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Scalar Waves
Konstantin Meyl
654 pages
ISBN 3-9802 542-4-0
610-SW ... $55.00


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DESCRIPTION:
From an extended vortex and field theory to a technical, biological and historical use of longitudinal waves.  Edition belonging to the Electromagnetic Environmental Compatibility seminar (part 1 - 3).

From Maxwell's field equations only the well-known (transverse) Hertzian waves can be derived, whereas the calculation of longitudinal electromagnetic waves gives zero as a result.  This is a flaw of the field theory, since longitudinal waves exist for all particle waves, like e.g. as plasma wave, as photon- or neutrino radiation.

Starting from Faradays discovery, instead of the formulation of the law of induction according to Maxwell, an extended field theory is derived, which goes beyond the Maxwell theory with the description of potential vortices (noise vortices) and their propagation as a longitudinal wave, but contains the Maxwell theory as a special case.  With that the extension is allowed and doesn't contradict textbook physics.

Besides the mathematical calculation of longitudinal EM waves this book contains a voluminous material collection concerning their technical use.  What if the useful signal and what would normally be called the interfering noise signal change their places?  What if a separate modulation of frequency and wavelength makes a parallel image transmission possible?  This book also addresses questions concerning the environmental compatibility of electromagnetic energy for the benefit of humanity (bio resonance, among others) or to harm humanity (electro smog).
 


PREFACE:
Preface to the lecture, 1st Edition 1996

The theme encloses the electromagnetic compatibility of both technical and biological systems.  Only part of the electromagnetic wave can be considered for function troubles, namely the part that was absorbed and has rolled up to a vortex.  The activity depends on the number of created vortices and of their lifetime, their decay.  The eddy current only manifests in conducting materials.  In the air and in dielectric" materials on the other hand the vortex of the electric field will form, also called the potential vortex.  To calculate and to measure this vortex is our goal.

First we'll carry out a survey of the problems and the usual methods.  From the analysis of unsolved problems the need for the introduction of the new vortex phenomena is deducted and an adequate field-theoretical approach will be chosen.  Afterwards the potential vortices are calculated and their properties are discussed and interpreted.

For the purpose of proving their existence, on the one hand the Schrodinger equation will be derived and on the other hand the quantum properties of the most important elementary particles will be calculated and compared with the well-known measured values.

Measurement and calculation are in excellent agreement for weight, charge, magnetic moment and spin.  So the theory not only proofs its correctness, in addition it demonstrates it can achieve much more.  The theory takes us to the unification of the well-known interactions and physical phenomena and shows itself as an unified theory.  In the practical conversion and usage of the theory there will not only be informed but by all means also be provoked as an entrance in a fruitfully discussion.  Fundamental questions will be taken up like: What is information, energy, temperature or smell? The connection to the theme of the electromagnetic environmental compatibility is formed by the technical and the biological usage of the potential vortices, the energy transmission of Nikola Tesla exactly like the in a similar way functioning nerve conduction.  Here we already can expect biological reactions.

This lecture, held for the first time in the winter semester of 1995/96, is available in book form, as an edition belonging to the lecture.  This lecture will not deliver ready recipes or instructions.  The goal is reached when the critical sense of the listeners and readers has been inspired and discussions have been set going.  Everybody has to draw the consequences out of such a theory by him- or herself.

In addition to this lecture a seminar is offered, wherein several themes are supplemented or deepened, different theories are compared and possible consequences are discussed.  The appearance of an edition belonging to the seminar has started in 1998 [i].  Regarding the conversion of consequences both politicians and scientists are equally addressed, because the electromagnetic environmental compatibility has developed to one of the most urgent problems of today's world.  But in last consequence all of us bury the worldwide responsibility for our environment.

[i]: K. Meyl: Electromagnetic environmental compatibility, Part 2 and 3 of this book, Edition belonging to the seminar.
 


INTRODUCTION:
Here the extremely controversially discussed question of the environmental compatibility of electromagnetic fields will be persuaded.  Limits should inform what is incompatible and what is compatible.  But there are as many limits as there are commissions and specialists.  And besides that differ the results from each other for several powers of ten.  In course of time the legitimate doubts become unmistakable and the representatives of science slowly get to feel the burden of proof.

For the sake of efficiency, the actual discussion concerning the theme of electro-smog is analysed and the necessity to involve an until now unnoticed field phenomenon in the discussion about limits is derived: It concerns vortices of the electric field.  These potential vortices, as they are called, have the corresponding properties to show biological effects even at the lowest field strengths.  In any case it is not possible to exclude that at present the wrong physical phenomena are measured and made responsible.

A parable should bring clarity.

Lets imagine that the to us well-known and over our sense of touch understandable physical phenomenon of the temperature is unknown to us, neither measurable nor perceptible.  Our weather station only exists of a barometer that could show us the air pressure and deliver us indications if good or bad weather is to be feared. 

We ready realize that there exists a connection between the air pressure and our health and make the to us well-known phenomenon responsible.  When the pointer points to good weather we can go out lightly dressed.  With bad weather we should take a coat, so we know from experience.

Now we imagine the realistic situation that in winter we have a weather situation of high pressure but it's stone-cold outside.  The weather station will display high temperatures with the result that some people will walk around with short-sleeved and open shirt, only to lie in bed with a cold in the evening.  Of course the air pressure was to blame! Logically the "pressure sensitive," as they are called mocking, demand the limits for the allowed pressure to be reduced so far that no consequences for health are to be feared.  Concerning the theme of allowed limits, science is asked and science proceeds in a systematic way: the pressure is investigated in the laboratory, isolated from all other parameters and so it is discovered that man catches no cold even at a substantially higher air pressure, so there is no reason to alter the limits.

Actually we would expect these at any time reproducible results to have a calming effect on the minds of the participants of the discussion and on the population.  Instead the pressure sensitives time and again cite new knowledge that won't fit in the scheme.  So is for instance stated that draught causes the same health problems although this pseudo effect has nothing at all to do with the air pressure.  So owing to incomprehensibility and emotions the discussion about limits becomes a farce.

The fact that sensitive people react to effects of air electricity and possibly get ill without proof that some today measurable physical quantities are responsible should make us think.  It is little calming watching our scientists poking at the dense fog whereas at the same time among the runners of the new telecommunication networks there spreads something like a gold-digger mood.

To introduce a new technology is not difficult, but to abolish it for reasons of the electromagnetic environmental compatibility is almost impossible!


EXCERPT:
Unified theory          169

8. Unified theory

With the theory of objectivity the longed for goal of a "theory of everything" (TOE), of an universal theory, seems to have moved within reach.  If in the nineteenth century still promising field theories and approaches were being discussed, then has at the latest Einstein's theory of relativity destroyed all hopes in such a theory .Science as a consequence has become very much more modest and understands a TOE only as the unification of all known interactions.

Einstein has stated the minimum demand so: "a theory should be favoured by far in which the gravitational field and the electromagnetic field together would appear as a whole" [i].  It is evident that a subjective or relativistic observer theory never is able to achieve this.

The presented theory of objectivity made it possible that the unification here for the first time actually has succeeded.  This undoubtedly brings science a whole lot further, but it still is not sufficient to lie one's hands in one's lap being content with oneself.  After all we still know very much more phenomena, which likewise should be unified.  After all it is no accident that both Maxwell and Einstein, to name only two prominent representatives, after completion of their well-known works have struggled for the question, what sort of phenomenon it concerns in the case of the temperature and how this could be integrated in their theory.

The requirement reads: We must be able to derive all basic factors, which influence our system of units with their basic units, as a compulsion-less result from the new theory.  Besides the dimensions of space and time which determine our continuum, the explanation and unification of the basic factors mass and charge has to be tackled.  If we have succeeded in doing so, we'll also tackle the problem of the fifth and last basic factor, which until now has put itself in the way of any unified theory as the question of fate, the problem of the temperature!

[i]: Einstein, A.: Grundzuge der Relativitatstheorie, Vieweg+Sohn, Braunschweig 1973, 5. Aufl., WTB 58. Seite 97.


Recapitulation from the viewpoint of textbook physics          531

26. Recapitulation from the viewpoint of textbook physics

Now that we in the meantime have accumulated innumerable mosaic parts as inspiring contributions to the discussion for the information technical seminar, it is time to sort the ideas and to put the parts together to an overall picture.

Skeptics and orthodox scientists can only be convinced, if we start from textbook physics and completely do without postulates.  Those demands will be fulfilled!

26.1 Common misinterpretation of the antenna losses

The mathematical description of physical relations leads to the well-known laws, which shouldn't be doubted anymore as soon as they are accepted to be correct.  But what about the interpretation?  Although a law dictates the interpretation and there is no choice, because laws must be adhered to, yet textbooks from time to time violate the mathematically dictated interpretation, a circumstance, which can't be accepted.  I would like to illustrate this with an example.

Let us assume that the measured degree of effectiveness of a transmitting antenna amounts to 80 percent.  There exist better antennas, but also distinctly worse antennas, but I'm not aiming at a certain construction.  The statement simply says, that 80% of the fed in HF-power is transformed into Hertzian waves.  Thus there arises a loss of power of 20 percent, and the question follows: of what do those 20% consist?

The answer, which is usual among experts and is supported by the textbooks, reads: the antenna wire gets hot and also the air around the antenna is heated by dielectric losses.  In short, heat is formed.

But I have to point out and will furnish proof that this interpretation is predominantly wrong!  It in any case isn't in accord with the laws of Maxwell.  Who namely obeys the laws, comes to an entirely different result!

A short derivation brings it to light (fig. 26.1).

We start with the formulation of Faraday's law of induction according to the textbooks (261), apply the curl-operation to both sides of the equation (26.3) and insert in the place of rot H Ampere's law (26.4-26.8). The generally known result describes a damped electromagnetic wave (26.11) <i>.

It on the one hand is a transverse wave, which represents 80% of the antenna power for our example.  On the other hand a damping term can be found in the equation, which obviously corresponds to the sought-for 20%.  With that the answer would have been found.  We realize that because of a damping of the wave 20% antenna losses arise.  These losses can't concern heat at all, since the damping term in the equation has got nothing in common with thermodynamics.  In the equation doesn't stand anything about heat!

Such a mistake!

26.2 Wave damping by field vortices

  • Mathematically seen the damping term describes vortices of the electromagnetic field.  This term for instance forms the basis of all eddy current calculations <ii>. 
     

  • Physically seen some waves--in our example it is 20 percent--roll up to field vortices, with which the wave damping and the antenna losses would be explained. 

In the course of time a substantial part of the generated vortices will fall apart.  These thereby will produce eddy losses in form of heat.  Thus eventually still heat is produced--agreed.  The criticism of the textbooks consists of the circumstance that we by no means can proceed from the assumption that all vortices spontaneously fall apart and a total conversion into heat will take place.  The process in addition takes place with a temporal delay.  The time constant τ gives information in this respect.  Field energy is buffered in the vortex, where some vortices live very long and it can't be ruled out that a few even exist as long as you like.

To find out more about these field vortices and their behaviour, one has to get deep into vortex physics.  Unfortunately nothing can be found about vortex physics in the textbooks.  The mistake is systematic.  The following short compendium should help close the gap: 

  • Mathematically seen a closed-loop electromagnetic field vortex will show as a scalar.  Such field vortices, which are mediated by a scalar field, are propagating exactly as charged particles in longitudinal manner as a "scalar wave."
     

  • Physically seen a closed-loop field vortex has got particle nature.  If one particle kicks off the next one then an impulse is mediated, then a shock wave is occurring, a longitudinal undulation of the particles.

From the vortex physical view the interpretation of the antenna example now sounds entirely different:

The charge carriers in an antenna wire oscillating with high-frequency form a longitudinal shock wave.  Between current and tension voltage usually a phase shift of 90deg is present.  The fields produced by these charge carriers form a [longitudinal EM] wave field in the immediate vicinity of the antenna, the so-called near-field zone, which likewise contains longitudinal field components and shows a phase shift of 90deg between electric and magnetic field (fig.  21.8 A).  As in textbooks is clarified by field lines, the generated fields actually form vortices, where one structure kicks off the next one (fig. 21.9 A). 

The vortices in the near-field zone of an antenna consist of standing waves, which obviously are transforming with increasing distance.  In our example 80% of these are unrolling and turn into transverse waves, whereby the characteristic phase angle between E- and H-field at that occasion becomes zero.

Let's turn again to those 20 percent loss.

<ii>: s.a.: K. Meyl: Wirbelstrome, Diss. Uni. Stuttgart 1984, INDEL Verlagsabt.

26.3 Laplace versus Maxwell

Longitudinal waves as is well-known don't know a fixed velocity of propagation at all.  Since they run in the direction of an oscillating field pointer also the vector of velocity will oscillate.  For so-called relativistic velocities in the range of the speed of light c the field vortices are subject to the Lorentz contraction.  That means, the faster the oscillating vortex is on its way, the smaller it gets.  The vortex, as a mediator of a [longitudinal EM] wave carrying impulse, permanently changes its diameter.

Since, in the case of the vortices, it should concern rolled up waves, the vortex velocity will continue to be c, with which the wave now runs around the vortex centre in a circle.  From that follows that if the diameter gets smaller, the wavelength of the vortex as well will decrease, whereas the eigenfrequency of the vortex accordingly increases.  

If the next moment the vortex oscillates back, the frequency again decreases.  The vortex acts as a frequency converter! The mixture of high-frequency signals distributed over a broad frequency band formed in this way, is called noise.  A noise signal indeed is measured from the outside with the help of broadband receivers.  We also speak of antenna noise and with this knowledge we can further specify the 20% antenna losses: The antenna produces 20 % noise, which can be put equal to the generated vortices because of the wave damping.

At this point the Maxwell theory doesn't leave us room for interpretation at all.  If in the textbooks the impression is aroused, as if the noise were an independent discipline, than that is not true at all.  How much the noise is connected with the electromagnetic waves, proves a short look at the wave equation.

The wave equation found in most textbooks has the form of an inhomogeneous Laplace equation.  The famous French mathematician Laplace considerably earlier than Maxwell did find a comprehensive formulation of waves and formulated it mathematically (eq.  26.12), which [up to] today is still accepted as valid.

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 vector analysis can be decomposed into two parts.  On the other side the description of the time dependency of the wave can be found as an inhomogeneous term. 

If the wave equation according to Laplace (26.12) is compared to the one, which the Maxwell equations have brought us (26.11), then two differences clearly come forward:

1. In the Laplace equation the damping term is missing. It doesn't describe the formation of vortices, and that means vortices do not exist at all, or vortices have been present there from the beginning.

2. With divergence E a scalar factor appears in the wave equation, which founds a [longitudinal EM] wave.

At this point at once hot tempered discussions concerning the question of the existence of [longitudinal EM] waves blaze up.  But this question has already been answered clearly with the vortex consideration.  Since an accepted description of . . . [longitudinal EM] waves exists with the plasma wave and the plasma wave can be derived directly without postulate from the term of the wave equation (chapter 21.4/21.5), which founds [longitudinal EM] waves, there are further arguments present for their existence.

26.4 Error term in the wave equation

From the comparison of coefficients of both wave descriptions follows even more:

  • Mathematically seen the damping--resp. [that is to say] vortex term according to Maxwell can be put equal to the [longitudinal EM] wave term according to Laplace.
     

  • Physically seen the generated field vortices form and found a [longitudinal EM] wave. 

Here also doesn't exist any room for interpretation, as long as we work with the wave equation according to Laplace and at the same time adhere to the Maxwell theory.  If however the [longitudinal EM] wave part is put equal to zero, as is common practice in the textbooks, then as a consequence neither vortices nor noise may exist.  But that contradicts all measuring technical experience!  Since every antenna produces more or less noise, the textbooks obviously only show half the truth.  Science however gropes for the whole truth and that should be fathomed.

If in the case of the antenna example the vortex part amounts to 20%, then that's tantamount to 20% [longitudinal EM] wave part, resp. [i.e.] 20% noise.  The [longitudinal EM] wave part constitutes with regard to the Hertzian useful wave something like an error term in the wave equation.  The part definitely is too big, as that it might be put equal to zero.  Even so all error consideration in the textbooks is missing, if the [longitudinal EM] wave term is assumed to be zero.  That violates all rules of physics and of taught scientific methodism.

In practice this shows by a useful signal going under in the noise and reception not being possible anymore as soon as the [longitudinal EM] wave part gets out of control.  Even in this case, for which the degree of effectiveness tends towards zero, it still is common practice to put the error term, which is dominating everything, equal to zero.  But who in this point follows the textbooks, disregards with that the wave equation and doing so by no means can refer to the circumstance that all colleagues make the same mistake.

The building of physics behaves like a house of cards, where the cards mutually support each other.  Perhaps that is the deeper reason why those, who have discovered a marked card, don't pull it out immediately.  In addition they are hindered by the self appointed guardians of the "pure doctrine," since everyone knows what happens with the house of cards if the marked card is pulled out.  Only, do we want to and can we live with that in the long run?  Is it a solution of the problem, if the so-called experts among the physicists and technicians look away and don't deal with the foundation of their branch anymore?  If universities crash their basis education into the wall and choke off every contradiction? 

Please allow me to pull out the marked card now and place it on the table!

It concerns the question: what is the nature of the field vortices, which form a [longitudinal EM] wave in space.  Eddy currents in the iron parts of the antenna are explained with the field equations, but not the noise, which is measured especially in the air.  If an antenna on the one hand produces field vortices and as a consequence eddy losses and on the other hand dielectric losses, then we can assume that besides the eddy currents in the conductor also vortices in the dielectric must exist.  Let's search for them!

Recapitulation from the viewpoint of textbook physics          539

26.5 Interim result

It shouldn't be a disadvantage, to interpret physical laws more consistently than usual, even if in the present case orthodox science through that at first should fall into a deep crisis.  If the way is worthwhile, only will show at the end.

Let us try to work out the contradictions in form of a comparison of arguments:

The Maxwell equations on the one hand dictate that as the reason for a wave damping only field vortices should be considered.

On the other hand the same laws merely describe eddy currents, which can only occur in the electrically conducting parts of the antenna.

On the one hand the field vortex interpretation makes it possible to explain the noise of an antenna perfectly. .

On the other hand does the noise appear in the neighborhood of the antenna, thus in the air and not in the iron parts! 

The mathematical formulation reveals, how wave and vortex, resp. [that is to say] noise, cooperate and how one should imagine the conversion of one form into the other form.

In field physics on the other hand is missing a useful description of electric field vortices in a dielectric, which could found the noise signal. 

The most obvious among all conceivable solutions is the one that we have to assume the existence of dielectric field vortices, so-called potential vortices.  We are challenged to search for a corresponding description.  If the quest should be successful, then the contradictions would be overcome.  In addition there is the promise of a whole number of simplifying explanations of various phenomena in the dielectric (see fig. 26.5 and fig. 26.7).

The phenomenon of noise becomes an aspect of wave physics, which is more than merely a field disturbance, which makes the reception of the useful wave more difficult.  If the [longitudinal EM] wave nature is realized, then applications can be imagined, in which the noise is used as useful signal. In the way that the scalar part in the wave equation doesn't have to be put to zero anymore to obtain freedom of contradiction, even optimizations of antennas or of capacitors are possible with regard to the dielectric losses by means of the calculation of the scalar part.

New in any case is the idea that the dielectric losses of a capacitor are eddy losses and not a defect in material of the insulating material.  With that the capacitor losses correspond to a generated noise power.  We also can say, every capacitor more or less produces noise!  The electric field lines point from one capacitor plate to the other plate.  If one plate radiates as a transmitter and the other plate functions as a receiver, then the field propagation takes place in the direction of the electric field pointer and that again is the condition for a longitudinal wave.  Here the circle closes in the conclusion, the capacitor field mediates dielectric field vortices, which following the field lines found a [longitudinal EM] wave because of their scalar nature.  The heating of the capacitor results from the decay of vortices.

Failure of the Maxwell theory          540

Potential vortices explain div. (divergence) phenomena in the dielectric:

1. Noise no longer is factored out of the field theory.

2. The scalar (noise) part in the wave equation no longer has to be put to zero (div E 0).

3. The wave descriptions according to Maxwell (26.11) and according to Laplace are consistent and free of contradiction.

4. The dielectric losses of an antenna can be found physically and even can be calculated with the wave equation.

5. Also the dielectric losses of a capacitor are eddy losses (and not a defect in material of the insulating material).

6. The capacitor losses correspond to a generated noise power.

7. The dielectric constant E doesn't have to be written down complex as until now to give reasons for the occuring losses, and so the inner contradiction is solved, which is hidden in a complex constant.  One should only remember the definition of the speed of light c = 1/ (eq. 26.10) and the insurmountable problems in the textbooks, which are brought about by complex E!

8. The field lines point from one capacitor plate to the other plate.  If one plate radiates as a transmitter and the other plate functions as a receiver, then the field propagation takes place in the direction of the electric field pointer and that again is the condition for a longitudinal wave.

9. The capacitor field mediates dielectric field vortices, which following the field lines found a [longitudinal EM] wave because of their scalar nature.

10. As an inhabitant of a dielectric between two capacitor plates (earth and ionosphere) also man is a product of these field vortices.

11. [longitudinal EM] waves can be modulated moredimensionally and be used as carrier of information, as Prof. Sheldrake has proven with his proof of the existance of morphogenic fields <i>.

Fig. 26.6: Advantages of a field description extended with potential vortices.

<i>: Rupert Sheldrake: Seven Experiments That Could Change the World. Riverhead Books, 1995

Recapitulation from the viewpoint of textbook physics 541

26.6 Failure of the Maxwell theory

If the capacitor losses or the antenna noise should concern dielectric losses in the sense of vortex decay of potential vortices. which don't occur in the Maxwell theory at all, then we are confronted with a massive contradiction:

For the description of the losses the Maxwell theory on the one hand only offers the field vortices and those only in the conductive medium.

On the other hand do the dielectric losses occur in the nonconductor and the air.

In conductive materials vortex fields occur, in the insulator however the fields are irrotational. That isn't possible, since at the transition from the conductor to the insulator the laws of refraction are valid and these require continuity! Hence a failure of the Maxwell theory (Fig. 26.7) will occur in the dielectric.

As a consequence the existence of vortex fields in the dielectric, so called potential vortices, should be required!

In electrodynamics as a help the approach of a vector potential A is used, which leads to a complex formulation of the dielectric constant E and in this way makes it possible, to mathematically describe the dielectric losses of a capacitor by means of the load angle, which stretches in the complex plane.  But which physical value does this approach have?  How can now the inner contradiction be explained, which is hidden in a complex constant of material?  One should only remember the definition of the speed of light c = 1/ (eq. 26.10) and its dependency of E.  For a complex E here are resulting insurmountable problems in the textbooks.

From the viewpoint of mathematics the introduction of the vector potential at first may represent a help.  The before mentioned contradictions however fast raise doubts to the model concept, which from a physical viewpoint eventually will lead to errors, if the speed of light isn't constant anymore and even should be complex.  These considerations should be sufficient as a motive to require potential vortices, even if for their description the field theory according to the textbooks has to be revised.  As a supplement there is pointed to the following points:

As an inhabitant of a dielectric between two capacitor plates also man is a product of these field vortices.

[longitudinal EM] waves can be modulated moredimensionally and be used as a carrier of information, as Prof. Sheldrake has proven with his proof of morphogenetic fields <i>.

The dielectric vortices moreover provide an explanation for natural events.  They form the key to numerous disciplines of science, from physics over biology up to medicine.

<i>: Rupert Sheldrake: Seven Experiments That Could Change the World. Riverhead Books, 1995

542 Concerning the evidence situation

Example: hightension cable

In conductive materials vortex fields occur in the insulator however the fields are irrotational.

That isn't possible since at the transition from the conductor to the insulator the laws of refraction are valid and these require continuity!

Hence a failure of the Maxwell theory will occur in the dielectric!

Conclusion: 

According to the Maxwell theory there exist no vortices of the electric field (no potential vortices) and therefore no [longitudinal EM] waves.

Without theory it is impossible to design a usable [longitudinal EM] wave gauge and to furnish evidence. ::::> Classic closed loop conclusion:

The missing of scientific evidence again "proves" the assumption of the irrotationality and "confirms" the correctness of the Maxwell theory.

Hence it cannot be, what shouldn't be!

26.7: Concerning the failure of the Maxwell theory

Recapitulation from the viewpoint of textbook physics          543

26.7. Concerning the evidence situation

In the question, if a physical phenomenon should be acknowledged as such, experimental, mathematical and physical evidence should be shown. In the case of the potential vortices, the vortices of the electric field and their propagation as a [longitudinal EM] wave, the historical experiments of Nikola Tesla <i> and the modem clone of these can be judged as experimental evidence <ii>.

With the well-known wave equation a mathematical description for this phenomenon has been specified and discussed <iii>.  It will be shown that both transverse and longitudinal wave parts are contained alongside in the wave equation, i.e. both radio waves according to Hertz and [longitudinal EM] waves according to Tesla.  Doing so the mathematically determined [longitudinal EM] wave properties are identical with the experimental results!  The wave equation is an inhomogeneous Laplace equation and the first and oldest description of [longitudinal EM] waves.  It thereby is unimportant, if the famous mathematician Laplace himself already may have realized and discussed this circumstance or not.  The description fits perfectly and that is what counts!

At this point the third point should be put on the agenda, the physical evidence.  This is connected very closely with the question for a suitable field theory and that again is basing on a corresponding approach.

<i>: N. Tesla: Apparatus for Transmission of Electrical Energy, U.S. Patent No. 649,621, New York 1900, Dr. Nikola Tesla: Complete Patents, pp. 318-321

<ii>: Johannes von Buttlar im Gesprach mit Prof. Dr. Konstantin Meyl: Neutrinopower, Argo-Verlag, Marktoberdorf, 1.Aufl. 2000.

<iii>: K. Meyl: Scalar Waves: Theory and Experiments, Journal of Scientific Exploration, Vol. 15, No. 2, pp. 199-205, 2001.


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