Scalar Wave Effects

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Prof.

Prof. Konstantin MeylKonstantin Meyl, Ph.D., Ph.D.

Faculty of Computer and Electrical Engineering, Faculty of Computer and Electrical Engineering, Furtwangen University, Germany

Furtwangen University, Germany e-mail: [email protected]

e-mail: [email protected]

Scalar Wave Effects according to Tesla

Field-physical basis for electrically coupled bidirectional

far range transponders, such as Tesla’s Wardenclyffe Tower

Abstract

With the current RFID technology the transfer of energy takes place on a With the current RFID technology the transfer of energy takes place on a chip card by means of longitudinal wave components in close range of the chip card by means of longitudinal wave components in close range of the transmitting antenna. Those are scalar waves, which spread towards the transmitting antenna. Those are scalar waves, which spread towards the electrical or the magnetic field pointer.

electrical or the magnetic field pointer.

In the wave equation with reference to the Maxwell field equations, these In the wave equation with reference to the Maxwell field equations, these wave components are set to zero, why only postulated model computations wave components are set to zero, why only postulated model computations exist, after which the range is limited to the sixth part of the wavelength. exist, after which the range is limited to the sixth part of the wavelength. A goal of this paper is to create, by consideration of the scalar wave A goal of this paper is to create, by consideration of the scalar wave compo-nents in the wave equation, the physical conditions for the development of nents in the wave equation, the physical conditions for the development of scalar wave transponders which are operable beyond the close range. The scalar wave transponders which are operable beyond the close range. The energy is transferred with the same carrier wave as the information and energy is transferred with the same carrier wave as the information and not over two separated ways as with RFID systems. Besides the not over two separated ways as with RFID systems. Besides the bi-direc-tional signal transmission, the energy transfer in both directions is tional signal transmission, the energy transfer in both directions is addi-tionally possible because of the resonant coupling between transmitter and tionally possible because of the resonant coupling between transmitter and receiver.

receiver.

First far range transponders developed on the basis of the extended field First far range transponders developed on the basis of the extended field equations are already functional as prototypes, according to the US-Patent equations are already functional as prototypes, according to the US-Patent No. 787,412 of Nikola Tesla, New York 1905 [1].

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Key words

Longitudinal wave, scalar wave, Tesla radiation, RFID, field theory. Longitudinal wave, scalar wave, Tesla radiation, RFID, field theory.

1. Introduction

Abstract of the practical setting of tasks

Transponders serve the transmission of energy e.g. on a chip card in Transponders serve the transmission of energy e.g. on a chip card in co

combmbininatatioion n wiwith th a a baback ck trtranansmsmissiission on of of ininfoformrmatatioion. n. ThThe e rarangnge e isis with the presently marketable devices (RFID technology) under one with the presently marketable devices (RFID technology) under one me-ter [2]. The energy receiver must be in addition in close range of the ter [2]. The energy receiver must be in addition in close range of the transmitter.

transmitter.

The far range transponders developed by the first transfer centre for The far range transponders developed by the first transfer centre for sca-lar wave technology are able to transfer energy beyond close range (10 to lar wave technology are able to transfer energy beyond close range (10 to 100 m) and besides with fewer losses and/or a higher efficiency. The 100 m) and besides with fewer losses and/or a higher efficiency. The en-ergy with the same carrier wave is transferred as the information and ergy with the same carrier wave is transferred as the information and not as with the RFID technology over two separated systems [2].

not as with the RFID technology over two separated systems [2].

A condition for new technologies is a technical-physical understanding, A condition for new technologies is a technical-physical understanding, as well as a mathematically correct and comprehensive field description, as well as a mathematically correct and comprehensive field description, which include all well known effects of close range of an antenna. We which include all well known effects of close range of an antenna. We en-counter here a central problem of the field theory, which forms the counter here a central problem of the field theory, which forms the em-phasis of this paper and the basis for advancements in the transponder phasis of this paper and the basis for advancements in the transponder technology.

technology.

Requirements at transponders

In today's times of Blue tooth and Wireless LAN one accustomed fast to In today's times of Blue tooth and Wireless LAN one accustomed fast to the amenities of wireless communication. These open for example garage the amenities of wireless communication. These open for example garage gates, the barrier of the parking lot or the trunk is lid only by radio. gates, the barrier of the parking lot or the trunk is lid only by radio. However, in the life span limited and the often polluting batteries in the However, in the life span limited and the often polluting batteries in the numer

numerous ous radio transmitradio transmitters and ters and remotremote e maintmaintenancenance e are are of of great disad-great disad-vantage.

vantage.

Ever more frequently the developers see themselves confronted with the Ever more frequently the developers see themselves confronted with the 244

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But new areas of application with increased requirements are constantly But new areas of application with increased requirements are constantly added apart from the desire for a larger range:

added apart from the desire for a larger range: •

• in telemetry plants rotary sensors are to be supplied with energy (in thein telemetry plants rotary sensors are to be supplied with energy (in the car e.g. to control tire pressure).

car e.g. to control tire pressure).

•

• also with heat meters the energy should come from a central unit and bealso with heat meters the energy should come from a central unit and be spread wirelessly in the whole house to the heating cost meters without

spread wirelessly in the whole house to the heating cost meters without

the use of batteries

•

• in airports contents of freight containers are to be seized, without thesein airports contents of freight containers are to be seized, without these to having be opened (security checks).

to having be opened (security checks).

•

• ththe e foforwrwarardiding ng trtradade e wawantnts s to to exaexaminmine e clclososed ed trtrucuck k chachargrges es by by trtranan- - sponder technology.

sponder technology.

•

• in the robot and handling technique the wirings are to be replaced by ain the robot and handling technique the wirings are to be replaced by a wireless technology (wear problem).

wireless technology (wear problem).

•

• porportabltable e radradio io devdevicesices, , mobmobile ile phophones, nes, NotNotebooebooks ks and and remremote ote concontrotrolsls wo

workrkining g witwithohout ut babattttereries ies anand d AcAccumcumululatatorors s (r(redueductctioion n of of ththe e enenvi-

vi-ron-mental impact).

ron-mental impact).

A technical solution, which is based on pure experimenting and trying, is A technical solution, which is based on pure experimenting and trying, is to be optimised unsatisfactorily and hardly. It should stand rather on a to be optimised unsatisfactorily and hardly. It should stand rather on a field-theoretically secured foundation, whereby everyone thinks first of field-theoretically secured foundation, whereby everyone thinks first of Maxwell’s field equations. Here however a new hurdle develops itself Maxwell’s field equations. Here however a new hurdle develops itself un-der close occupation.

der close occupation.

Problem of the field theory

In the close range of an antenna, so the current level of knowledge is, are In the close range of an antenna, so the current level of knowledge is, are longitudinal -towards a field pointer, portions of the radiated wave longitudinal -towards a field pointer, portions of the radiated wave pres-en

ent. t. ThThesese e arare e ususabable le in in ththe e trtrananspsponondeder r tetechchnonolology gy fofor r ththe e wiwirerelelessss transmission of energy. The range amounts to however only

transmission of energy. The range amounts to however onlyll /2 /2 p p and thatand that is approximately the sixth part of the wavelength [3].

is approximately the sixth part of the wavelength [3].

The problem consists now of the fact that the valid field theory, and that The problem consists now of the fact that the valid field theory, and that is from Maxwell, only is able to describes transversal and no longitudinal is from Maxwell, only is able to describes transversal and no longitudinal wave components. All computations of longitudinal waves or wave wave components. All computations of longitudinal waves or wave com-ponents, which run toward the electrical or the magnetic pointer of the ponents, which run toward the electrical or the magnetic pointer of the field, are based without exception on postulates [4].

field, are based without exception on postulates [4].

Annual Report on the Activities of the Croatian Academy of Engineering (HATZ) in 2006

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Field equations according to Maxwell

A short derivation brings it to light. We start with the law of induction A short derivation brings it to light. We start with the law of induction

according to the textbooks according to the textbooks

curl

curl EE = = –– ddBB / / ddtt ((11..11)) with the electric field strength

with the electric field strength EE == EE((rr,t) and the magnetic field strength,t) and the magnetic field strength H

H == HH((rr,t),t) and:

and: BB == mm ·· HH ((11. . rreellaattiioon n oof f mmaatteerriiaall)), , ((11..22)) apply the curl-operation to both sides of the equation

apply the curl-operation to both sides of the equation – curl curl

– curl curl EE == mm ·· dd(curl(curl HH)/ )/ ddt t ((11..33)) and insert in the place of curl

and insert in the place of curl HH Ampere’s law:Ampere’s law: curl curl HH == jj ++ ddDD / / ddt t ((11..44)) with with jj == s s · · E E ((OOhhmm’’s s llaaww) ) ((11..55)) with with DD == ee · · E (E (22. . rreellaattiioon n oof f mmaatteerriiaall) ) ((11..66)) and and tt₁₁ == ee / / s s ((rreellaaxxaattiioon n ttiimme e [[55]]) ) ((11..77)) curl curl HH == ee · · ((EE / / t t₁₁ ++ ddEE / / ddtt) ) ((11..88)) – curl curl – curl curl EE == mm ·· ee · (1/ · (1/ t t₁₁ ·· ddEE / / ddt t ++ dd22_E_E_/_/_d_dt_t22₎₎ ₍₍₁_1._.9₉₎₎

with the abbreviation:

with the abbreviation: mm ·· ee = 1/c= 1/c22_._. ₍₍₁_1._.1₁₀₀₎₎

The generally known result describes a

The generally known result describes a damped damped electrelectro-magno-magnetic etic wavewave [6]: [6]: – curl curl – curl curl EE · · cc22 ₌₌ _d_d22_E_E_/_/_d_dt_t22 _{+ (1/}_{+ (1/}_t_t 1 1) ) ·· ddEE / / ddt t ((11..1111)) tr

tranansvsveersrse e – – wawave ve + + vovortrteex x dadampmpining g 246

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ing waves, which can be also called field vortices, that produce vortex ing waves, which can be also called field vortices, that produce vortex losses for their part with the time constant

losses for their part with the time constant tt₁₁ in the form of heat.in the form of heat.

Where however do, at close range of an antenna proven and with Where however do, at close range of an antenna proven and with tran-sponders technically used longitudinal wave components hide themselves sponders technically used longitudinal wave components hide themselves in the field equation (1.11)?

in the field equation (1.11)?

Wave equation according to Laplace

Wave equation according to Laplace T

The he wwaavve e eeqquuaattiioon n ffouounnd d iin n mmosost t tteexxttbboookoks s hhaas s ththe e ffoorrm m oof f aann inh

inhomoomogengeneoueous s LapLaplaclace e equequatiation. on. The The famfamous ous FreFrench nch matmathemhematiaticiaciann Laplace

Laplace considerably earlier than Maxwell did find a comprehensive for-considerably earlier than Maxwell did find a comprehensive for-mulation of waves and formulated it mathematically:

mulation of waves and formulated it mathematically: D

DEE · · cc22 _{= – curl curl}_{= – curl curl} _E_E _·_·_c_c22 _{+ grad div}_{+ grad div} _E_E _·_{· c}_c22 ₌₌ _d_d22_E_E_/_/_d_dt_t22 _(1.12)_(1.12)

L

Laappllaacce e ttrraannssvveerrssee- - lloonnggiittuuddiinnaall- - wwaavvee o

oppeerraattoor r ((rraaddiio o wwaavvee) ) ((ssccaallaar r wwaavvee))

On the one side of the wave equation the Laplace operator stands, which On the one side of the wave equation the Laplace operator stands, which describes the spatial field distribution and which according to the rules of describes the spatial field distribution and which according to the rules of vector analysis can be decomposed into two parts. On the other side the vector analysis can be decomposed into two parts. On the other side the de

descscririptptioion n of of ththe e titime me dedepependndenency cy of of ththe e wawave ve cacan n be be fofounund d as as anan inhomogeneous term.

inhomogeneous term.

The wave equations in the comparison

If the wave equation according to Laplace (1.12) is compared to the one, If the wave equation according to Laplace (1.12) is compared to the one, which the Maxwell equations have brought us (1.11), then two which the Maxwell equations have brought us (1.11), then two differ-ences clearly come forward:

ences clearly come forward: 1.

1. In the Laplace equation the damping term is missing.In the Laplace equation the damping term is missing. 2.

2. With divergenceWith divergence EE a scalar factor appears in the wave equation, whicha scalar factor appears in the wave equation, which

founds a scalar wave.

One practical example of a scalar wave is the plasma wave. This case One practical example of a scalar wave is the plasma wave. This case

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the space charge density consisting of charge carriers

the space charge density consisting of charge carriers rr_el_el the scalar por-the scalar por-tion. These move in form of a shock wave longitudinal forward and tion. These move in form of a shock wave longitudinal forward and pres-ent in its whole an electric currpres-ent.

ent in its whole an electric current.

Since both descriptions of waves possess equal validity, we are entitled in Since both descriptions of waves possess equal validity, we are entitled in the sense of a coefficient comparison to equate the damping term due to the sense of a coefficient comparison to equate the damping term due to eddy currents according to Maxwell (1.11) with the scalar wave term eddy currents according to Maxwell (1.11) with the scalar wave term ac-cording to Laplace (1.12).

cording to Laplace (1.12).

Physically seen the generated field vortices form and establish a scalar Physically seen the generated field vortices form and establish a scalar wave.

wave.

The presence of div

The presence of div EE proves a necessary condition for the occurrence of proves a necessary condition for the occurrence of eddy currents. Because of the well known skin effect [7] expanding and eddy currents. Because of the well known skin effect [7] expanding and damping acting eddy currents, which appear as consequence of a current damping acting eddy currents, which appear as consequence of a current density

density jj , set ahead however an electrical conductivity, set ahead however an electrical conductivity s s (acc. to eq. 1.5).(acc. to eq. 1.5).

The view of duality

Within the near field range of an antenna opposite conditions are Within the near field range of an antenna opposite conditions are pres-ent. With bad conductivity in a general manner a vortex with dual ent. With bad conductivity in a general manner a vortex with dual char-act

acterierististics cs wouwould ld be be demdemandanded ed for for the the formformatiation on of of lonlongitgitudiudinal nal wavwavee components. I want to call this contracting antivortex, unlike to the components. I want to call this contracting antivortex, unlike to the ex-panding eddy current, a potential vortex.

panding eddy current, a potential vortex.

If we examine the potential vortex with the Maxwell equations for valid If we examine the potential vortex with the Maxwell equations for valid- -ity and compatibil-ity, then we would be forced to let it fall directly again. ity and compatibility, then we would be forced to let it fall directly again. The derivation of the damped wave equation (1.1 to 1.11) can take place The derivation of the damped wave equation (1.1 to 1.11) can take place in place of the electrical, also for the magnetic field strength. Both wave in place of the electrical, also for the magnetic field strength. Both wave eq

equauatitionons s (1(1.1.11 1 and and 1.1.1212) ) do do nonot t chchanange ge ththererebeby y ththeieir r shshapape. e. In In ththee inhomogeneous Laplace equation in this dual case however, the inhomogeneous Laplace equation in this dual case however, the longitudi-nal scalar wave component through div

nal scalar wave component through div HH is described and this is accord-is described and this is accord-ing to Maxwell zero!

ing to Maxwell zero! 4.

4. MaMaxwxwelell’l’s es eququatatioion: n: didivv BB == mm · div· div HH = = 0 0 ((11..1144)) If is correct, then there may not be a near field, no wireless transfer of If is correct, then there may not be a near field, no wireless transfer of energy and finally also no transponder technology. Therefore, the energy and finally also no transponder technology. Therefore, the correct-ness is permitted (of eq. 1.14) to question and examine once, what would ness is permitted (of eq. 1.14) to question and examine once, what would 248

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Besid

Besides still es still anotheanother r boundboundary problem will be ary problem will be solvesolved: since d: since in divin div DD elec- elec-trical monopoles can be seen (1.13) there should result from duality to trical monopoles can be seen (1.13) there should result from duality to div

div BB magnetic monopoles (1.14). But the search was so far unsuccessfulmagnetic monopoles (1.14). But the search was so far unsuccessful [8]. Vortex physics will ready have an answer.

[8]. Vortex physics will ready have an answer.

2.

2. The approacThe approachh

Faraday instead of Maxwell

If a measurable phenomenon should, e.g. the close range of an antenna, If a measurable phenomenon should, e.g. the close range of an antenna, not be described with the field equations according to Maxwell not be described with the field equations according to Maxwell mathe-matically, then prospect is to be held after a new approach. All efforts matically, then prospect is to be held after a new approach. All efforts th

that at wawant nt to to prprovove e ththe e cocorrrrecectntnesess s of of ththe e MaMaxwxwelell l ththeoeory ry wiwith th ththee Maxwell theory end inevitably in a tail-chase, which does not prove Maxwell theory end inevitably in a tail-chase, which does not prove any-thing in the end.

thing in the end.

In a new approach high requirements are posed. It may not contradict In a new approach high requirements are posed. It may not contradict the Maxwell theory, since these supply correct results in most practical the Maxwell theory, since these supply correct results in most practical cases and may be seen as confirmed. It would be only an extension cases and may be seen as confirmed. It would be only an extension per-missible, in which the past theory is contained as a subset e.g. Let’s go on missible, in which the past theory is contained as a subset e.g. Let’s go on the quest.

the quest.

Vortex and anti-vortex

In the eye of a tornado the same calm In the eye of a tornado the same calm prevails as at great distance, because prevails as at great distance, because here a vortex and its anti-vortex work here a vortex and its anti-vortex work against each other. In the inside the against each other. In the inside the

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itself with water above the open ocean, then the contracting potential itself with water above the open ocean, then the contracting potential vortex is predominant and the energy density increases threateningly. If vortex is predominant and the energy density increases threateningly. If it however runs overland and rains out, it again becomes bigger and less it however runs overland and rains out, it again becomes bigger and less dangerous.

dangerous.

In fluidics the connections are understood. They are usually also well In fluidics the connections are understood. They are usually also well vis-ible and without further aids observable.

ible and without further aids observable.

In electrical engineering it’s different: here field vortices remain In electrical engineering it’s different: here field vortices remain invisi-ble. Only so a theory could find acceptance, although it only describes ble. Only so a theory could find acceptance, although it only describes mathematically the expanding eddy current and ignores its anti-vortex. I mathematically the expanding eddy current and ignores its anti-vortex. I call the contracting anti-vortex “potential vortex” and point to the call the contracting anti-vortex “potential vortex” and point to the cir-cumstance, that every eddy current entails the anti-vortex as a physical cumstance, that every eddy current entails the anti-vortex as a physical necessity.

necessity.

By this reconciliation it is ensured that the condition in the vortex centre By this reconciliation it is ensured that the condition in the vortex centre corresponds in the infinite one, complete in analogy to fluid mechanics. corresponds in the infinite one, complete in analogy to fluid mechanics.

The Maxwell approximation

The approximation, which is hidden in the Maxwell equations, thus The approximation, which is hidden in the Maxwell equations, thus con-sists of neglecting the anti-vortex dual to the eddy current. It is possible sists of neglecting the anti-vortex dual to the eddy current. It is possible that this approximation is allowed, as long as it only concerns processes that this approximation is allowed, as long as it only concerns processes inside conducting materials. The transition to insulants however, which inside conducting materials. The transition to insulants however, which requires for the laws of the field refraction steadiness, is incompatible requires for the laws of the field refraction steadiness, is incompatible with the acceptance of eddy currents in the cable and a nonvortical field with the acceptance of eddy currents in the cable and a nonvortical field in air. In such a case the Maxwell approximation will lead to considerable in air. In such a case the Maxwell approximation will lead to considerable errors.

errors.

If we take as an example the lightning and ask how the lightning channel If we take as an example the lightning and ask how the lightning channel 250

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We imagine now a spherical vortex, in whose inside an expanding vortex We imagine now a spherical vortex, in whose inside an expanding vortex is enclosed and which is held together from the outside by the is enclosed and which is held together from the outside by the contract-ing potential vortex and is forced into it’s spherical shape. From the ing potential vortex and is forced into it’s spherical shape. From the infi-nite measured this spherical vortex would have an electrical charge and nite measured this spherical vortex would have an electrical charge and all the characteristics of a charge carrier.

all the characteristics of a charge carrier.

The mistake of the magnetic monopole

With the tendency of the potential vortex for contraction, inevitably the With the tendency of the potential vortex for contraction, inevitably the ability is linked to a structural formation. The particularly obvious ability is linked to a structural formation. The particularly obvious struc-ture of a ball would be besides an useful model for quanta.

ture of a ball would be besides an useful model for quanta.

A to the sphere formed field-vortex would be described mathematically in A to the sphere formed field-vortex would be described mathematically in

its inside with the expanding vortex div

its inside with the expanding vortex div DD. For the potential vortex work-. For the potential vortex work-ing against from the outside div

ing against from the outside div BB would apply.would apply.

The divergence may be set therefore neither with the electrical field (4th The divergence may be set therefore neither with the electrical field (4th Maxwell equation) nor with the magnetic field (3rd Maxwell equation) to Maxwell equation) nor with the magnetic field (3rd Maxwell equation) to

Annual Report on the Activities of the Croatian Academy of Engineering (HATZ) in 2006 251251

In

Insisidede: : exexpapandndining g ededdy dy cucurrrrenent t (s(skikin n efeffefecct)t) Ou

Outstsidide: e: cocontntraractctining g anantiti-v-vorortex tex (p(pototenentitial al vovortertex)x) Co

Condndititioion: n: for for cocomiming ng offoff: e: eququalally ly popowewerfrful ul vovortrticiceses Cri

Criteriterion: on: eleelectrctric ic conconducductivtivity ity (de(determtermineines s diadiametmeter)er) Res

Resulult: t: spspheheriricacal l strstrucuctuture re (c(cononseseququenence ce of of ththe e prepressssurure e of of the the vavacucuumum))

Figure 2.

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The discovery of the law of induction

In the choice of the approach the physicist is In the choice of the approach the physicist is fr

freeee, , as as lolong ng as as ththe e apapprproacoach h is is rereasasononabablele an

and d wewell ll fofounundeded. d. In In the the cacase se of of MaMaxwxwelell’l’ss fi

fieleld d eqequauatitionons s twtwo o exexpeperirimementntalally ly dedeteter- r-mined regularities served as basis: on the one mined regularities served as basis: on the one hand Ampçre’s law and on the other hand the hand Ampçre’s law and on the other hand the law of induction of Faraday. The law of induction of Faraday. The mathemati-ci

cian an MaMaxxwewelll l ththeerereby by gagave ve ththe e fifininishshiing ng touches for the formulations of both laws. He touches for the formulations of both laws. He int

introdroduceuced d the the disdisplaplacemcement ent curcurrenrent t D D andand completed Ampçre’s law accordingly, and that completed Ampçre’s law accordingly, and that without a chance of already at his time being without a chance of already at his time being able to measure and prove the measure. Only able to measure and prove the measure. Only af

afteter r hihis s dedeatathh this was possible experimentally, what this was possible experimentally, what after-wards makes clear the format of this man. wards makes clear the format of this man. In the formulation of the law of induction In the formulation of the law of induction Max

Maxwelwell l was was comcomplepleteltely y frefree, e, becbecausause e thethe discoverer

discoverer MicMichaehael l FFaraaradayday hahad d dodonene without specifications. As a man of practice without specifications. As a man of practice and

and of of expexperierimenment t the the matmathemhematiatical cal notnota- a-tion was less important for Faraday. For him tion was less important for Faraday. For him the attempts with which he could show his the attempts with which he could show his discovery of the induction to everybody, e.g. discovery of the induction to everybody, e.g. hi

his s ununipipololar ar gegeneneraratotorr, , ststooood d in in ththe e foforere- -ground.

ground.

His 40 years younger friend and professor of mathematics Maxwell His 40 years younger friend and professor of mathematics Maxwell how-252

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magnetism and the representation as something unified and belonging magnetism and the representation as something unified and belonging togeth

together [10]er [10]than for than for mathemathematicmatically giving reasons for ally giving reasons for the principlthe principle dis-e dis-covered by Faraday.

covered by Faraday.

Nevertheless the question should be asked, if Maxwell has found the Nevertheless the question should be asked, if Maxwell has found the suit-able formulation, if he has understood 100 percent correct his friend able formulation, if he has understood 100 percent correct his friend Far-aday and his discovery. If discovery (from 29.08.1831) and mathematical aday and his discovery. If discovery (from 29.08.1831) and mathematical formulation (1862) stem from two different scientists, who in addition formulation (1862) stem from two different scientists, who in addition be-long to different disciplines, misunderstandings are nothing unusual. It long to different disciplines, misunderstandings are nothing unusual. It will be helpful to work out the differences.

will be helpful to work out the differences.

The unipolar generator

If one turns an axially polarized magnet or a copper disc situated in a If one turns an axially polarized magnet or a copper disc situated in a magnetic field, then perpendicular to the direction of motion and magnetic field, then perpendicular to the direction of motion and perpen-dicular to the magnetic field pointer a pointer of the electric field will dicular to the magnetic field pointer a pointer of the electric field will oc-cur, which everywhere points axially to the outside. In the case of this by cur, which everywhere points axially to the outside. In the case of this by F

Faraaraday day devdeveloeloped unipoped unipolar lar gengeneraerator tor henhence ce by by meameans ns of of a a brubrush sh be- be-tween the rotation axis and the circumference a tension voltage can be tween the rotation axis and the circumference a tension voltage can be called off.

called off.

The mathematically correct relation The mathematically correct relation

E

E == vv xx BB (2.1)(2.1) I call Faraday-law, even if it only appears in this form in the textbooks I call Faraday-law, even if it only appears in this form in the textbooks later in time [11]. The formulation usually is attributed to the later in time [11]. The formulation usually is attributed to the mathema-tician

tician Hendrik LorentzHendrik Lorentz, since it appears in the Lorentz force in exactly, since it appears in the Lorentz force in exactly this form. Much more important than the mathematical formalism this form. Much more important than the mathematical formalism how-ever are the experimental results and the discovery by Michael Faraday, ever are the experimental results and the discovery by Michael Faraday,

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In that place stands the time derivation of

In that place stands the time derivation of BB, with which a change in flux, with which a change in flux is necessary for an electric field strength to occur. As a consequence the is necessary for an electric field strength to occur. As a consequence the Maxwell equation doesn’t provide a result in the static or Maxwell equation doesn’t provide a result in the static or quasi-station-ary case, for which reason it in such cases is usual, to fall back upon the ary case, for which reason it in such cases is usual, to fall back upon the un

unipipololar ar inindducuctition on acaccocordrdining g to to FarFaradaday ay ((e.e.g. g. in in the the cacasse e of of ththee Hall-probe, the picture tube, etc.). The falling back should only remain Hall-probe, the picture tube, etc.). The falling back should only remain restricted to such cases, so the normally used idea. But with which right restricted to such cases, so the normally used idea. But with which right the restriction of the Faraday-law to stationary processes is made?

the restriction of the Faraday-law to stationary processes is made? 254

254 Meyl, K.:Meyl, K.: Scalar Wave Effects according to TeslaScalar Wave Effects according to Tesla

Figure 5.

Figure 5. Two formulations for one law: As a mathematical relation between theTwo formulations for one law: As a mathematical relation between the vectors of the electric field strength

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pointers however stand perpendicular to each other, so that the magnetic pointers however stand perpendicular to each other, so that the magnetic field pointer wraps around the pointer of the electric field in the form of a field pointer wraps around the pointer of the electric field in the form of a vortex ring in the case that the electric field strength is being measured vortex ring in the case that the electric field strength is being measured and vice versa. The closed-loop field lines are acting neutral to the and vice versa. The closed-loop field lines are acting neutral to the out-side; they hence need no attention, so the normally used idea. It should side; they hence need no attention, so the normally used idea. It should be examined more closely if this is sufficient as an explanation for the be examined more closely if this is sufficient as an explanation for the ne-glect of the not measurable closed-loop field lines, or if not after all an glect of the not measurable closed-loop field lines, or if not after all an ef-fect arises from fields, which are present in reality.

fect arises from fields, which are present in reality. Another difference concerns the commutability of

Another difference concerns the commutability of EE- and- and HH-field, as is-field, as is sho

shown wn by by the the FFaradayaraday-ge-generneratoatorr, , how how a a magmagnetnetic ic becbecomeomes s an an eleelectrctricic field and vice versa as a result of a relative velocity v. This directly field and vice versa as a result of a relative velocity v. This directly influ-ences the physical-philosophic question: What is meant by the ences the physical-philosophic question: What is meant by the electro-magnetic field?

magnetic field?

The electromagnetic field

The textbook opinion based on the Maxwell equations names the static The textbook opinion based on the Maxwell equations names the static field of the charge carriers as cause for the electric field, whereas moving field of the charge carriers as cause for the electric field, whereas moving ones cause the magnetic field [7, i.e.]. But that hardly can have been the ones cause the magnetic field [7, i.e.]. But that hardly can have been the idea of Faraday, to whom the existence of charge carriers was completely idea of Faraday, to whom the existence of charge carriers was completely

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Contradictory opinions in textbooks

Obviously there exist two formulations for the law of induction (2.1 and 2.2), Obviously there exist two formulations for the law of induction (2.1 and 2.2), which more or less have equal rights. Science stands for the question: which which more or less have equal rights. Science stands for the question: which mathematical description is the more efficient one? If one case is a special mathematical description is the more efficient one? If one case is a special case of the other case, which description then is the more universal one? case of the other case, which description then is the more universal one? What Maxwell’s field equations tell us is sufficiently known, so that What Maxwell’s field equations tell us is sufficiently known, so that deriva-tions are unnecessary. Numerous textbooks are standing by, if results should tions are unnecessary. Numerous textbooks are standing by, if results should be cited. Let us hence turn to the Faraday-law (2.1). Often one searches in be cited. Let us hence turn to the Faraday-law (2.1). Often one searches in vain for this law in schoolbooks. Only in more pretentious books one makes vain for this law in schoolbooks. Only in more pretentious books one makes a find under the keyword “unipolar induction”. If one however compares a find under the keyword “unipolar induction”. If one however compares the number of pages, which are spent on the law of induction according to the number of pages, which are spent on the law of induction according to Maxwell with the few pages for the unipolar induction, then one gets the Maxwell with the few pages for the unipolar induction, then one gets the impression that the latter only is a unimportant special case for low impression that the latter only is a unimportant special case for low fre-quencies.

quencies. KüpfmüllerKüpfmüller speaks of a “special form of the law of induction”speaks of a “special form of the law of induction” [12], and cites as practical examples the induction in a brake disc and the [12], and cites as practical examples the induction in a brake disc and the Hal

Hall-el-effeffect. ct. AfAfterterwarwards ds KüpKüpfmüfmülleller r derderiveives s frofrom m the the “sp“speciecial al forform” m” thethe “general form” of the law of induction according to Maxwell, a postulated “general form” of the law of induction according to Maxwell, a postulated generalization, which needs an explanation. But a reason is not given [12]. generalization, which needs an explanation. But a reason is not given [12]. Bosse

Bosse gives the same derivation, but for him the Maxwell-result is thegives the same derivation, but for him the Maxwell-result is the special case and not his Faraday approach [13]! In addition he addresses special case and not his Faraday approach [13]! In addition he addresses 256

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Written down according to the rules of duality there results an equation Written down according to the rules of duality there results an equation

(2.3), which occasionally is mentioned in some textbooks. (2.3), which occasionally is mentioned in some textbooks.

While both equations in the books of Pohl [14, p.76 and 130] and of While both equations in the books of Pohl [14, p.76 and 130] and of

Simonyi

Simonyi [15] are written down side by side having equal rights and are[15] are written down side by side having equal rights and are com

comparpared ed witwith h eaceach h othotherer,, GrimsehlGrimsehl [16] [16] derderiveives s the the duadual l regregulaularitrityy (2.3) with the help of the example of a thin, positively charged and (2.3) with the help of the example of a thin, positively charged and rotat-ing metal rrotat-ing. He speaks of “equation of convection”, accordrotat-ing to which ing metal ring. He speaks of “equation of convection”, according to which moving charges produce a magnetic field and so-called convection moving charges produce a magnetic field and so-called convection cur-re

rentntss. . DoDoining g so so he he rerefefers rs to to woworkrkinings gs of of RöntgenRöntgen 1885,1885, Himstedt,Himstedt,

Rowland

Rowland 1876,1876, EichenwaldEichenwald and many others more, which today hardlyand many others more, which today hardly are known.

are known.

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tions and the scopes of the derived theories should result correctly, e.g. of tions and the scopes of the derived theories should result correctly, e.g. of what the Maxwell approximation consists and why the Maxwell what the Maxwell approximation consists and why the Maxwell equa-tions describe only a special case.

tions describe only a special case.

Derivation of the field equations acc. to Maxwell

As a starting-point and as approach serve the equations of As a starting-point and as approach serve the equations of

transforma-tion of the electromagnetic field, the Faraday-law of

tion of the electromagnetic field, the Faraday-law of unipolar inductionunipolar induction (2.1) and the according to the rules of duality formulated law called

(2.1) and the according to the rules of duality formulated law called equa-

equa-tion of convecequa-tion tion of convection (2.3).(2.3). E E == vv xx BB (2.1)(2.1) and and H H = = –– vv xx DD (2.3)(2.3) If we apply the curl to both sides of the equations:

If we apply the curl to both sides of the equations: curl

curl EE = curl (= curl (vv xx BB) ) ((33..11)) and

and 258

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One term concerns ’the vector gradient (

One term concerns ’the vector gradient (vv grad)grad)BB, which can be repre-, which can be repre-sented as a tensor. By writing down and solving the accompanying sented as a tensor. By writing down and solving the accompanying deriv-ative matrix giving consideration to the above determination of the

ative matrix giving consideration to the above determination of the vv-vec- -vec-tor, the vector gradient becomes the simple time derivation of the field tor, the vector gradient becomes the simple time derivation of the field vector vector BB((rr(t)),(t)), ( (vv grad)grad)BB == dd dt dt B B a annd d ((vv grad)grad)DD == dd dt dt D D , , ((33..66)) according to the rule [17]:

according to the rule [17]: d d tt dt dt t t d d tt dt dt V V r r V V r r rr r r r r ( ( ( ( ))) ) ( ( ( ( ))) ) ( ( )) = = ¶¶ == × × == ¶ ¶ ((vv grad)grad)V V . . ((33..77))

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moves with the velocity

moves with the velocity vv for instance through a conductor (in the x-di-for instance through a conductor (in the x-di-rection).

rection).

The current density

The current density jj and the dual potential densityand the dual potential density bb mathematicallymathematically seen at first are nothing but alternative vectors for an abbreviated seen at first are nothing but alternative vectors for an abbreviated nota-tion. While for the current density

tion. While for the current density jj the physical meaning already couldthe physical meaning already could be clarified from the comparison with the law of Ampçre, the be clarified from the comparison with the law of Ampçre, the interpreta-tion of the potential density

tion of the potential density bb still is due:still is due: b

b = = –– vv divdiv BB ((= = 00) ) , , ((33..1100)) From the comparison of eq. 3.8 with the law of induction (eq.1.1) we From the comparison of eq. 3.8 with the law of induction (eq.1.1) we merely infer, that according to the Maxwell theory this term is assumed merely infer, that according to the Maxwell theory this term is assumed to be

to be zero. But that zero. But that is is exacexactly the tly the MaxweMaxwell approximall approximation and tion and the restricthe restric- -tion with regard to the new and dual field approach, which roots in tion with regard to the new and dual field approach, which roots in Fara-260

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duced and by means of the calculation of a complex dielectric constant a duced and by means of the calculation of a complex dielectric constant a loss angle is determined. Mathematically the approach is correct and loss angle is determined. Mathematically the approach is correct and di-electric losses can be calculated.

electric losses can be calculated. Physic

Physically however the ally however the resulresult t is is extreextremely questiomely questionablenable, , since as since as a a conseconse- -quence of a complex

quence of a complex ee a complex speed of light would result,a complex speed of light would result, ac

accocordrdining tg to to the he dedefifininitiontion: : c = 1c = 1/ / e e ××mm (3.12).(3.12). With that electrodynamics offends against all specifications of the With that electrodynamics offends against all specifications of the text-books, according to which c is constant and not variable and less then books, according to which c is constant and not variable and less then ever complex.

ever complex.

But if the result of the derivation physically is wrong, then something But if the result of the derivation physically is wrong, then something

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and the relation of material and the relation of material

D

D = = ((((E E ((11..66)) the current density

the current density

j

j = = DD//((1 1 ((33..1133)) al

also so cacan n be be wrwrititteten n dodown wn as as didielelecectrtric ic didispsplalacecemement nt currecurrent nt wiwith th ththee characteristic relaxation time constant for the eddy currents

characteristic relaxation time constant for the eddy currents (

(1 1 = = ((//( ( ((11..77)).. 262

262 Meyl, K.:Meyl, K.: Scalar Wave Effects according to TeslaScalar Wave Effects according to Tesla

ε ε ·· EE τ τ₁₁ == εε//σσ τ τ₁₁ D D D D