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Unravelling the potentials puzzle and corresponding case for the scalar

longitudinal electrodynamic wave

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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

torsionpower@yahoo.com

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 − v∙A/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 qϕ 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 qϕ 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.

L

EM

2 2

2 2

2

2 2

11

22

cA c

AJA A

ct ct

(8)

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.

2

22

22

B

B B J.

ct

, (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.

2

22

22

.

EJ

EE

ct t

, (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

description.

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.

References

[1] Giuliani G 2010 Vector potential, electromagnetic induction and ‘physical meaning’ (arXiv:

physics.hist-ph/1005.2350v1); Barbieri S Cavinato M and Giliberti M 2013 An educational

path for the vector potential and it physical implications (arXiv: physics.class-ph/1303.5619

v1); Bork A M 1967 Maxwell and the vector potential Isis 58 2 210-222

[2] Faraday M 1839-1855 Experimental Researches in Electricity vol. 1-3 London paras. 60 71;

T Martin ed. Faraday’s Diary 1820-1862 vol. 1-7 1932-1936 London G Beus & Sons; Jones

H B The Life and Letters of Faraday vol. 1 & 2 1870 London vol 2 9; Faraday M 1852 Phil.

Trans. R. Soc. London 142 25; Faraday M 1852 Electricity 3 328-370 407-437; Faraday M

1852 Phil. Mag 4, 3 401

[3] Maxwell J C 1856 Trans Camb Phil Soc 10 27; Maxwell J C 1861 Phil Mag 21 161; Maxwell J

C 1865 Phil Trans R Soc London 155 Part III.

[4] Weber W E 1846 Abh Leibnizens Ges. Leip 316; Weber W E 1846 Ander Phys 73 229; Wilhelm

Weber’s Werke 1-6 1893 Berlin Julius Springer; Ampere A M 1823 Mem Acad R Sci 6 175;

Memoires sur l’Electrodynamique vol I 1882 Paris Gauthier Villars

[5] Smirnov-Rueda R 2005 On the incompleteness of Hertz’s experiments on propagation of

electromagnetic interactions (arXiv: physics.hist-ph/0510015)

[6] Bork A M 1967 Maxwell and the vector potential Isis 58 210-222

[7] Heaviside O 1888-1889 Electromagnetic waves, the propagation of potential, and the

electromagnetic effects of a moving charge The Electrician

[8] Konopinski E J 1978 What the electromagnetic vector potential describes Am J Phys 46 499

[9] Konopinski E J 1978 What the electromagnetic vector potential describes Am J Phys 46 500

[10] Konopinski E J 1978 What the electromagnetic vector potential describes Am J Phys 46 499

[11] Olario S and Popescu I 1985 The quantum effects of electromagnetic fluxes Revs Mod Phys 57 2

339

[12] Liebowitz B 1965 Significance of the Aharonov-Bohm effect Il Nuovo Cimento 38 2 932

[13] Chambers R 1960 Shift of an electron interference pattern by enclosed magnetic flux Phys Rev

Lett 5 3

[14] Boyer T 1985 Comments on experiments related to the Aharonov-Bohm phase shift Found Phys

57 2 339

[15] Varma R K 2012 Curl-free vector potential observation on the macroscale for charged particles

in a magnetic field compared with that on the micro-scale: the Aharonov-Bohm effect Phys

Scr 86 045009

[16] Varma R K 2010 Observability of the effects of curl-free magnetic vector potential on the

macroscale and the nature of the ‘transition amplitude wave’ Pramana J Phys 74 4 491-511

[17] Varma R K 2012 From hunches to surprises – discovering macro-scale quantum phenomena in

charged particle dynamics Current Sci 103 5 497

[18] Varma R K 2007 Quantum manifestation of systems on the macroscale – the concept of transition

state and transition amplitude wave Pramana J Phys 68 6 901

Vigier

IOP Conf. Series: Journal of Physics: Conf. Series 1251 (2019) 012043

IOP Publishing

doi:10.1088/1742-6596/1251/1/012043

19

[19] Varma R K Puntihavelu P K and Banerjee S B 2002 Observation of matter wave beat phenomena

in the macrodomain for electrons moving along a magnetic field Phys Rev E 6 026503

[20] Shukla P K 2012 Curl-free vector potential observed at the macroscale Phys Scr 86 048201

[21] Giuliani G 2010 Vector potential, electromagnetic induction and ‘physical meaning’ (arXiv.org/

physics.hist-ph/1005.2350v1); Blondel A 1914 Sur l’é noncé le plus general des lois de

l’induction Compte Rend Ac Sc bf159 674 (http://gallica.bnf.fr)

[22] Rousseaux G Kofman R and Minazzoli O 2008 The Maxwell-Lodge effect: significance of

electromagnetic potentials in the classical theory Eur Phys J D 10 1140

[23] Leus V A Smith R T and Maher S 2013 The physical entity of vector potential in

electromagnetism App Phys Res 54 56

[24] Daibo M 2016 Vector potential generation device, vector potential transformer US Patent Appl

20160300652A1

[25] Daibo M Oshima B Sasaki Y and Sugiyama K 2013 Vector potential coil and transformer IEEE

Trans On Magn 51 11 100604

[26] Nikolova N K and Zimmerman R K 2007 Detection of the time-dependent electromagnetic

potential at 1.3 Ghz CEM-R-46, Dept of Electrical and Computer Engineering McMaster Univ

[27] Bettini G 2011 Clifford Algebra 3- and 4-dimensional analytic functions with applications,

Manuscripts of the last century (viXra.org), Quantum Physics, 1-63 (http://viXra.org/abs/

1107.0060)

[28] Bettini G 2012 Can electromagnetic scalar waves be radiated by a metal sphere?

(viXraorg/pdf/abs/1109.0034v1.pdf)

[29] Aharonov Y and Bohm D 1959 Significance of electromagnetic potentials in the quantum theory

Phys Rev 115 485-491

[30] Fock V and Podolsky E 1932 On the quantization of electro-magnetic waves and the interaction

of charges in Dirac theory reprinted in Fock V A Selected Work – Quantum Mechanics and

Quntum Field Theory 225-241 ed. L D Faddeev et al New York NY Chapman & Hall/CRC

[31] Arbab A I and Satti Z A 2009 On the generalized Maxwell’s equations and their prediction of

the electroscalar wave Prog Phys 28 8-13

[32] Arbab A I 2018 The modified electromagnetism and the emergent of longitudinal wave

(arXiv/abs/physics.gen-phys/1403.2687)

[33] Tomilin A K 2017 J Electromagn Anal Appl 5 347; 2017 Pro Electromagn Res Symp St

Petersburg Russia 1414

[34] van Vlaenderen K and Waser A 2001 Generalization of classical electrodynamics to admit a

scalar field and longitudinal waves Hadronic Journal 24 pp 609-628

[35] van Vlaenderen K 2003 A generalization of classical electrodynamics for the prediction of scalar

field effects (arXiv e-prints, https://arxiv.org/pdf/physics/0305098.pdf)

[36] Celani F Di Tommaso A and Vassallo G 2017 Maxwell’s equations and Occam’s razor J

Condensed Matter Nucl Sci 25 1-29

[37] Hively L M 2012 Toward a more complete electrodynamic theory Int J Signals and Imaging

systems Eng 51

[38] Hively L M 2015 Implications of a new electrodynamic theory (https:/www.researchgate.net)

[39] Woodside D A 1999 Uniqueness theorems for classical four-vector fields in Euclidean and

Minkowski spaces J Math Phys 40 4911

[40] Woodside D A 2000 Classical four-vector fields in the longitudinal gauge J Math Phys 41 4622

[41] Woodside D A 2009 Three-vector and scalar field identities and uniqueness theorems in

Euclidean and Minkowski spaces Am J Phys 77 438

[42] Hively L M April 2016 Methods and apparatus for generation and detection of a scalar

longitudinal electromagnetic wave US Patent 9,306,527

[43] Valone T ed. 2013 Nikola Tesla’s Electricity Unplugged Ultimate Adventures Pub

[44] Monstein C & Wesley J P 2002 Observation of scalar longitudinal electrodynamic waves

Europhys Lett 594 514-520

Vigier

IOP Conf. Series: Journal of Physics: Conf. Series 1251 (2019) 012043

IOP Publishing

doi:10.1088/1742-6596/1251/1/012043

20

[45] Meyl K 2000 Teslastrahlumg – die drahtlose Ubertragung von Skallerwellen INET Congress

aumenergie –technologie Bregenz Austria

[46] Park L Aug 2008 US Patent 8,023,360, Seismic Activity Detector

[47] Zaimidoroga O 2016 An electroscalar energy of the sun Jour Mod Phys 7 806

[48] Wesley J P 1990a Weber electrodynamics: Part I – general theory, steady current effects Found

Phys Lett 3 443-469

[49] Camara C G Escobar J V Hird J R and Putterman S J 2008 Correlation between nanosecond x-

ray flashes and stick-slip friction in peeling tape Nature 455 1089

[50] Constance E Horvat J and Lewis R A 2010 Mechanisms of x-ray emissions from peeling of

adhesive tape Appl Phys Lett 97 131502

[51] Rein G 1991 Effect of non-Hertzian scalar waves on the immune system Health Consc; Rein G

The biological effects of quantum fields (www.item-bioenergy.com/infocenter/

biologicaleffectsofquantumfields.pdf )

[52] Andreev E Dovbeshko G and Krasnoholovets 2007 The study of the influence of the TESLAR

technology on aqueous solution of bio-molecules Res Lett in Phys Chem Article ID 94286

[53] Krasnoholovets V and Tane Jean Louis 2006 An extended interpretation of the thermodynamic

theory including an additional energy associated with a decrease in mass International Journal

of Simulation and Model Processing 2 1-2 67-79

[54] Szabo I Sodderman M Leanza L and Gubbins E 2011 Cell Death and Differentiation 18 427

[55] Alken P Moute A and Richmond A D 2016 The F-region gravity and pressure gradient current

systems: a review Space Sci Rev 1-19

[56] Peralta R G and Andino S 2015 Electrical neuroimaging with irrotational sources Comput Math

in Medecine 8010307