Maxwell's equations describe correctly all macroscopic electromagnetic phenomena. It will probably require reformulation for the microscopic ones required in the interpretarion of electromagnetic nanotechnologies, but I'm no experte in this field.

The two articles listed here may be of interest to some.

"Maxwell’s electromagnetic equations revisited”

Hadronic Journal 25 (2002) 251-260

“A re-examination of Maxwell’s electromagnetic equations”

Progress in Physics 3 (2005) 48-50

http://uk.arXiv.org physics/0406056

Also, it might be worth checking up on the work of the later Dr. Kenneth Thornhill.

Dear Dunning-Daves,

Thank you very much for your kind reply and for referring me to your interested article that I haven't seen before. I my self had some publications in this regard. These are

http://ptep-online.com/index_files/2009/PP-17-03.PDF

and

http://iopscience.iop.org/1674-1056/22/3/030301

They are available through researchgate.

Best wishes.

Arbab

Do torsional waves exploit hadronic features and associated phenomena - out of which one may have been decribed by TESLA.

http://www.tandf.co.uk/journals/authors/tphm-tphl-prize.asp

http://www.sciencedirect.com/science/article/pii/0021850282900192#

Dear Dr Arbab,

Thank you. I'm looking forward to reading your articles.

Best wishes,

Jeremy.

You may be interested in these articles, which contain both practical examples and mathematical derivations for longitudinal waves:

'Introduction to the Propagating Wave on a Single Conductor' by Glenn E Elmore, 2009.

http://www.corridor.biz/FullArticle.pdf (from http://www.corridorsystems.com/Technology.html).

The following two articles go together.

'Derivation Of An ‘Inverse Liénard-Wiechert Effect’ From The Lorentz Force And Its Application To The Wireless Power Transfer' by V. Onoochin in 'Progress In Electromagnetics Research Letters', Vol. 35, pp 181-190, 2012.

http://www.jpier.org/PIERL/pierl35/19.12080701.pdf

'On Solution for the Longitudinal Electromagnetic Waves Derived from the Jefimenko Wave Equation and Its Application to Wireless Power Transfer', by V. Onoochin,

'Progress In Electromagnetics Research M', Vol. 34, pp 73-78, 2014.

http://www.jpier.org/PIERM/pierm34/09.13101401.pdf

This IEEE paper is also relevant:

'Low-loss RF transport over long distances' by M Friedman and Richard Fernsler, 2001.

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=903095

Regards,

Ian.

Honestly, Nikola Tesla was interested in field of scalar waves (longitudinal waves) - not to be  astrologist of some kind .Only way for scalar wave to be reality is to find existence of monopols. To answer your question. Maxwell's equations need revision , I am not the expert but I hope that in near future we will be able to discover scalar waves and with that discovery the idea of free energy exploitation can relive again. (I know this sounds too simplified but I guess this question was more philosophical than scientific ):

Edit: There are only claims that he experimentally found those scalar waves. No solid proof for that yet exists! (Only speculations)

Dear Osman,

Thank you very much for your kind answer. In fact I published a paper that predicts the scalar wave by extending Maxwell equations. Her is the link

http://www.ptep-online.com/index_files/2009/PP-17-03.PDFhttp://www.ptep-online.com/index_files/2009/PP-17-03.PDF

Best wishes.

Dear Arbab, 

I get 404 error, can you re-upload your paper .

Edit:Dont bother, you just merged two links and it redirected me to duplicated link (I resolved it )

Dear Osman,

Here the paper is attached. Thank you for your interest.

Maxwell's equations are both inconsistent and incomplete.

Dale Woodside published a 2009 paper in the American Journal of Physics that proves a more complete formulation using only 4-vectors. A copy of his paper is at:

http://ricardoheras.com/wp-content/uploads/2016/05/Woodside.pdf

Aharonov and Bohm published a 1963 paper in Physical Review, Vol. 130, Number 4, pages 1625-1633. They obtain the very same form (page 1631) that Woodside proved.

If anyone would like to work with me to validate this more complete formulation of electrodynamics by experiments, please contact me at [email protected]

This paper is interesting:

https://www.researchgate.net/publication/255000872_Toward_a_More_Complete_Electrodynamic_Theory

In the last figures, they present results from another group concerning longitudinal fields.

There is also this paper:

https://www.researchgate.net/publication/274734326_Potential_Theory_in_Classical_Electrodynamics

Article Toward a More Complete Electrodynamic Theory

Article Potential Theory in Classical Electrodynamics

Hi Arbab  Read my work on self-field theory (there's a paper -copy attached- in physics essays) this already been started with a view to solving for nuclear regions where the longitudinal field becomes another vector in addition to the electric and magnetic fields.

This changes the FOUR Maxwell equations to become SIX equations.

Lee Hively: What did you have in mind as far as experimental work goes?

regards Tony

Tony - I have several comments to answer your question. First, classical electrodynamics (CED) consists of two scalar equations and 2 vector equations, for a total of 8 scalar equations. The no-magnetic monopoles equation [div(B)=0] can be derived from Faraday's law, so there are really only 7 scalar equations. The unknowns are E(vector) and B(vector) for a total of 6 unknowns. Thus, CED is over-determined and leads to inconsistent solutions. Lorenz recognized this over-determination, and proposed what is now called the Lorenz gauge to complete the system, which has been taught to every graduate student over the last century. Second, a 2009 paper by Woodside (available at the following URL):

http://ricardoheras.com/wp-content/uploads/2016/05/Woodside.pdf

uses only Minkowski 4-vector geometry to prove a more complete form of electrodynamics, which includes a scalar field (C) that completes the system  of equations. When C=0, classical electrodynamics is recovered (C=0 is the Lorenz gauge). When C is a non-zero, dynamical quantity, there are novel predictions: a wave equation for C, additional terms in the momentum and energy balance equations, and a new free-space wave [variously called a scalar-longitudinal wave (SLW) or an electro-scalar wave in the literature]. See the attachments for details. Third, the key prediction is the SLW, for which the second attachment shows partial experimental validation. So, to answer your question, the experimental work that I have in mind is completion of that experimental validation of the theory (and publication of the results in a major international journal).

Article Toward a More Complete Electrodynamic Theory

Patent Systems, apparatuses, and methods for generating and/or util...

It is incomplete, since it is inconsistent (longitudinal electric far field inconsistency, when considering Jefimenko's general field solutions of the Maxwell equations). After repairing the Maxwell Lorentz theory, by means of the definition E = -grad Phi - dA/dt and div(d(A)/dt) =0 (apply Occam's razor by theoretical exclusion of non-divergence free electric fields induced by time varying currents, which should be veryfiable by experiment), the resulting consistent theory only describes electric currents that form closed loops ( div J = 0 = d(rho)/dt ). This is a very limited and incomplete theory of electrodynamics, though consistent. In the more general case of div J 0 (open currents situation), the Lorentz force law does not satisfy Newton's third principle of motion for stationary currents, such that Classical Physics (mechanics and electrodynamics) is inconsistent. Lorentz' force law must be replaced by a more general force law that allows for longitudinal Ampere forces. And again this shows that the Maxwell-Lorentz theory is incomplete, since it does not predict longitudinal Ampere forces. The Aharonov Bohm effect shows that the vector potential has a wider physical meaning apart from the magnetic field B = rot(A), which indicates that the longitudinal Ampere force should be expressed as f = - J div(A). With B = -div(A) also the longitudinal far field inconsistency is solved, if we assume that time varying longitudinal electric fields can induce scalar magnetic fields. A third inconsistency of Maxwell-Lorentz theory is the 4/3 problem in the derivation of electric mass such that E = mc^2. All inconsistencies are solved by assuming the velocity of the scalar potential is much higher than the velocity of the vector potential. If it is assumed that the scalar potential has velocity 'c', then only the inconsistent Maxwell-Lorentz theory is allowed (no observable scalar field effects), so this assumption must be incorrect.

Dear All

If we look at the equations, that's one thing, but we have to look at the metric too. I find the comments that say the problems are with Maxwell's Equations are missing the problem and that lies with BOTH classical electromagnetics based on maxwell's equations (CEM) AND quantum theory (QT) which sprang up from 1927 onwards. BOTH methods use a Pythagorean metric where the fields and forces don't move along this direction; these forces only move along the adjacent and opposite lengths and not along the hypotenuse.

I suggest there is one problem with completeness of the system of the Maxwell equations.

It is known that the EM fields propagate as the waves so both E and H fields should be described by the wave equations. But one can derive the wave equations (in the Lorenz gauge) only for the potentials. Because it is accepted in the classical electrodynamics that the potentials are not the physical quantities these equations formally don't describe the propagation of the EM waves. Moreover, one can use different sets of the potentials in different gauges. Different sets of the equations cannot describe the only physical process.

The second point. As O'Rahilly writes (Electromagnetic theory, Ch. IV.) Lorenz showed that using his gauge one can obtain the Maxwell equations from his wave equations for the potentials. But there is a problem to obtain the wave equations from the Maxwell equations.

The official definition of Magnetostatics is already incomplete and needs revision, before one even begins to treat Electrodynamics. Every text book will tell you that 'magnetostatic electric currents' are such that d(J)/dt =0 and div J =0 everywhere in a 'closed' circuit, so, in fact one cannot even use a standard battery for magnetostatic force experiments. For magnetostatics, the Ampere law is defined as rot B = mu_0 J and since div rot B = 0 then div J = 0. In order to garantee the validity of Newton's third law, two static current circuits (that interact with forces) must form closed loops, which again means that one cannot even apply standard batteries for such tests. And yet, Richard Feijnman describes in his Feijnman lecture on Magnetostatics (see after eq 13.13 on http://feynmanlectures.caltech.edu/II_13.html) that "one can use batteries for doing Magnetostatics tests". This must have been one of Feijnman's biggest jokes ever, you know. I have really no idea why this is accepted/interpreted as "physics". It is a joke, and even a high school kid can understand this. Another of Feijnman's mistakes is applying the relation J = rho v in the same paragraph, as if this relation has general validity, which is not true. In most cases J rho v, and the only relation that is generally true is: div J + d(rho)/dt =0. If even Richard Feynman (the 4th most important physicist of all times, according to some rankings) did not have his facts straight on this important topic, I simply give up on physicists alltogether. The correct definition of Magnetostatics should be determined by the condition d(J)/dt = 0 only, but then it is simple to prove in case of Magnetostatic systems that the LORENTZ force interaction does not necessily satisfy Newton's third law, such that momentum conservation is violated by Magnetostatic systems. Obviously, classical physics is inconsistent according to the standard theory on Magnetostatics, because of the Lorentz force, and this can only be fixed/solved considering longitudinal Ampere forces as well. And all this is pre university level physics, simply misunderstood by the biggest minds in physics. I have no words.

@LeeHivey

said (a year ago) " Tony - I have several comments to answer your question. First, classical electrodynamics (CED) consists of two scalar equations and 2 vector equations, for a total of 8 scalar equations. "

First, sorry about the year delay in replying Lee; I must have missed your reply.

Yes and no Lee; those 8 equations are not independent but linearly dependent on each other, whereas the Maxwell's equations (two curls and two divs) can be solved (in terms of eps_0 and mu_0, the consitutive relationships of free space) as two 'bispinors' r*exp(j*omega*t where we are interested in the motions of both the electron and the proton, or alternatively the motions of the photons that can be an electric field and a magnetic field within the atom. In other words FOUR independent equations in self-field theory. Note we have SIX equations if we allow eps-0 and mu-0 to vary from free-space, e.g. in biological tissue.

I haven't yet thought about your other comments but this one needs to be commented upon, so I'll answer you in the short term about anything else you said.

PS Hi Arbab, I must write to you soon (offline).

Forgive my ignorance, but I do not understand some of the answers and comments I have read. As far as I know macroscopic Maxwell's equations have been repeteadly verified in their realm of validity. There are some questions about its generalization to differente space-time frames due to Einstein´s original work on Special Relativity, but I do not think there are inconsistencies in this respect. They are not valid for microscopic phenomena, as shown by difference between what is called the local electric field and the macroscopic one, subject discussed in Solid State Physics textbooks. This has lead to the formulation of Quantum Electrodynamics, which solves also problems such as the divergence of the electron's self energy (see Feynman's Lectures on Physics).

As refers to the longitudinal electromagnetic waves, several authors have shown that there exist and are valid solutions of the original Maxwell's equations, but are transient and require the presence of appropiate sources and boundary conditions. There many wrong proofs that this is false, but all the ones I know have flaws because of the aforesaid conditions. Does anybody here know otherwise?

Some recent papers on this subject:

Article Maxwell's Equations and Occam's Razor

Article The Electron and Occam's Razor

see also:

http://www.ecat-thenewfire.com/blog/electromagnetic-electron-new-fire/

Wheeler and Feynman introduced absorber theory, in which, the field is a action between at least two charge. The absorber theory tell us without absorbers the radiation cannot send out. Absorber theory is based on action-at-a-distance theory of Schwarzschild, Tetrode and Fokker. Tetrode said without absorber the sun cannot shine.

Maxwell theory is wrong because in it even there is only one charge, it can radiate the wave. That is not correct.

This is known problem of Maxwell theory, however no one found a solution, some one said this is the intrinsic problem of Maxwell theory, that means even it is wrong you cannot overcome this problem. This problem actually cause lot of other problem for example the problem of wave and particle duality, the conflict of superposition with energy conservation and so on.

Recently I have found a solution to solve the problem, I have introduced the mutual energy principle and self-energy principle which is based on the mutual energy theorem published by me 1987. This theory remedy the Maxwell theory by introduced 4 waves for photon, the retarded wave, the advanced wave and two corresponding time-reversal waves. The 4 waves can have 4 self-energy flows, and 2 mutual energy flow. Hence a photon is a consist of 4 waves and 6 flows. This theory solved the wave particle duality. Please see the details from the following:

http://www.openscienceonline.com/journal/archive2?journalId=726&paperId=4042

Arbab I. Arbab

Dear Arbab,

We must create physical models of electron, charge, electric and magnetic fields and electromagnetic waves. Only after that we can answer your question. Such work has already been done. It turned out that the Maxwell equations describe vortex electrons and vortex radio waves Tesla longitudinal waves. Minor clarifications needed. We decomposed the vector E into the vortex and gradient components.

More in the book "Electromagnetic Gravity. Part 3" in my profile.

Yours

Valeriy Pakulin

I have applied Helmholtz decomposition to rotational (vorticity) tensor & the gradient tensor modeling microblackhole & zero point tensors. These appear in various working papers that I have on the RESEARCHGATE forum.

To take onto account monopole aspects that I am developing along Emmanouil Markoulis' team which I'm too part of, I have modified Maxwell Equations & they appear in articles of RESEARCHGATE forum as well. We are hoping to have peer-reviewed publications with quantum field magnetic vortex model having experimental proof with theoretical analyses coming up soon enough. Hence monopole magnetic quagmire will modify Maxwell equation of EM phenomena.

Definitely revise the direction of magnetism not the maths that measure it. Visit 'exorcising Oersted and Maxwell'

http://www.yowahbooks.com/2019/11/15/714/