics not only in future technological infrastructure, but as
possibly already exhibited in both inanimate and biological systems in nature.
2. The physical significance of the magnetic vector potential
Historically, a great degree of controversy has surrounded the conceptual interpretation of the role the
magnetic vector potential should play in classical electrodynamics [1]. This can be attributed to the
fundamental mathematical relationship between the scalar potential (ϕ) and the vector potential (A), and
the electric (E) and magnetic (B) fields. Any electromagnetic field may be described by giving E, B, or
by giving potentials A, ϕ, from which E and B are derivable, via:
However, only E, B are usually regarded as “real” physical fields, whereas to consider the
introduction of the vector potential as no more than a mathematical convenience, useful as an aid in
solving the Maxwell’s equations for E, B. This interpretation derives from the “operational” definitions
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of E and B, their detectability through forces qE and v x (qB/c) on a test charge q, that is supposed to
lend them reality through the Lorentz-force equation:
with E, B to be evaluated at positions rq(t) of the point particle.
However, this practice of attributing non-physical significance to the magnetic vector potential
couldn’t have been further from the thoughts of the original architects of what eventually became
modern classical electrodynamics. Particularly, from the astute intuitive observations of Faraday, of
electrodymnamic phenomena in the early 19th century, the magnetic vector potential was originally
christened by him as the “electrotonic state”[2]. It was to Maxwell’s great credit to recognize the key
import of these nascent, metaphysically inspired intuitions of Faraday and reframe this electrotonic state
in precise mathematical formalism, the measure of which he renamed the magnetic vector potential [3]
This turned out to be a turning point in the formalistic development of the theory.
Now, before Maxwell, the only extant mathematical representations of electric and magnetic dynamics
was derived from the work of Ampere-Weber, describing forces between current elements which
assumed direct action-at-a-distance, without the aid of a material medium [4]. However, basing the new
model of electrodynamics on causality of interactions, it was due to this alternate structure originally
proposed by Faraday – with the electrotonic state as its centerpiece, that later through Maxwell’s
codification, brought to the fore the first theory of action by local contact - the precursor to the modern
field conception of electrodynamics [5].
The electrotonic state could be best described as the ability for the field medium surrounding a
(primary) electrical conductor, to possess the latent readiness to respond with current flow in a
(secondary) circuit, if the magnetic flux linking the primary conductor changed in time. Thus, the
electrotonic state became an intensity of a level previous to electric and magnetic field properties and
measurable forces, and consequently represented to Faraday and Maxwell, a “store” of potential
dynamism, playing a role on the same physical footing as that of the fields [6].
Yet these potentials, introduced by Maxwell as physical, were summarily unceremoniously
discarded by Heaviside [7] as “non-physical”. He argued, basically from his engineering background in
telegraphy, that they they rendered the equations of propagation, in his words “unmanageable and also
not sufficiently comprehensive”. Heaviside (and Hertz independently) stated that the standard “duplex”
field equations (now known as Maxwell’s equations) and the associated two field vectors (E,B) were
the sole basis of electromagnetism.
However, the original descriptive conception of the magnetic vector potential, and its corresponding
physical significance, has recently been brilliantly articulated in the insightful modern under-appreciated
dissertation by Konopinski [8]. Quite close to the spirit of Faraday’s inspiration, Konopinski’s views the
vector potential as a “store” of field momentum available for exchange with the kinetic momentum of
charged matter or charges in a conductor [9]. Konopinski then proceeds to show that operational
definitions of ϕ, A can now be ascertained from the equation of motion (2) when it is reexpressed in
terms of the field description by the potentials, through substitutions from (1):
This is also the form that follows most directly from the variational principle, and the Lagrangian or
Hamiltonian representations of mechanics, all dealing with energy and momentum exchanges without
regarding an explicit conception of forces. Equation (3) gives changes in “conjugate momentum” p =
Mv + qA/c, that are generated wherever there are gradients in an “interaction energy” q[ϕ vA/c]. To
demonstrate that A can be measured at all points in space Konopinski introduces the engaging gedanken
experiment involving a solenoid outside of which a macroscopic bead of unit charge slides freely on a
circular fiber of insulator material concentric with the cross-section of the solenoid. Since A everywhere
has only an azimuthal component parallel to the current flow, the gradients of ϕ and A vanish making
the right side of (3) zero. Consequently, the generalized momentum p is a conserved quantity. The vector
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potential is then obtained by monitoring the associated changes in the bead’s momentum Mv arising
from changes in the solenoid’s current and by applying conservation of momentum. Thus qA/c is the
momentum “stored” in the system comprised of a unit test charge in an external magnetic field.
Consequently, just as serves as a store of field energy, so qA/c measures a store of field
momentum available to a charge’s motion [10]. The potentials thus represent field energies and field
momenta, per unit charge, as those participate in the universal conservation of energy and momentum,
whereas force and work rate per unit charge, can be regarded as convenient terms for the transfer rates.
The and qA/c are joint properties of the superposed fields arising from their interference – important
because they determine the processes through which fields and charges become observable.
Apart from such theoretical considerations, there has been a host of empirically-based evidence
surrounding the phenomenon of the curl-free magnetic vector potential that continues to emerge.
Observations of this nature have been reported across the board of both microscale and macroscale
domains, as well as spanning across the historical spectrum of both modern and antiquarian research.
For instance, the well-plumbed Aharonov-Bohm (A-B) effect [11] has certainly certified the inextrcable
link of the magnetic vector potential to quantum effects. This phenomenon demonstrated that the
wavefunction of electrons passing around a long solenoid, accumulates a phase determined by the line
integral of the vector potential in the space along a path from the source to the screen [12]. This is a
quantum-mechanical phenomenon in which a quantum particle is affected by static electromagnetic
fields which are topologically confined to regions not accessible to the particle. Consequently the
particle sees only null magnetic field (curl-free vector potential) during its transit [13].
When this was first discovered, physicists were incredulous, since the A-B effect went against the
prevailing dogmatic wisdom which held that the magnetic vector potential could not have any physical
effect [14]. Now, the A-B effect, dealing with quantum effects at the microscale, was predicted and
verified in the mid 20th century. Yet very recently, Varma et al. [15] has demonstrated the existence of
a similar effect, the observation of a static curl-free vector potential on the macroscale as well, in a
system of charged particle dynamics in an external magnetic field. This new phenomenon, albeit as of
this writing yet to be duplicated, is demonstrated by observing the effect in the variation of a curl-free
vector potential by varying the current in a toroidal solenoid (which produces it) on a very low current
electron beam of of a few tens of nano-amperes, of a given energy propagating linearly along a magnetic
field, as detected by a detector plate [16]. Contrary to what would be expected to be observed on the
macroscale as a flat current, as per the classical view, the detector-plate current was found to vary in a
periodic manner with the linear variation of the vector potential [17]. This undulatory behavior thus
signals the detection of a curl-free vector potential on the macroscale. However, according to Varma
[18] though on the macroscale, the observation does not belong to classical physics. Rather, it is
mediated through a matter wave which is on the macroscale, similar to the A-B effect being modulated
by the de Broglie matter wave. Although in the Varma protocol, it is essentially a quantum modulation
of the de Broglie matter wave along the magnetic field lines of force, which is brought about by a
scattering-induced transition across electron Landau levels [19].
In commenting on this result, Shukla [20] states that the matter wave is surprisingly shown to be on
the macroscale of a few centimeters for typical laboratory parameters, and thus could be considered a
classical effect. But then he remarks that it is not since a curl-free vector potential would not affect a
particle or electrical system ‘classically’. However, as we will see, even this supposed assumed tenet of
electrodynamics may also be in need for a major re-tooling. Indeed, recent studies as well as those in
the distant past have determined that a curl-free vector potential may cause robust unexpected physical
effects (e.m.f.’s) in classical electrodynamic systems via what has been recently coined the “Maxwell-
Lodge” effect [21].
As a matter of fact, nowhere in the pantheon of electrodynamic protocols that shall be cited, has the
impact of the curl-free vector potential most clearly been shown to be felt, than with the Maxwell-Lodge
effect. So much so, that when the significance of this phenomenon is duly appreciated by mainstream
physics, it might represent the underpinnings to finally elevate the vector potential to its natural birthright
physical status in CED; for this was the mantle it was originally intended to take on according to the
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worldviews of Maxwell and Faraday in the 19th century.
It derives from a key observation from Oliver Lodge harkening back to the beginnings of the original
formulation of CED. From the results of an electromagnetic experiment, Lodge was confronted with a
conundrum based upon an apparent paradox, in connection with standard effects expected from the
canonized tenets of Maxwellian electrodynamics. Unfortunately, his findings were essentially ignored,
and a fluke attributed to deficiencies in precision due to relatively primitive 19th century electrical
equipment. Specifically Lodge used a torus solenoid wound on to a ring shaped iron core; stray magnetic
fields could only be detected by the use of iron filings, alternating voltage was simulated by including a
reversing key in a direct current circuit, and induced voltage in the ring was detected by a quadrant
electrometer with a movable needle Nevertheless, despite these obvious shortcomings, taking up the
gauntlet, over a century later, Rousseaux et al. [22] emphasized that the Maxwell-Lodge effect still
presents a fundamental problem to the foundations of CED. To most simply state it, a very long solenoid
is circled in its central plane by a conducting loop (Fig. 1). When a sinusoidal current is applied to the
solenoid, there is a corresponding voltage induced in the loop, despite the fact that no sensible magnetic
flux exists in proximity to the loop. The magnetic field of an infinitely long solenoid is nonzero only
inside the solenoid; however, outside an infinitely long solenoid, the magnetic field is zero. In contrast,
because the vector potential is present everywhere around a current-carrying conductor and is parallel
to the current, it can exist both inside and outside an infinitely long solenoid. Despite no magnetic field
existing outside the solenoid, a secondary voltage appears across a loop secondary coil placed around
the outside of the solenoid. Also, it should be noted that Blondel, also performed a similar type of
experiment that apparently verified this effect in 1914 (details in [21]).
Figure 1. Circuits for the Maxwell-Lodge effect representation
The phenomenon associated with the induction of e.m.f. in a magnetic field-free region has then
been termed the Maxwell-Lodge effect. The Rousseaux team used for their experiment a diversity of
Lodge’s apparatus with voltmeter instead of a movable needle (Fig. 1). Assuming the voltage induced
in the ring was due to the dynamics of the vector potential (A) outside the solenoid via the relation, E =
tA , they split the vector potential up according to the Stokes-Helmholtz-Hodge decomposition:
where the third term (the harmonic part) meets the conditions div Ah = 0, curl Ah = 0. It is well known
that it this harmonic part that it is cause of the Aharonov-Bohm effect. As we will show, the Maxwell-
Lodge effect demonstrates its necessity in classical physics as well. However, the harmonic component
of the vector potential was conventionally falsely perceived not to induce any effect because it is always
possible to “gauge” it away by subtracting the gradient of an appropriate scalar function. Nevertheless,
since the space is multiply-connected, this proves to be false since in the quantum/classical protocols
above the observables are related to the circulation of the external vector potential (the holonomy), that
is associated with the phase differences in the Aharonov-Bohm effect, and the internal magnetic flux in
the Maxwell-Lodge effect.
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Outside an ideal solenoid of infinite length, the vector potential is precisely equal to the harmonic
component (or a gradient) because of its divergenceless/curl-less nature, as expressed by the following
formula in cylindrical coordinates, by using Stokes theorem on a closed circular path of radius r:
where Φ is the flux of the magnetic field inside the solenoid or the circulation of the vector potential
outside the solenoid. The magnetic field is null outside a perfect solenoid of infinite length in the
stationary regime. Moreover, it is pointed out that the supposed mathematical indeterminacy due to the
gauge transformations is negated by the boundary conditions which give a physical determination to the
vector potential outside a solenoid. If the current varies slowly in time the magnetic field is still null
outside the perfect solenoid but because the vector potential is not null outside the solenoid and varies
with time, it creates an electric field outside the solenoid:
Moreover, in their experimental findings on the Maxwell-Lodge effect, Rousseaux et al. have offered
the compelling argument that lends support to the view that an electromagnetic influence can be
propagated, free of a magnetic field. Thus, given the results that a constant magnetic field plays no role
in the mechanism of electromagnetic transmission, Rousseaux et al. have proposed to consider the
harmonic part of the vector potential to be the actual agent for propagation.
Besides confirming the findings of Rousseaux et al., in their own follow-up experimental study, the
team of Leus and Taylor [23] have added an additional proposal - positing that in electromagnetic
transmission, it is not just the harmonic part, but the vector potential in total that should regarded as
playing a part in this process; that it is highly plausible that electrodynamic flow of energy, in general,
is related to the time variation of the vector potential. By considering the subtle but important distinction
between kinematical and dynamic systems, Leus et al. [23] have suggested that the acceleration of a
charge which is associated with creating and propagating an electromagnetic disturbance, seems
inseparably linked to the ‘trinity’ of vectors (A, E, B). It is due to the charge’s acceleration that A and ϕ
are simultaneously varying in parallel with the electromagnetic field. All these entities in total make up
the integral parts of a physical unity.
Recently, the operational implementation of the Maxwell-Lodge effect has been embodied in a
patent issued to M. Daibo [24]. In an associated paper [25] Daibo et al. have described this surprisingly
simple apparatus. In order to disentangle the space to be used where the vector potential and the magnetic
field are superimposed, they constructed a nested structure comprising a coiled coil, as depicted in Fig.
2 below. To eliminate the magnetic field and generate a pure vector potential, they constructed a very
long flexible solenoid whose current-return wire runs through the core of the solenoid itself. This
current-return wire was also oriented coaxially within the flexible solenoid. This so-called vector
potential coil (VPC) was then outfitted with several secondary coils passing through the hollow core of
the VPC. The VPC was then driven with alternating current causing a voltage difference across these
various secondary coils, even though the secondaries were not exposed to any magnetic fields. The
whole primary-secondary coil configuration was termed vector potential transformer (VPT).
They found that the VPT has the unique property that the secondary voltage does not depend on the
path followed by the secondary coil. Moreover, the secondary voltage appeared even when the secondary
coil was enclosed by a conducting material. Other features of the VPC that make it attractive for various
industrial applications are that it generates ac electric fields without requiring bare electrodes, which
means that it can be used in corrosive media, such as blood. Because of its transparent characteristics,
the vector potential can penetrate through conductive materials, such as a living organism, deep sea
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water, and even reactor pressure vessels in nuclear power plants. Of course, since the VPT does not
generate magnetic fields, this makes it quite suitable for medical or high precision measurements.
Figure 2. VPT with secondary circuit coil configurations
In a recent paper whose subject matter is in connection with another patent that utilizes a curl-free
vector potential ansatz, albeit at microwave frequencies, N. Nikolova comments [26] that the non-
uniqueness of the potentials as a reason for considering them as non-physical is untenable, and is an
opinion that deserves a closer look as it does not seem to have solid foundations. Also, she points out
that in antenna theory, where the electric and magnetic vector potentials are common analytical tools, a
number of paradoxes can occur, in which the mathematical models predict nonzero propagating
potentials with zero field vectors. The most striking example is the expansion of the free-space field in
spherical harmonics where the vector potential is radially polarized. The 0th - order solution, which
features a spherically symmetric potential, appears to be non-physical because the field vectors are zero
everywhere. At the same time the wave impedance remains finite and exactly equal to that of free space.
No energy can be coupled to this impdeance, however, because the model implies a radially propagating
“potential wave” with no power transport (the Poynting vector is zero). In general, the relativistic 4-
vector potential (A, ϕ) results in zero field vectors in the far zone when A is purely longitudinal
(polarized in the direction of propagation).
It is abundantly clear, from the above theoretical and empirical evidence, that the received practice
of assigning to the vector potential a purely non-physical status in CED, has been first of all premature,
extraordinarily misplaced, and essentially ill-conceived. Accordingly, the related emphasis on placing
only the field vectors E and B (and their six 3-space components) as the sole basis of electromagnetism,
has come to markedly disagree with quantum electrodynamics where the covariant 4-vector potential
has the intrinsic ability to describe the momentum-energy state of an electromagnetic system; the
inevitable result is a science of electromagnetism unnaturally split into two branches with contradicting
views on the basics.
Moreover, make no mistake about it, these discussed experimental protocols outlining the apparent
paradoxes with the potentials, are not mere trivial flukes that can be written off as minor peccadillos
incapable of changing the standard view of the role of the latter – they represent major flaws preventing
a fuller proper understanding of CED. Indeed, as we will show, failure to recognize the import of of
these relatively simple low-energy processes involving the curl-free vector potential, has totally masked
a new dimension of electrodynamics that has yet to be appreciated and exploited.
In order to reveal the hidden frontiers of CED, and repair cracks in its current edifice, two directives
must be implemented. First, as we have argued in this paper, is to acknowledge the physical significance
of the potentials at all levels of nature. Classical physics has for far too long, taken a non-productive
non-holistic - almost schizoid stance - when it comes to interpreting the role of the potentials which, as
stated above, and forcefully repeated here, has caused an unnatural separation of electromagnetism into
two branches – quantum and classical – with conflicting views on its foundational elements.
Part of the reason for this unsettling split, has been the common practice of assigning specific so-
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called “gauge restraints” on the potentials for solving particular problems in electromagnetism in order
to fix boundary conditions for either the process of finding proper electric and magnetic fields from
given charge and current distributions or for the inverse problem. Accordingly, the usual electromagnetic
theory then specifies that the potentials may be chosen arbitrarily, based on the specific so-called gauge
that is chosen for this purpose. The gauge is a supplementary condition which is injected into Maxwell’s
equations, expressed as a function of the potentials. This convention is now so engrained in the practice
of CED that it is now considered to be a de rigeur requirement. Yet, while effective as a mathematical
tool, the setting of a gauge places undue restriction on the potentials; for instance the Lorenz gauge,
makes the scalar and vector potentials totally dependent on each other.
Consequently, we propose the second directive –confluent with the first – to make the potentials
completely independent of one another, resulting in a unique purely “gauge-free” electrodynamics. This
novel prescription also closely follows the principle of Occam’s razor, which dictates that a system of
scientific knowledge should not introduce concepts or entities that are not strictly necessary,
emphasizing the simplicity and conciseness of the model. Consequently, a wholesale reinterpretation
of Maxwell’s equations is proposed without gauged potentials. Also, according to Occam’s razor, this
reformulation must also of necessity, invoke the constraint that the electromagnetic 4-potential, as per
the Minkowski space-time prescription, should be considered as an inseparable single unit entity. This
ansatz will give rise to an electromagnetic field composed not only of the six-component classical
vectorial electrical field intensity and magnetic flux density, but also by a scalar longitudinal field. This
hypothetical entity has often been referred to by various sources with the equivalent alternate
terminology as an electroscalar field. Later we will clarify appropriate use for these two designations.
Although few researchers have considered this possibility, notable key exceptions are the work by
Bettini [27,28], the Lagrangian given in Aharonov & Bohm [29], and that introduced earlier by Fock &
Podolsky [30], papers by Arbab [31,32], Tomilin [33], van Vlaenderen [33,34], Vassallo et al.[36], two
papers by Hively [37,38], and the central scholarly recent series of dissertations by the mathematician-
physicist Woodside [39-41]. The last two researchers have done yeoman’s work of monumental scope
in formulating the basics of this vangaurd model. For instance, to touch base with actual viable real-
world applications based on this gauge-free CED, we shall focus on the recent revealing ground-
breaking 2016 patent issued to physicist Lee M. Hively [42], the embodiments of which receive solid
support from from a brilliant rigorous first-principles demonstration of the existence of of the scalar
longitudinal field by Dale A. Woodside [39]. The related emergence of the scalar longitudinal wave
(SLW) will then be naturally derived, whose existence will be shown to produce many interesting
implications and consequences of electrical charges and currents. Although empirical findings of mostly
an anecdotal nature of the unconfirmed occurrence of such a non-Hertzian SLW have emerged over the
years (e.g., Tesla [43], Monstein & Wesley [44], Meyl [45]), they have been summarily discounted by
mainstream physics and efforts of the corresponding researchers generally maligned. However, as
technology inexorably drives this understanding forward via the concrete embodiments outlined in the
landmark Hively patent, we are certainly approaching a time where these findings can no longer be
pushed aside and ignored by orthodox physics, and physics must come to terms with their potential
physical and philosophical impacts on our world society.
3 Emergence of the scalar longitudinal electrodynamic wave
Insight into the incompleteness of electrodynamics can begin with the Helmholtz theorem which states
that any sufficiently smooth three-dimensional vector field can be uniquely decomposed into two parts:
irrotational and solenoidal. By extension, a generalized theorem now exists, certified by the recent work
of Dale A. Woodside [39-41], for unique decomposition of a sufficiently smooth Minkowski four-vector
field (three spatial dimensions plus time), into four-irrotational and four solenoidal parts, together with
the normal and tangential components on the bounding surface. With this background, the theoretical
existence of the electroscalar field can be attributed to the failure to include certain terms in the standard
Stuckelberg four-dimensional electromagnetic Lagrangian density that are related to the four-irrotational
parts of the vector field.:
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Fμν is the Maxwell tensor, c is speed of light, c2 = 1/με (not necessarily vacuum); the 4-current is Jμ =
(ρc,J); the 4-potential is Aμ = (Φ/c,A). Here, ε is the electrical permittivity – not necessarily that of the
vacuum. Now, k = 2πmc/h must be zero, otherwise the existence of the last term implies massive photons
which has been shown to be essentially false, since the upper bound for photon mass, if it exists at all,
has determined to be ~10-53kg. Specifically, the electroscalar field becomes incorporated into the
structure of electrodynamics if we let γ = 1 and k = 0. As we can see in this representation, it is the
presence of the third scalar-valued term that describes these new features.
2 2
2 2
2 2
cA c
ct ct
  
 
  
  
We can see more clearly how this term arises by writing the Lagrangian density in terms of the standard
scalar (Ф) and magnetic vector potentials (A) for a massless 4-vector field (Aμ) that is no more than
quadratic in its variables and derivatives:
We will see that it is the relationship between the potentials that underscores the disclosure of the
missing electroscalar field and its hitherto unsuspected key role in electrodynamics. First, equation 8
allows only two potentially physical classes of 4-vector fields [40]. As case in point, without the last
term, equation (8) describes zero 4-divergence of Aμ (which we have formally called four-solenoidal
above). The second class of four-vector fields has zero 4-curl of Aμ, Fμν = − =0 (four-
irrotational vector field). This will emerge if and only if this last scalar factor term is included, as
represented by the total Lagrangian density above. In fact the expression in the parentheses in this term,
when set equal to zero, describes the Lorenz condition, as was mentioned previously, which restricts the
scalar and vector potentials in their usual form, to be mathematically dependent on each other. However,
as we have stressed above, the new model allows for a non-zero value for this scalar-valued expression,
achieving the directive of making the potentials completely independent of one another. This results in
the previously stated gauge-free electrodynamics, where this new scalar-valued component (C), is a
dynamic function of space and time represented by the following relation:
As can be clearly seen, application of the Lorenz gauge, where C = 0, totally denies the status of real
physical entity to the scalar field. However, it is this new idea of the independence of the potentials in
this gauge-free electrodynamics out of which the scalar value C is derived, and from which the unique
properties and dynamics of the scalar-longitudinal electrodynamic wave arises.
A more complete electrodynamic model may be derived from equation (8) of the Lagrangian density.
The Lagrangian expression is important in physics, since invariance of the Lagrangian under any
transformation gives rise to a conserved quantity. Now, as is well known, conservation of charge-current
is a fundamental principle of physics and nature. Conventionally, in classical electromagnetics charged
matter creates an electric E field. Motion of charged matter creates a magnetic B field from an electrical
current which in turn influences the B and E fields. These dynamics produce what is known as transverse
wave excitations perpendicular to the direction of propagation. These effects can be modelled by
Maxwell’s equations. Now, exactly how and to what degree do these equations and dynamics of E and
B change when we include the new scalar factor of C.
Those who are familiar with classical electrodynamics will notice the two homogeneous Maxwell’s
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equations – representing Faraday’s law and the standard Gauss-Ostragradsky equation for
divergenceless magnetic field, are both unchanged from the classical model.
However, notice the above three new eqns. incorporate this new scalar component which is labelled C.
This formulation as defined by new eqn. (10), whose construction we observed above, creates a radical
revision of Maxwell’s equations, with one new term (C/t) in Gauss-Ostragradsky Law for the
electrical field (eqn.11), where ρ is the charge density, and one new term (C) in Ampere’s Law (eqn.
12), where J is the current density. We see these new eqns. lead to some important conditions. First,
relativistic covariance is preserved. Second, the classical fields E and B are unchanged in terms of the
usual classical potentials (A and Ф)-see equations (1),(2). We have the same classical wave eqns. for A,
Ф, E and B without the use of a gauge condition (and its attendant incompleteness). The EED theory
shows cancellation of C/t and  in the classical wave equations for Ф and A; and a scalar-
longitudinal wave (SLW) is revealed, composed of two interdependent agents: the scalar field C we
spoke of above, and a concomitant longitudinal-vectorial electric field whose origin we will speak of
next. The term longitudinal wave refers to a wave that has excitations which are parallel to the direction
of propagation.
This can be more clearly seen to emerge by examining the new wave equation for C, which is
revealed by use of the time derivative of (eqn. 11), added to divergence of (eqn. 12). Now, as is known,
matching conditions at the interface between two media with different electrical properties are required
to solve Maxwell’s eqns. Interface matching conditions for (13) uses a Gaussian pill box with end faces
parallel to the interface in regions ‘1’ and ‘2’. In the limit of zero pill box thickness, the divergence
theorem can be used on eqn. (13) will yield interface matching in the normal component (‘n’) of C/μ
as shown in eqn. (14). The subscripts in eqn. (14) denoted by C/µ in medium 1 or medium 2,
respectively. (µ is magnetic permeability – again not necessarily that of the vacuum). In this regard, with
the vector potential (A) and scalar potential (Ф) now stipulated as independent of each other, this
significantly changes the usual matching conditions between the two media.
For instance, it is now the surface charge density at the interface which produces a discontinuity in
the gradient of the scalar potential (Ф), which is inconsistent with the standard (CED) discontinuity in
the normal component of E. Also, it should be noted that the wave equations for A, Ф, E, and B are
unchanged under time reversal; t -t, produces a sign change on both sides of equation (13) that also
involves time invariance. The sign change in C indicates its pseudoscalar nature. The time reversibility
of EED implies that reciprocity holds; a SLW transmitter can also be used as a receiver. Above all, there
are truly remarkable properties of this new wave equation. Notice from eqn. (13), the driving factor or
source for the scalar field C implies a violation of charge-current conservation (RHS non-zero), a
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situation which we noted cannot exist in macroscopic nature. Nevertheless, this will be compatible with
standard Maxwellian theory if this violation occurs at very short time scales, such as occur in sub-atomic
interactions. Now, interestingly, with the stipulation of charge conservation on large time scales, giving
zero on RHS of eqn. (13), these predicted longitudinal wave-like solutions are produced, as represented
here with the lowest order form in a spherically symmetric geometry at a distance (r), C = Coexp[j(kr -
t)]/r. The C wave therefore, is a radial pressure wave, similar to that in acoustics and hydrodynamics,
which expands and contracts along the direction of propagation. This is unique under the new EED
model since, although classical electrodynamics forbids a spherically symmetric transverse wave to
exist, this constraint will be absent under the EED theory, which admits a longitudinal wave as well.
B B J.
  
, (15)
Why this constraint prohibiting a spherically symmetric wave is lifted in EED can also be seen in
eqn. (15) – the wave eqn. for the vectorial magnetic field. Notice, the source of the magnetic field (RHS)
is a non-zero value of curl J, which signifies solenoidal current density, implying circulating currents,
as is the case in standard Maxwellian theory. When B is zero, so is curl A which is equal to B. This is
an important result. Automatically, since B = curl A = 0 (A is irrotational), and equation (15) then implies
that J is also curl-free, leading to J = . Here κ is a scalar function of space and time. Thus, in contrast
to closed current paths generated in ordinary Maxwell theory, due to solenoidal current density, J for the
SLW is gradient-driven and is uniquely detectable. Now, since in linearly conductive media, the current
density (J) is directly proportional to the electric field intensity (E) that produced it, this gradient driven
current will then produce the previously noted longitudinal E-field which accompanies the scalar
pressure field C. It is thus apparent that B = 0 is a necessary and sufficient condition for the existence of
the SLW.
 
, (16)
We can also see how this longitudinal E-field results from examining the standard vectorial wave
eqn. for the electric field (16). When the RHS of eqn. (16) is zero, as will be the case in free-space with
no currents and charges, the lowest order, outgoing spherical wave is E = Eor[j(kr ωt)]/r, where r
represents the unit vector in the radial direction and r represents the radial distance. The electrical field
is also longitudinal. This equation (16) has zero on the RHS for propagation in conductive media. An
important observation here is a scalar longitudinal pressure field (C) is always accompanied by a
corresponding vectorial longitudinal E field. As stated above, these two are interdependent, just as in
standard CED, a transverse E field will always be dynamically associated with its transverse B field
counterpart in a push-pull fashion. Interestingly, the nature of this unique two-fold electrodynamic wave
structure then informs the various terminology that has been invoked to describe the phenomenon. For
instance, focusing on the scalar component, we then use scalar longitudinal wave nomenclature;
emphasis on the longitudinal electric field component would suggest we use the electroscalar wave
Now, the above noted fact that B=0 for the SLW, implies no back electromagnetic field from B/
in Faraday’s law which in turn gives no circulating eddy currents conventionally subject to Lenz’s Law.
Accordingly, corresponding experimentation by Hively’s team has shown that the SLW is not subject to
the skin effect in media with linear electric conductivity, and travels with minimum resistance in any
conductive media. This is unprecedented in the annals of electrodynamics. This significant property of
the SLW certainly has great bearing on many practical issues, not only on the future engineering protocol
for generating of widespread wireless power efficiently and abundantly, but speaks directly to the current
state of weaknesses in the world electrical grid and currently unknown or unsuspected future demands
which might be placed on our aging power production and distribution systems by possible extreme
climate effects.
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Figure 3: Comparison between EED and CED
In summary Fig. 3 shows the key structural differences in standard CED versus EED (Gauge-Free
Electrodynamics). In addition to the standard CED side of things in which a restricted dependence of
the potentials necessarily leads to solenoidal (circulating currents) and the concomitant transverse
electromagnetic wave, we have this whole new dimension of gauge-free electrodynamics resulting from
the assumption of independence of the potentials that is now ripe for exploration. In the above cited
protocols, the VPT is just one of these many new innovations that exploits the gradient-driven current
SLW and its important feature of lack of attenuation that, as was earlier stated, has the potential to
produce a virtual revolution in how electricity is generated and distributed.
From the new EED model, many potential transformational principles have emerged to challenge
the current landscape of electrodynamics. Here we summarize some of these unique properties of the
scalar-longitudinal wave. Five of these seven properties have been verified by Hively’s team, setting the
stage for understanding the specific technological aspects of the Hively patent. Please note: the equation
numbers correspond to those of Hively’s specific equations in his patent – not those of this paper.
From the above considerations, it can be seen how the SLW has not been acknowledged theoretically
as part of the structure of classical electrodynamics. Compounding this issue is corresponding failure to
physically detect this phenomenon. The reason this SLW has not been detected can be attributed to the
fact that all electromagnetic antennas are of the dipole-type, designed to detect only TEM and the
solenoidal current that is its foundation, and not the longitudinal wave which is a function of gradient-
driven current dynamics, which requires a monopole antenna, as will now be described. Concerning the
specific engineering embodiments in the Hively patent required to reveal these unique effects. Fig. 4
illustrates a cross-sectional view of a linear monopole antenna apparatus. In the middle is a first
conductor (202), a tubular second conductor (204) and an annular skirt balun (206). The balun is
configured to cancel most or all of the returning current on the outer surface of the second conductor.
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This is achieved with the length of the balun being one-quarter of a wavelength corresponding to the
first operating frequency. The skirt balun (of ¼ wavelength) causes a phase shift in in the current flow
along the guided path from the bottom (inside surface) of the outer balun (0°), to the top (inside surface)
of the skirt balun (90°) and back down the outer surface of the coax outer to the end of the balun (180°).
The 180o phase shift cancels the return current flow along the outside of the outer coaxial conductor.
During operation an electric current on the balun is appx. 180o out of phase relative to the electric current
wave on the outer surface of the second conductor adjacent to the balun thereby cancelling the return
current on the outer surface of the second conductor, effectively creating a zero magnetic field, which
in turn is a necessary and sufficient condition for producing the SLW. Thus, essentially all the electric
current goes into charging and discharging the antenna.
Figure 4: Cross-section of SLW monopole antenna
Also, from Hively’s 2016 patent, Figure 5 illustrates an alternate method to produce the same results
- a bifilar coil apparatus configured to transmit and/or receive scalar-longitudinal waves. The first and
second conductor making up this coil are conductively coupled such that an electric current in the coil
will propagate in opposite directions in adjacent turns of the coil, represented by the alternate dotted
(704) and solid (702) lines, thus cancelling any magnetic field so that during the operation the coil
transmits or receives only scalar-longitudinal waves. The coil is thus configured to create a gradient-
driven current, which arises from the magnetic field cancellation, and has zero inductance due to counter-
going electrical currents in adjacent turns of the coil. Also, there is zero capacitance as a result of adjacent
coil turns having the same electric charge density. This bifilar coil is a two-dimensional monopole that
accumulates positive and negative charge over each sinusoidal cycle. We will return to discuss other
interesting potential implications of this patent for power generation and conversion later.
Figure: 5: Bifilar-coil-type SLW monopole antenna
4. Evidence of the SLW in patents, and in nature - both inanimate and biological
For now, let’s look at other patents that may indicate dynamics of an electroscalar nature. Larry Park has
invented a device [46] that has apparently detected seismic precursor earthquake signals earlier than any
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previous systems of this type. His device detected SPI (single phase impulses) and MPB (multiple phase
bursts) signals in strong correlation with earthquakes actually occurring 8 to 80 hours later. These unique
impulses are induced by slow pressure variations in the crust of the Earth from the breaking of chemical
bonds as the rock fractures, leaving positive and negative charges on opposite sides of the fault.
Eventually enough charge builds up to cause current flow (arcing) across the fault. This gradient-driven
current creates the SLW. Although Park assumed he was detecting TEM, nevertheless, these signals,
unlike anything previously detected from movement of the Earth crust as precursor seismic activity
manifest as low frequency waves w/ high frequency signals imposed thereon and travelling through
matter itself. These scalar longitudinal waves produced are saturated over the frequency spectrum – as
being spectrally rich. This description is one reason why these detected signals may be scalar-wave
mediated. Another reason why is clearly evident from the depiction of the coil windings in the Park
patent [46]. Notice the characteristic flat pancake coils illustrated earlier in the Hively patent, specifically
designed to eliminate inductance and capacitance in order to create the gradient-driven current, enabling
this detector to be sensitive to scalar longitudinal seismic wave precursor signals from Earth movement.
Figure 6: Possible registration of scalar solar radiation
Thus, we see that the SLW may already be a dynamical feature of natural phenomena. The scalar-
longitudinal wave may be a feature of some astrophysical phenomena, particularly highlighting its
enormous predicted penetration power. The most favorable conditions for the registration of solar
electroscalar radiation was realized by Russian researchers during the eclipse of the sun in Aug. 2008
[47]. During the eclipse the moon shields most of the flux of the transverse electromagnetic solar waves,
while the longitudinal waves, having greater penetration power, do reach the Earth’s surface. The
incident solar radiation may lead to self-excited radial oscillations in conductive substances. Specifically,
the EED theory predicts that a charged sphere, oscillating in a ballooning (monopolar) mode will radiate
the SLW, and that higher order (multi-pole) oscillations will also create the SLW. Considering this
physics, metallic spheres were used to measure such radiation. This protocol had four copper spheres
placed in a metallic box (Faraday cage), connected to each other’s centers by a copper wire. The Faraday
cage protocol eliminates any possible registration of TEM radiation. The result of measurements are
shown in this Fig. 6. Notice how the maximum effect occurred at the peak of the eclipse. Now, since the
detection of solar electroscalar energy should technically occur anytime the moon is between the Earth
and the sun, the amplification of the signal would be expected during the regular monthly new moon
phase. This result was also seen by the Russian team [47]. Unfortunately, since no other independent
groups have attempted to duplicate this expt., there is controversy as to the veracity of these claims.
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This brings us back to the particulars of the Hively patent that might exploit this solar SLW to
generate electrical power. Accordingly, the sun is a very hot ball of charged particles (electrons and ions
in a plasma) that undergoes longitudinal oscillations producing a radial gradient-driven current density.
A specific application of this patent involves electric power generation on the basis of new terms in the
momentum balance eqn. (17). Here T represents the Maxwell stress tensor. More specifically electrical
power can be generated by charging a flat-plate capacitor to give a large directed E-field. Then SLW
emission from the sun will generate force variations across the capacitor plates via the term (CE/μ) in
this equation, corresponding to a voltage to yield a power-producing current. This power is thus
proportional to E (and therefore to the capacitor voltage) and the solar SLW emissions C. The variable-
frequency power can then be rectified, and subsequently be converted to alternating current via an
alternator. It is this term (CE/μ) that implies the possible transmission of wireless power over large
distances in a directed fashion. When we add the new energy-balance eqn. (18) to the new momentum-
balance equation, we see another practical role for this key term (CE/μ). It may correspond to an increase
(or decrease) in longitudinal electrodynamic momentum in equation. (17) along the direction of motion,
with a concomitant decrease (increase) in electrical energy as per equation (18). Because of the sign
difference for this term in both eqns. there arises an inverse-intensive relationship. Specifically,
longitudinal electrodynamic power loss (or gain) may drive a corresponding kinetic energy gain (loss)
in the physically massive object that is emitting these waves. Consequently, EED theory may predict a
propulsion mechanism without the use of propellant mass.
Looking at the significance of another key term in these equations, specifically, EED theory predicts
a new term (CJ) in eqn. (17). As previously noted, the longitudinal electric field E induces an electric
current density (J) in any distant conductive object in its path according to their direct proportionality.
Thus, the concomitant presence of a scalar field (C) may interact with this current to produce a force
(CJ) on the distant object. By the use of a phased array of SLW emitters, the relative phase of E (and
thus J) may be shifted with regard to the phase of C. This may then produce the engineering equivalent
of a “tractor” beam. Another reason for the significance of the new term (CJ), may be in supporting the
experimental evidence for what is known as Weber electrodynamics, which involves forces that are
parallel to the electrical current density (J). The specific controversial tests which have claimed to justify
this thesis included: the force on Ampere’s bridge, the tension to rupture current-carrying wires, the force
on the Graneau-Hering submarine, the mercury-driving force in Hering’s pump, and the oscillation-
driving force in a current-carrying mercury wedge. These test results [48] are not inconsistent with –
and may be implied by - the new force term (JC) in eqn. (17); namely, the force is independent of the
electrical current’s direction, since JC~ (current)2 in the conductor with a gradient-driven current.
Figure 7: Spectral output of radiation as a function of tape angle
Surprisingly, the protocol for producing the electroscalar field may extend to embrace some of the
more mundane phenomena in which very low energy levels of excitation are required. As a possible case
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in point, in the 300 or so year history of electrodynamics, tribo-electrification is one of the least
understood electrical phenomena and up to present it has not been shown how to derive it from first
principles. Triboelectrification refers to the process of separating positive and negative charges by means
of mechanical action. Now, over the course of the last 100 years, x-ray imaging has conventionally relied
upon the availability of a high-voltage supply to accelerate electrons to sufficient energies for x-ray
emission. It is thus no less surprising that in 2008 [49] it was revealed that, hitherto unsuspected, x-ray
energies can be generated by the common tribo-electrification process of peeling ordinary adhesive tape
in low pressure or vacuum. According to mainstream physics, similar to atmospheric lightning, the
precise method of charge separation is still unknown. However, once again we see the theme of chemical
bond breaking re-surfacing, which leaves positive and negative charges on opposite sides of the
interface. The charge buildup eventually causes arcing and possible production of a gradient-driven
current producing the SLW.
Specifically, in this protocol, the mechanical energy of tape peeling creates electrostatic energy due
to charge separation, and the breaking of adhesive (chemical) bonds. Electrons that are accelerated,
when striking the opposite side of the tape produce photons to conserve momentum. Now, according to
the CED view, it is believed these high energy photons produce transverse bremsstrahlung (or braking
radiation). However, the transient charge densities of 1012 electrons/cm2, was more than an order of
magnitude greater than is measured in typical tribo-charging systems; This also indicates support for a
model including the SLW that may be required for explanation of these observations.
More conundrums surfaced to challenge the current model as to the actual nature of the radiation
produced [50]. As case in point, there has been a significant doubt raised as to why the spectral frequency
of the radiation does not correspond to that commonly understood to be a signature of bremsstrahlung
or polarizational bremsstrahlung. This has been particularly true since the output of spectral radiation
frequency is a function of the angle between the tape and normal to the tape surface, as depicted in this
graph in Fig. 7, measuring photon count rate as a function of this tape angle. This graph clearly shows
that ordinary bremsstrahlung would smoothly bound the angular distribution from below, while
polarizational bremsstrahlung bounds the angular distribution from above. However, interestingly,
neither mechanism shows the 20% highly discontinuous rise/fall in sharp angular distribution between
80°- 100°. Now, according to theory of electroscalar radiation the SLW is considerably more penetrating
in matter due to not being subject to the skin effect, and might explain this anomalous angular radiation
distribution. Thus, humble physical objects such as adhesive tape may reveal the existence of
electroscalar radiation.
Fig. 8. Alteration of index of refraction on human blood plasma by irradiation from TC (TESLAR chip)
The scalar longitudinal wave may also be an inherent component of human biophysical systems as
well, affecting the alpha brain wave rhythm, the parametric resonance of organs, and could be
responsible for primary human perception. One of these devices that is claimed to have measurable
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biological effects is known as the TESLAR watch. Its inventors have asserted that it produces a SLW at
very low frequency. In testing this instrument, Rein [51] has showed that the presence of the TESLAR
chip (TC) showed 137% enhancement of human lymphocyte proliferation (immune system). Another
test demonstrated that nerve cells could inhibit their uptake of noradrenalin (depression-fighting process)
by as much as 19.5% in presence of the TESLAR watch.
The Krasnoholovets comprehensive studies are particularly relevant in this regard. For instance, in
Fig. 8 [52], we see the results of laser irradiation on an aqueous highly non-equilibrium solution of
human blood plasma, demonstrating the change in the index of refraction (n) of the liquid over a short
period of time (~1 min.) causing definite changes in fringe patterns of laser light, by operation of a
TESLAR watch. The possible effects of temperature on the solution’s index of refraction by the heating
of the laser light was ruled out since the maximum change of n of the blood protein solution by the TC
was an order of magnitude higher than that predicted from the temp change. It should be noted here that
all living processes involve concentration gradient-driven ion currents across the cellular membrane.
Imposing a SLW on living cells will alter these currents. The TC apparently alters the currents in a
therapeutic fashion.
Also, changes of n are produced by changes in the structure of the network of hydrogen bonds of
water. This last effect was demonstrated by the same team in a dramatic fashion when examining effects
by the TC [53]. For instance, in another embodiment of an experimental protocol test showed the results
of irradiation by the TC on the infrared spectrum of the evaporation of an aqueous solution of hydrogen
peroxide. The spectra demonstrated that the TESLAR watch suppresses the vibration of the molecules
in the solution and, in particular, strongly freezes vibrations of O–H bonds. Thus it was concluded that
the TC can strongly affect a significantly non-equilibrium system. In this regard, the physics here alters
the chemical potential in the molecules via a bond angle change, not unlike modifying the nuclear
potential in a nucleus.
Other experiments demonstrate the EED feature of irrotational (gradient-driven current) that was
discussed in section 3 (for example): arc discharges [49,50], ion-concentration-gradient-driven current
across living cell walls [54], atmospheric pressure gradient-driven current [55], and irrotational
electroencephalogram current [56].
5. Conclusions and prospects
The above represent adequate examples to show the field of electrodynamics (classical and quantum) is
incomplete. In this regard, the experimental evidence shows that classical electrodynamics was
seriously remiss in terms of omitting the electroscalar component. Anomalies previously not completely
understood may get a boost of new understanding from the operation of electroscalar energy. We have
seen in the three instances examined – the mechanism of generation of seismic precursor electrical
signals due to the movement of the Earth’s crust, the ordinary peeling of adhesive tape, as well as
irradiation by the special TESLAR chip, the common feature of the breaking/altering of chemical bonds.
In fact, we may ultimately find that any phenomena requiring the breaking of chemical bonds, in either
inanimate or biological systems, may actually be scalar-wave mediated. Thus, we may discover that the
scientific disciplines of chemistry and/or biochemistry may be more closely related to physics than is
currently thought. It may even turn out that the gradient-driven current, and associated scalar-
longitudinal wave could be the umbrella concept under which many of the currently unexplained
electrodynamic phenomena might find a satisfying explanation.
Above all, these new findings provide an able challenge to the worldview by physicists that the
magnetic vector potential A is just a mathematical device and has no physical reality in the description
of electrodynamics, unlike the electric and magnetic field intensities. The Maxwell-Lodge effect, as
certified by the empirical evidence of such devices as the VPT, unquestionably now raises the
significance of the magnetic vector potential to primary status, not only in quantum mechanics where
the Aharanov-Bohm effect holds sway, but boosting its respectability in classical electrodynamics
through appreciation of the compelling elements of the gauge-free electrodynamic system. The new
scalar longitudinal wave patent itself [42] is a primary example of the type of invention that probably
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would not have seen the light of day even ten years ago. Now, its existence may represent a real game
changer in this area. It will unquestionably bring the subject of scalar electrodynamics to the sharpest
positive focus it has been to date. Not only will it provide the springboard for development of the long
sought-for sound theoretical basis for the inclusion of the SLW in electrodynamics, motivate a re-
evaluation of the current structure of CED in regards to model completeness and consistency, but is
destined to forecast a paradigm revolution in our modes of energy generation and power conversion.
Despite what mainstream physics may claim, the study of classical electrodynamics is by no means
a closed book. On a grander panoramic scale, our expanding knowledge gleaned from further examining
the electro-scalar wave concept, as applied to areas of investigation such as developing wireless sources
of energy, etc., will explicitly shape the future of society as well as science, especially concerning our
openness to phenomena that challenge our current belief systems.
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... Prior to [22,11], gaugeless electrodynamics has been already introduced and explored by other authors [1,18,19,21,29,30,31,33,34,39,41]. Most of these preceding works introduce the electromagnetic scalar eld as an additional entity besides charges and currents, rather than the entity that actually produces the apparent charges and currents. ...
Full-text available
Otto Stern's 1933 measurement of the unexpectedly large proton magnetic moment indicated to most physicists that the proton is not a point particle. At that time, many physicists modeled elementary particles as point particles, and therefore Stern's discovery initiated the speculation that the proton might be a composite particle. In this work, we show that despite being an elementary particle, the proton is an extended particle. Our work is motivated by the experimental data, which we review in section 1. By applying Occam's Razor principle, we identify a simple proton structure that explains the origin of its principal parameters. Our model uses only relativistic and electromagnetic concepts, highlighting the primary role of the electromagnetic potentials and of the magnetic flux quantum Φ = h/e . Unlike prior proton models, our methodology does not violate Maxwell's equations, Noether's theorem, or the Pauli exclusion principle. Considering that the proton has an anapole (toroidal) magnetic moment, we propose that the proton is a spherical shaped charge that moves at the speed of light along a path that encloses a toroidal volume. A magnetic flux quantum Φ = h/e stabilizes the proton's charge trajectory. The two curvatures of the toroidal and poloidal current loops are determined by the magnetic forces associated with Φ . We compare our calculations against experimental data.
... Prior to [22,11], gaugeless electrodynamics has been already introduced and explored by other authors [1,18,19,21,29,30,31,33,34,39,41]. Most of these preceding works introduce the electromagnetic scalar eld as an additional entity besides charges and currents, rather than the entity that actually produces the apparent charges and currents. ...
Otto Stern's 1933 measurement of the unexpectedly large proton magnetic moment indicated to most physicists that the proton is not a point particle. At that time, many physicists modeled elementary particles as point particles, and therefore Stern's discovery initiated the speculation that the proton might be a composite particle. In this work, we show that despite being an elementary particle, the proton is an extended particle. Our work is motivated by the experimental data, which we review in section 1. By applying Occam's Razor principle, we identify a simple proton structure that explains the origin of its principal parameters. Our model uses only relativistic and electromagnetic concepts, highlighting the primary role of the electromagnetic potentials and of the magnetic flux quantum Φ = h /e. Unlike prior proton models, our methodology does not violate Maxwell's equation, Noether's theorem, or the Pauli exclusion principle. Considering that the proton has an anapole (toroidal) magnetic moment, we propose that the proton is a spherical shaped charge that moves at the speed of light along a path that encloses a toroidal volume. A magnetic flux quantum Φ = h /e stabilizes the proton's charge trajectory. The two curvatures of the toroidal and poloidal current loops are determined by the magnetic forces associated with Φ. We compare our calculations against experimental data.
... where 0 C ≠ constant, and followingly [43]: ...
Full-text available
In this paper a straightforward application of Occam's razor principle to Maxwell's equation shows that only one entity, the electromagnetic four-potential, is at the origin of a plurality of concepts and entities in physics. The application of the so called "Lorenz gauge" in Maxwell's equations denies the status of real physical entity to a scalar field that has a gradient in space-time with clear physical meaning: the four-current density field. The mathematical formalism of space-time Clifford algebra is introduced and then used to encode Maxwell's equations starting only from the electromagnetic four-potential. This approach suggests a particular Zitterbewegung (ZBW) model for charged elementary particles. .
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The scalar and vector potentials were introduced into electromagnetic physics in the second half of the nineteenth century. The chief aim was to use them as auxiliary mathematical quantities in order to solve certain practical problems.Nevertheless the discovery of the Aharonov-Bohm effect (1959) in quantum mechanics has suggested that vector potential rather than magnetic field is the causal agent in such an effect. Recent research on the Maxwell-Lodge paradox--induction of voltage in the loop circling a long solenoid carrying alternating current--has confirmed that induction occurs in a region of space effectively free from magnetic field. This again reinforces the idea of vector potential as a physical entity rather than the auxiliary artificial quantity of classical electrodynamics. The present investigation is intended to provide some degree of corroboration of the previous result.The experimental arrangement consists of a ‘special’ transformer containing movable, single turn coils wound onto rectangular frames. The primary coil is powered from a signal generator providing alternating current over a variable frequency range while the secondary output voltage is connected across a C.R.O./precision voltmeter. Measurements of transformer e.m.f. were carried out at several frequencies in the range 100 Hz–20 kHz and with various conditions of shielding around the primary and secondary coils.Certain additional experiments were carried out with a long solenoid and torus solenoid supplied with different core materials. Experimental results for induced e.m.f’s are presented and in special cases correlated with the calculated values of mutual inductance. Overall the results tend to confirm the primacy of vector potential over magnetic field as an explanation of the phenomenon.
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The observation of an electroscalar signal during the eclipse of the Sun by the Moon in 2008 was a starting point for the development and creation of the electroscalar field theory. This observation shows that such radiation has a long wavelength, and is longitudinal and extremely penetrating. The properties of the electroscalar and electromagnetic dynamics of a massive charged particle have been studied. An analogy between the linear theory of elasticity and Maxwell electrodynam-ics is made. The observed spectrum of radiation clarifying peculiar properties. Real sources of electroscalar radiation are determined. In accordance with the principle of least action, the La-grangian of the electroscalar field and the field force acting on the particle are defined. The spectral expansion of the electroscalar field allowed us to establish that the field is longitudinal and aligned with the wave vector. At the heart of the electroscalar theory, which is compliant with the experimental data, is the four-dimensional scalar potential that describes radial vibrations of the electroscalar field source. The four-vector Maxwell electromagnetic potential and four-scalar potential neither form a single object in the Minkowski space nor interfere and, as a consequence, prove to be independent and unrelated differential relations. Moreover, a strong correlation between the spatial position of the particle and the field components allows and demonstrates a new degree of freedom in the electrodynamics of charged particles.
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This paper discusses theoretical aspects of the modeling of the sources of the EEG (i.e., the bioelectromagnetic inverse problem or source localization problem). Using the Helmholtz decomposition (HD) of the current density vector (CDV) of the primary current into an irrotational (I) and a solenoidal (S) part we show that only the irrotational part can contribute to the EEG measurements. In particular we present for the first time the HD of a dipole and of a pure irrotational source. We show that, for both kinds of sources, I extends all over the space independently of whether the source is spatially concentrated (as the dipole) or not. However, the divergence remains confined to a region coinciding with the expected location of the sources, confirming that it is the divergence rather than the CDV that really defines the spatial extension of the generators, from where it follows that an irrotational source model (ELECTRA) is always physiologically meaningful as long as the divergence remains confined to the brain. Finally we show that the irrotational source model remains valid for the most general electrodynamics model of the EEG in inhomogeneous anisotropic dispersive media and thus far beyond the (quasi) static approximation.
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The recently reported curl-free vector potential observation (Varma et al 2012 Eur. Phys. J. D 66 38) in relation to a system of charged particles in a magnetic field points to the existence of a new state of the electron—a quantum modulated state—which arises through a scattering-induced transition across Landau levels. This quantum modulated state has been shown to account for some very unusual effects on the macro-scale, which are distinct from the ones which can be understood in terms of a 'classical electron' and also from the ones which can be understood in terms of a 'quantum electron' on the micro-scale characterized by the Planck quantum. This quantum modulated state has been shown to account for the observation of a static curl-free vector potential on the macro-scale alluded to above, as well as other matter wave manifestations on the macro-scale. The macro-scale curl-free vector potential observation differs fundamentally from the corresponding micro-scale effect—the well-known Aharonov–Bohm effect. These two effects—on the macro-scale and the macro-scale—are compared and contrasted to each other here in their manner of detection of the static curl-free vector potential. Such a comparative study helps gain a deeper understanding of the nature of the quantum modulated state and the macro-scale matter wave it represents.
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Maxwell's equations require a gauge condition for specific solutions. This incompleteness motivates use of a dynamical quantity, ζ = -â · A - εμ âÏ/ât. Here, A and Ï are the vector and scalar potentials, with permeability and permittivity, ε and μ respectively. The results are: relativistic covariance; classical wave solutions; elimination of inconsistency between the media-interface matching for Ï and for Gauss law; independent determination of A and Ï; prediction of two new waves, one being a charge-fluctuation-driven scalar wave, having energy but not momentum; a second longitudinal-electric wave with energy and momentum; experimental suggestions.
The ionospheric gravity and pressure-gradient current systems are most prominent in the low-latitude \(F\)-region due to the plasma density enhancement known as the equatorial ionization anomaly (EIA). This enhancement of plasma density which builds up during the day and lasts well into the evening supports a toroidal gravity current which flows eastward around the Earth in the \(F\)-region during the daytime and evening, and eventually returns westward through the \(E\)-region. The existence of pressure-gradients in the EIA region also gives rise to a poloidal diamagnetic current system, whose flow direction acts to reduce the ambient geomagnetic field inside the plasma. The gravity and pressure-gradient currents are among the weaker ionospheric sources, with current densities of a few \(\mbox{nA/m}^{2}\), however they produce clear signatures of about 5–7 nT in magnetic measurements made by low-Earth orbiting satellites. In this work, we review relevant observational and modeling studies of these two current systems and present new results from a 3D ionospheric electrodynamics model which allows us to visualize the entire flow pattern of these currents throughout the ionosphere as well as calculate their magnetic perturbations.
This article describes how, an intuitive guess - a hunch - in relation to a system of charged particles in a magnetic field pursued over four decades, has led to the discovery of an entirely new set of phenomena, which could not have been conceived in view of the prevailing conceptions. They pertain to the existence of quantized residence times in an adiabatic magnetic trap, and more surprisingly, the existence of macroscale matter wave interference effects, with an h{stroke} independent matter wavelength. They even include the observation of a curl-free vector potential on the macro-scale as against its micro-scale detection à la Aharonov-Bohm. Though on the macro-scale, these results cannot be understood in terms of the Lorentz equation, which is known to govern the dynamics on the macro-scale. They have, in fact, been shown to be of quantum origin and are found to be attributed to the quantum modulation of the de Broglie wave, and hence could not have been covered by the Lorentz equation. All these phenomena are seen to run counter to the well-entrenched canonical perception that matter wave interference effects and the vector potential observation - the Aharonov-Bohm effect - pertain only to the micro-scale. The unusual phenomena so discovered constitute a complete surprise as they are entirely unexpected under the canonical view and appear to upturn the latter.
An explicit physical interpretation of the electromagnetic vector potential is here pointed out-as field momentum available for exchange with kinetic momenta of charged matter. It is shown that the vector potential can be quite as directly measurable, without recourse to only quantum-mechanical effects, as are scalar potential differences and the force fields E, B. This suggests, in keeping with quantum electrodynamics, that the equations for potentials may be regarded as more ''basic'' than the Maxwell equations-but only because the potentials most directly represent interaction energy-momenta through which fields and charges become observable.