There is no need to exclude Maxwell's equations from physics, because they are equivalent to the relativistic equations for the field strength tensor. So even if we threw them out, they would still be there in disguise. An axial vector is equivalent to an antisymmetric tensor, so the B field axial vector does not cause any problems either.

Moreover, there are still many physicists who find it easier to think in terms of Maxwell's equations than in terms of the curl and divergence of a four-tensor.

And finally, as Feynman states, physicists should always be willing to keep several different formulations of the same physical laws in mind as there is no rule that tells us which form is the best when the necessity of generalizations arises due to more precise experiments or some other reason breaking the old laws. For example, there is no need for the Lagrangian or Hamiltonian formulations of mechanics, because essentially they do not go beyond Newton's laws. Nevertheless, it is much easier to find the Schrödinger equation or Feynman's path integrals if you know Hamiltonian and Lagrangian mechanics.

I do not think that the integral form and the differential form of Maxwell's equations are equivalent notions in the presence of sources.

In the integral and experimental form, a source will generates fields that are only intended to influence test particles different from the source. And yet in the differential form (Maxwell-Gauss and Maxwell-Ampère), a source generates fields even at its own location and that is how a meaning is give to the "continuity equation".

Rommel Nana Dutchou : Thanks. The integral and differential forms of Maxwell's equations are related to each other, by the generalized Stoke's Theorem, there is no new physics. By excluding one, we exclude the other.

They connect an integral of a differential form w with a higher integral of its derivative dw. Thus, the higher integral of its derivative impose some new restrictions on the regions, surfaces, or curves on which it is carried out (so-called experimental forms). The exact nature of these restrictions depend on the tools employed. See, for example, "Foundations of Potential Theory" by O. D. Kellogg, and more recent journals.

In quantum mechanics, which must be obeyed by the EM field, a photon (only) interferes with itself (Dirac), so it is no mystery that a source should generate fields even at its own location.

"In introductory electromagnetism classes in college-level instruction, one obtains Maxwell's equations from the application of Coulomb's Law, Faraday’s Law, special relativity, and other laws that should agree with empirical evidence [1]. The derivation of such equations relies upon trusting that framework to hold, through various laws and relationships.

In common words, the student expects the exposition to "make sense" as it is, not with a "deus ex machina" approach in science!

However, one can not derive these equations neatly, with the fewest physical assumptions needed. There seem to be extra statements introduced, e.g., about special relativity, without justification, or just questionable, concurrently with the instruction.

This is not a fault of the professors, it is found to be caused mainly by historically valid, popular, but scientifically anachronic textbooks, that are, nonetheless, used in many top colleges and selective universities, such as Caltech," in Preprint There Must Be Light!

@ Ed Gerck

The physical interpretation of (mathematical notions of) electric and magnetic fields is conceived solely by the expression of the Lorentz force, that is to say, how a test particle is locally influenced in the presence of these fields.

And it is not easy to think in an experiment that any source can exert a Lorentz force on itself.

Historically, if we consider that the Maxwell equations in vacuum (associated with the Lorentz force) are a postulate in a given inertial reference frame, then the Liénard-Wiechert potentials are a solution to calculate the fields generated by different sources in this frame of reference. The solutions obtained in this way are not modified by the theory of special relativity because Maxwell's equations in vacuum and Lorentz force are compatible with the principle of relativity (through the transformation of Lorentz)

However, from a theoretical point of view, it is not necessarily essential to use Maxwell as a postulate of the physics of electric sources.

Using the Lorentz force generated by non accelerated sources, and the relativity principle, and the Lorentz transformation (existence of a limit speed for the transmission of influences) as basic postulates, on can consider the Coulomb formula in the inertial frame where a source is constantly at rest to compute the field electromagnetic that exists in an inertial reference system where the source has a rectilinear and uniform motion, and we then see that the Maxwell equations in the vacuum are satisfied !

If the source is accelerated, it will still exert an electromagnetic influence on the test particles (and perhaps Maxwell in the vacuum will still be valid), but we do not have to assume that the source will not generate any other kind of influence on test particles, for example gravitational:

https://www.researchgate.net/post/Has_this_interpretation_of_the_Machs_principle_already_been_explored

When Minkowski formulated Einstein special relativity (SR) in terms of spacetime, he changed the basis of the discussion from Lorentz transformation (LT) to the invariance of the interval ds2 to any observer, in inertial motion.

The LT became a consequence, as well-known, not a cause. GR was created on this new SR, not the old SR, and depends on this insight. The new SR (more than 100 years old) is also valid for arbitrary motion --- accelerated, inertial, or at rest.

All accelerated motion, also arbitrary motion, can be converted to inertial motion in Minkowski's SR, charged particle or not. We are on top of Earth, hurling through space, around the Sun, and yet we are not radiating in this accelerated frame.

It is simple, the same way that the electron emits, it absorbs energy. An electron, sufficiently isolated (adiabactic), goes into accelerated motion along a geodesic (e.g., a great circle, around the Sun, or near Mars), emits a photon, then absorbs the same photon, but can be seen at all times as at rest in proper time.

All magnetic fields are created by motion of charges, even a permanent magnet bar resting on the palm of your hand; there are no monopoles.

This can be seen using Minkowski’s SR, where a comoving observer has no length contraction and no time dilation, sees no magnetic field B (due to that electron) and sees no acceleration --- although a non-comoving observer sees the magnetic field B and the acceleration. An observer is comoving if it has the same position and same velocity (but not necessarily identical to the object).

Approximations is a valid method to solve problems that we do not know how to solve. But not to stay with; one needs to face the difficult waters of the ocean, the ship can't be good only for the bay with easy waters --- but if the ship is the highest priority for the captain, staying in the bay is the best strategy.

On mathematical elegance or geometry, that is just human-defined. One should, rather, concentrate on the primacy of physical laws --- nature.

When (as an undergrad student), dissatisfied with teaching methods, I was learning how to educate others, by myself. I could not just copy what I saw, and did not like. McLuhan had a powerful picture of a horse and a bowl of water. He asked, how to make the horse drink the water?

My answer was, first, not to beat or cajole the horse. As the old adage goes, you can bring the horse to the water, but you can't force it to drink. Second, make the horse thirsty, before. Then, teaching can become education, where educare in Latin means to bring out.

There is no need to exclude Maxwell's equations from physics, because they are equivalent to the relativistic equations for the field strength tensor. So even if we threw them out, they would still be there in disguise. An axial vector is equivalent to an antisymmetric tensor, so the B field axial vector does not cause any problems either.

Moreover, there are still many physicists who find it easier to think in terms of Maxwell's equations than in terms of the curl and divergence of a four-tensor.

And finally, as Feynman states, physicists should always be willing to keep several different formulations of the same physical laws in mind as there is no rule that tells us which form is the best when the necessity of generalizations arises due to more precise experiments or some other reason breaking the old laws. For example, there is no need for the Lagrangian or Hamiltonian formulations of mechanics, because essentially they do not go beyond Newton's laws. Nevertheless, it is much easier to find the Schrödinger equation or Feynman's path integrals if you know Hamiltonian and Lagrangian mechanics.

K. Kassner and all: Yes, Maxwell's equations in electromagnetism were covariant with special relativity (SR) before Einstein was even born (as it says in the discussion head).

However, SR has difficulties today, whatever formulation you choose. Feynman was referring to the need to understand Minkowski's SR formulation, mostly accepted in Physics but rejected by adherents to the Einstein SR formulation --- he even suggested that using "relativistic mass" was OK.

We have large evidence that the Lagrangian or Hamiltonian formulations of mechanics go beyond Newton and go where (e.g., inside a an atom or near a large mass) Newtonian mechanics can NOT. Wikipedia (WP) is just wrong on that, and one can not change because of WP editor activism. There are other examples, also in quantum mechanics, where the Lagrangian or Hamiltonian formulations are crucial, and Newtonian mechanics do NOT even apply.

Also, mathematics and geometry are all made up, made by humans. There is no Euclidean geometry or non-euclidean geometry. The insistence that it must obey geometry has been a straight-jacket for ideas since the times of Euclid and Lobachevsky. GR is, essentially, geometry, while SR is, essentially, mathematics. On mathematical elegance, that is just a value that is human-defined. One should, rather, concentrate on the primacy of physical laws --- defined by Nature.

This discussion relates to the preprint at

Preprint The Electron Magnetism Model (EMM)

Dear Ed, you wrote: "SR has difficulties today".

Could you briefly indicate what those supposed difficulties are?

Hugo Alberto Fernández and all: There are many formulations to choose from in SR, which are actively used. In addition, irrespective of formulations, SR has difficulties itself by being based on geometry, a work of humans, as seen at the end of this posting.

From a geometrical viewpoint, according to the theory of Minkowski SR, space and time constitute a four-dimensional continuum with pseudo-Euclidean structure. This has recently begun to be a practically important statement in accelerator physics, according to DESY. The SR versions can be so ordered:

1. Minkowski SR, preferred by physicists, with different versions, all 4D, is general covariant, at https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html

2. Einstein SR, with different versions, all consider 3D + 1D. Not used in GR. Non-covariant. See https://arxiv.org/pdf/1709.09408.pdf

3. Updated Einstein SR, with different versions, all consider 4D, used in GR. Is general covariant. Did not credit Minkowski, not used significantly.

4. Accelerator physics, traditional with (2), considers "relativistic mass" and 3D + 1D. Non-covariant. See https://arxiv.org/pdf/1709.09408.pdf

5. No SR. Not used in GR. Valid when comoving. Non-covariant.

Also, there is the Mashoon version, the Clifford algebra version with Cl(3,1), even the Brown (not a physicist) version of as recent as 2006, all 3D + 1D. See philosophical discussion at http://philsci-archive.pitt.edu/13405/1/Physical%20Relativity%20from%20a%20Functionalist%20Perspective%20blinded.pdf

We realize that even famous DESY could use non-Minkowski SR, reducing that 4D be accepted by all, which Feynman also said -- so "relativistic mass" lives on. Not everyone has to accept the ontological implications, even though physicists are in the front line, see (1).

However, they must support GR. GR was created on (1) and (3) above, not (2) or (4), and depends on this insight. The Minkowski SR (more than 100 years old) is also valid for arbitrary motion --- accelerated, inertial, or at rest. Brown's version of SR was evaluated negatively in this aspect as cited ," it commits Brown to an implausible relationism in the case of general relativity. "

The main difference of them all is what to consider the postulate for SR, which gives different assumptions ontologically (4D or 3D+1D), and includes or not a real time dilation and length contraction. What is real in Physics?

In my view it makes sense geometrically, but does not solve the physical problem, when Minkowski formulated Einstein special relativity (SR) in terms of spacetime, he changed the basis of the discussion from Lorentz transformation (LT) to the invariance of the interval ds2 to any observer, in inertial motion. Hence, we, geometrically speaking, live in 4D, not 3D + 1D, spacetime not space and time; the division is arbitrary.

However, I consider all too dependent on geometry (see above), and while (1) has the least assumptions and allows the LT to be deduced from the interval ds2 , it still considers geometry as, somehow, imposing the physics under mathematical elegance, but elegance is just a value that is human-defined. One should, rather, concentrate on the primacy of physical laws --- defined by Nature., not humans.

As a solution we are looking into Galileo invariance, which can include (1-4), for the EM field, concentrating on the primacy of physical laws and supporting whatever use one understands.

Mathematics, Geometry, and Physics are all made up, made by humans. There is no Euclidean geometry or non-euclidean geometry. There is just ageometry -- meaning, the absence of geometry -- from the Greek suffix "a-". The insistence that physics must obey geometry has been a straight-jacket for ideas since the times of Euclid and Nikolai Lobachevsky.

Caratheodory, for example, did not follow in this trap, but provided us with a global framework using differential forms. The generalized Stokes theorem is another example, that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω.

BTW, my feedback on Harvey Brown's book on SR, follows.

First, Brown is a philosopher, not a physicist, with a history of profit by means of inflammatory articles. That means he can play "fast and loose" with arguments that will give a physicist pause, with self-empowered impunity. This is both good and bad, in his book. A philosopher simply does not have the same arbiter --- for the physicist it the arbiter is objective, is Nature; whereas for a philosopher it is subjective, is himself (not even other philosophers matter, it is a subjective view).

A review is already available, which says:

"In 2006, Harvey Brown and Oliver Pooley published a paper entitled “Minkowski space-time: a glorious non-entity” [where Brown's bias is evident before the judgment, it is a leading argument]. This paper sets out some of the central arguments that are developed and expanded in Brown’s book. [where the bias continues in the titles of the book's chapters names, leading, and also exemplifying his confirmation bias]"

and "... it commits Brown to an implausible relationism in the case of general relativity. "

Physicists, furthermore, generally consider Minkowski SR, with the reasoned in Nature exclusion of other forms, and Einstein also agreed when he created GR based on Minkowski SR, even though it was not his dear original SR.

Brown, however, "paints himself" in a corner there, with no path to GR, as noted by the review quoted. He is no neutral observer, making such primitive logical errors.

In his book, Brown is best seen as giving an analysis of his own (Brown) subjective concept of spacetime, rather than as defending an objective view about the reality of spacetime (as a physicist would be trained to do).

That is also the opinion of other publications. Brown's book is not physics or SR, and it shows.

(quotes in http://philsci-archive.pitt.edu/13405/1/Physical%20Relativity%20from%20a%20Functionalist%20Perspective%20blinded.pdf )

Dear Ed,

I misunderstand your post. It would be convenient to wrote “SR different formulations have difficulties today”.

Anyway, the 4D and 3+1space-time formulations are necessary and, if correctly used, will gave identical results.

Hugo Alberto Fernández : Not quite, it is not the SR different formulations that have difficulties only, as explained at the end on of my posting. The 4D and 3+1 space-time formulations are also not both necessary and will provide the wrong answers, as they report at DESY -- moving to 4D, and rejecting 3D + 1D. It is in the first two sentences of the abstract, at the given URL https://arxiv.org/pdf/1709.09408.pdf

Dear Ed,

Modern approach (Logunov) of SR theory has one single postulate: Space-time has Pseudo Euclidean geometry (Minkowski space). So, it is no relevant the mathematical structure used. Any formulation preserving such space-time geometry will be equivalent and, as I said before, will gave identical results.

The shared article in your last comment does not correctly refer to 3+1space-time formulation preserving the pseudo Euclidean geometry. What they named (3+1) approach is non-covariant (see Conclusions). So, it is not a SR formulation.

Hugo Alberto Fernández and all: Thanks for your input, I have clarified. Let us say that using SR includes two types of problems:

For example, a theory that would allow one to derive the structural properties of spacetime, cannot start with Clifford Algebra or Cl(3,1), by definition, that separates space and time.

Using slow transport to synchronize clocks and thus to define a temporal variable in a three-dimensional Euclidean space, in which we consider the relativistic modification of Newton's second law, is a rather strange process, and an approximation that can naturally provide doubtful results when a certain accuracy is reached in the analysis of the experimental results.

Indeed, the theory provides that the modification of Newton's second law has the usual form when the temporal variable is defined independently of the three-dimensional space but in accordance with the Poincaré-Einstein's procedure, that is to say through the hypothesis of the constancy of the motion of the electromagnetic signal in the vacuum.

Thus, for a theorist, it is disturbing to read the conclusion of the DESY's report:

>

On the other hand, it is not easy to make a comparison with the theoretical extension of defining the temporal and spatial derivatives of electric and magnetic fields that a source generates in a place where it is located, but mathematics can sometimes surprise and the theory can turns out to be not directly related to its practical approximations:

Anatoly A. Logunov (April 2000, monograph relativistic theory of gravity RTG):

>

https://www.researchgate.net/post/Error_in_the_mathematical_formulation_of_Einsteins_equivalence_principle

Dear Ed,

the root causes for all the physical properties we observe, are not expressed within the equations, we use to describe these properties. Therefore the validity of all equations including the Maxwell equations is limited to length scales >>Planck Length and to length scales

The book "Principles of Electrodynamics" by Melvin Schwartz, of Stanford Univ., of 1972, can serve to illustrate some of the points here, in looking to eliminate Maxwell equations in EM, nothing against him of course.

It is reviewed online: Unlike most textbooks on electromagnetic theory, which treat electricity, magnetism, Coulomb's law and Faraday's law as almost independent subjects within the framework of the theory, this well-written text takes a relativistic point of view in which electric and magnetic fields are really different aspects of the same physical quantity.

Suitable for advanced undergraduates and graduate students, this volume offers a superb exposition of the essential unity of electromagnetism in its natural , relativistic framework while demonstrating the powerful constraint of relativistic invariance. It will be seen that all electromagnetism follows from electrostatics and from the requirement for the simplest laws allowable under the relativistic constraint. By means of these insights, the author hopes to encourage students to think about theories as yet undeveloped and to see this model as useful in other areas of physics.

After an introductory chapter establishing the mathematical background of the subject and a survey of some new mathematical ideas, the author reviews the principles of electrostatics. He then introduces Einstein's special theory of relativity and applies it throughout the rest of the book. Topics treated range from Gauss's theorem, Coulomb's law, the Faraday effect and Fresnel's equations to multiple expansion of the radiation field , interference and diffraction, waveguides and cavities and electric and magnetic susceptibility.

Carefully selected problems at the end of each chapter invite readers to test their grasp of the material. Professor Schwartz received his Ph.D. from Columbia University and has taught physics there and at Stanford University. He is perhaps best known for his experimental research in the field of high-energy physics and was a co-discoverer of the muon-type neutrino in 1962. He shared the 1988 Nobel Prize in Physics with Leon M. Lederman and Jack Steinberger.

On multivectors, I want to comment that they are mathematically correct, but not physically correct.

Multivectors do not apply to describe SR, because they are themselves generally non-covariant. By using a generally non-conforming tool (aka Clifford algebra, Cl(3,1), Hestenes, Chappel, Waldyr Rodrigues, etc.) with multivectors, one gets false positives and false negatives in the Hamiltonian, along with true values. By filtering (e.g., with a Hamiltonian itself), one can keep the true values, get rid of some of the false positives, and get rid of some of the false negatives. It is easy to prove that one does NOT get rid of ALL the "junk" -- all the false positives and all the false negatives! In particular, ALL the false negatives dot not even reach the second stage, the Hamiltonian filter.

Therefore, the results are provably wrong using multivectors (aka ...) in the first place, including missed good results and falsely accepted results, ever. One needs to use tensors, which ARE generally covariant, notwithstanding the difficulties -- even better if it is difficult, there is more space at the top.

No, Maxwell's Equations can never be excluded from Electromagnetism. These are principles of Electromagnetism, and cannot be excluded.

they (at least) must be revided

Dear Paul,

What do you mean from "revided"? I think that you mean "revised".

Anyway, Maxwell's Equations are necessary and sufficient for Classical Electrodynamics. These equations cannot be revised in Classical Electrodynamics.

sorry: revised is the right word

I already wrote the theory in the language of distributions (i.e. all physical terms (and laws) must be described by using functionals)

What would be the aim of a revision of the Maxwell Equations?

Is it an extension of the validity range to small or giant length/time/energy scales or to extremly high energy densities (e.g. photon/photon interaction) or to fully cover relativistic effects (keywords: QED,"tensor formulation of the angular momentum")?

Or is it only a revision of the mathematical formulation with the aim to simplify calculations?

Maxwell's equations need to be excluded even in Classical Electrodynamics, because they lead to nonphysical results there too. Details in the discussion head and ff.

But, experimental laws are vital in Physics. The laws must be independent and universal. Four Maxwell's Equations are vital in Classical Electrodynamics.

I do not know what you mean from exclusion of the Equations. With no doubt, if one of the Maxwell's Equations is excluded, another equation has to be included, which should be independent of the other three equations.

Houshyar Noshad : Note that, as said in the discussion head, the Maxwell's equations are redundant themselves. What I mean by exclusion is not that of a member of the set, is to exclude them all -- it is also in the discussion title and head, "Can we build a complete theory of EM without mentioning historical causes, without mentioning for any physical reason the Maxwell's equations, even indirectly? "

“The electron is a photon around Dark Matter”

Adrian Ferent

“The photon wavelength is 2πr, r the electron radius”

Adrian Ferent

“The high energy Gravitons emitted by Dark Matter keep the photon inside the electron”

Adrian Ferent

“In Ferent Quantum Gravity is important the energies of the Gravitons emitted by Dark Matter, not the Dark Matter mass”

Adrian Ferent

“Inside the electron, Dark Matter mass is much smaller than electron mass, but has much bigger energy”

Adrian Ferent

“Ferent electron and positron collision:”

Adrian Ferent

“Photon momentum after n interactions:“

Adrian Ferent

“The way how the photon ‘oscillates’ inside the electron will give the electron spin”

Adrian Ferent

“The way how the photon ‘oscillates’ inside the electron will give the electron charge, negative charge – electron, positive charge – positron””

Adrian Ferent

“Because electron–positron pair is produced by a photon – photon interaction and two gamma rays of 0.5 MeV each will be created in electron and positron collision, I considered only one photon inside the electron”

Adrian Ferent

“Gamma ray is inside the electron because of electron’s electromagnetic properties and electrons interactions with photons”

Adrian Ferent

Einstein said; “You know, it would be sufficient to understand the electron” which is still true today.

“Conclusion: No Conclusion. So, what is an electron? An electron is a particle, and a wave; it is ideally simple, and unimaginably complex; it is precisely understood, and utterly mysterious; it is rigid, and subject to creative disassembly. No single answer does justice to reality. ” – Frank Wilczek

Our civilization is based on electrons, without knowing what electron is.

Electrons cannot be described as solid particles. An electron is a quantum object.

Because of Heisenberg uncertainty principle, particles cannot be restricted to a geometric point in space because this would require an infinite particle momentum.

Atomic orbital is a function that describes the wave-like electron inside the atom and this function is used to calculate the probability of finding the electron around the nucleus.

Electron and positron collision: at low energies the result of the collision is the annihilation of the electron and the positron and gamma ray are created.

If the annihilating electron and positron are at rest, each of the resulting gamma rays has energy of 0.5 MeV and frequency of 123 EHz.

“Ferent electron and positron collision:”

Adrian Ferent

Where: DMe is the Dark Matter inside the electron

DMp is the Dark Matter inside the positron

“Dark Matter interacts only gravitationally with matter”

Adrian Ferent

“The elementary particles are created around Dark Matter”

Adrian Ferent

That is why at CERN they do not know what they collide, that is why they do not detect Dark Matter.

“Because the elementary particles contain Dark Matter with the mass much smaller than particles mass, Dark Matter is not detected at CERN”

Adrian Ferent

Photon – photon interaction: both photons are gammas rays with just enough energy to produce an electron–positron pair.

“Ferent equation for the energy of a photon E = h × f + a × f ”

Adrian Ferent

One possible explanation for the electron:

“Because the photon has Dark Matter, the interaction Dark Matter photon with Dark Matter electron, keep the photon inside the electron”

Adrian Ferent

“Ferent equation for photon – graviton interaction: E = h × f + a × f - a × ν “

Adrian Ferent

Another possible explanation for the electron:

If I take in consideration the gravitons pe emitted by the photon, the equation will be:

“Photon momentum after n interactions:“

Adrian Ferent

The momentum of gravitons pe emitted by the photon, it is smaller than the momentum pk of the gravitons received by photon from a galaxy.

That is why the photon will move towards the galaxy and this is Gravitational lensing.

In the same way, was created the electron:

“The high energy Gravitons emitted by Dark Matter keep the photon inside the electron”

Adrian Ferent

A single-photon pulse is a pure quantum state.

“The electron is a photon around Dark Matter”

Adrian Ferent

Because the photon must be very close to Dark Matter, in classical view:

“The photon wavelength is 2πr, r the electron radius”

Adrian Ferent

Scientists will say for that radius is required a huge mass for Dark Matter, this means the electron will have a huge mass.

The Schwarzschild radius, the radius of the event horizon:

In Ferent Quantum Gravity this is not relevant, because Einstein Gravitation theory is wrong.

“In Ferent Quantum Gravity is important the energies of the Gravitons emitted by Dark Matter, not the Dark Matter mass”

Adrian Ferent

“Mass–energy equivalence for Dark Matter: E = md × vp^2”

Adrian Ferent

That is why:

“Inside the electron, Dark Matter mass is much smaller than electron mass, but has much bigger energy”

Adrian Ferent

That is why particles like axions, neutrino, neutralinos…are not Dark Matter particles.

“What you learned from your professors, from peer-reviewed journals, from your books, from the greatest scientists about Gravitation, Black Holes, Dark Matter… is wrong” Adrian Ferent

“The elementary particles contain Dark Matter”

Adrian Ferent

“Unification between Matter and Dark Matter:”

Adrian Ferent

“Ferent equation for elementary particles:”

Adrian Ferent

“Ferent equation for N elementary particles:”

Adrian Ferent

“Ferent equation for elementary particle, made of 2 particles, a Matter particle and a Dark Matter particle, is the Unification between Matter and Dark Matter!”

Adrian Ferent

“The way how the photon ‘oscillates’ inside the electron will give the electron spin”

Adrian Ferent

“The way how the photon ‘oscillates’ inside the electron will give the electron charge, negative charge – electron, positive charge – positron””

Adrian Ferent

“Because electron–positron pair is produced by a photon – photon interaction and two gamma rays of 0.5 MeV each will be created in electron and positron collision, I considered only one photon inside the electron”

Adrian Ferent

“Gamma ray is inside the electron because of electron’s electromagnetic properties and electrons interactions with photons”

Adrian Ferent

AF: this is fake, off-topic, and spam. You are called to delete it and stop.

THIS QUESTION IS NOW CLOSED.

In classical electrodynamics, the magnetic moment of an electron and a neutral particle is not taken into account. In this regard, it can be supplemented.

Dear Seil Sautbekov ,

Yes, you are quite right. The magnetic moment of an electron needs quantum electrodynamics.

All: There are other causes for the magnetic field, some listed above, which might also be hidden by our history; history can also be a drag.

The magnetic moment of particles need to follow QM, not Maxwell, and are included in the EMM. In other planets, maybe the electron was discovered earlier, and maybe E and B were never considered to be independent.

There are benefits in separating science from history -- for example, it shows that history cannot define nor limit science, and it prepares us scientifically for meeting other civilizations in space, as NASA and other seek.

This discussion was closed because it already includes all the points that need to be mentioned from a science perspective -- and it excludes history, for a reason. Therefore, to keep it open only invites spam. Your interest is appreciated, and the questions above complement well the discussion text, and give them a higher value.

I propose to consider taking into account of the magnetic moment in classical electrodynamics with help of the potential of a magnetic dipole (or neutral currents) obtained in

https://authors.elsevier.com/a/1YvLP15Kgb69JJ

In the EMM model, electrodynamics is never classical in any sense of the term. If if were classical, such as not adopting QM from the start, it would necessarily be wrong there.

QM is not optional, Mikowski SR is also not optional. No system is too slow, for example, to not use SR, because velocity is relative -- what is slow or even at rest near an electron maybe 0.5c in the lab frame.

this potential is relativistic

Classical Electrodynamics with four Maxwell's Equations is quite perfect, and is able to explain all the phenomena in this field.

None of the equations can be excluded, and another equation cannot be included. Never doubt the truth and universality of Maxwell's Equations in Classical Electrodynamics.

Some subjects such as the magnetic dipole moment of an electron, which is directly related to its angular momentum, is not in the scope of Classical Electrodynamics.

Conclusion: CLASSICAL ELECTRODYNAMICS IS PERFECT AND NO IMPERFECTION CAN BE FOUND.

SS: Using SR makes it more useful, one more reason no to depend on Maxwell's equations. A magnetic dipole is observer-dependent.

In general, magnetic force is observer-dependent. But, it can be properly explained using the Maxwell's equations. The reason is that Maxwell's equations are invariant under Lorentz transformations.

HN: It is well-known the reverse of what you say -- namely, that the magnetic field B cannot be properly explained by the Maxwell's equations (ME). For example, E and B could be independent as far as ME is concerned. But, they are not.

The fact that ME is Lorentz invariant (LI) is misunderstood as meaning that every equation that is LI is valid, which is not true in physics. If one changes "is valid" for the conditional "may be valid" then it is what is meant in SR. It is NOT determining to be LI as the only condition.

SS, HN, EL, and all: Please read the discussion head and prior answers. You are just rehashing arguments asked before. In summary, by asking why the Maxwell's Equations (ME) are needed, the question arrives at the contrapositive answer -- the ME are NOT needed to explain classical and up to quantum electromagnetism. This is the scientific answer.

Historically, the ME are needed for history reasons only -- another planet might follow a different, shorter, history. There are scientific reasons to NOT follow the dominant or any historical version, for example, the contradictions and their unnecessary weight.

All: In today's race of students to learn now at college, and earlier, it may be better to forgo history of science and focus on science. Some curriculum and seminars claim otherwise, but historic paths will never define science, and may act against, in confirmation bias, for example, and time lost.

Take, as another example, the Newtonian Mechanics (NM) versus the Lagrange Formulation (LF). Today, any problem in NM can be solved using LF, but not the reverse. When reaching the LF, though, the Maxwell's Equations (ME) are no longer valid. Having to unlearn NM and EM together, still leaves in the student the wrong intuition, in addition to more time and confusion. Suddenly, E and B are NOT independent, and have the same units. There are other differences, even more fundamental.

Rather than a "simplified" view of reality, the student gets a wrong view of reality. Instead, we investigated long ago if it is possible to reduce history of sciences to zero, in science, and only focus on what is essential.

It turns out that only science is important to science, even in learning it, so one can forgo history of science -- and its time load to learn and unlearn. Also in new developments, in the same way that all fear in unfounded (because fear is irrational), history of science acts often as a "naysayer" that is artificial and stymies the very new developments that it is supposed to foster. For example, on developing a cure for ulcer, in special relativity, or in electromagnetic theory.

Understanding special relativity (SR), leads to a better understanding of the classical (SR included, but not QM yet) EM field.

Then, E or B can be zero, and have the same units (e.g., gauss), but they are not independent -- and this is proven in experiments also. This is well-known. It is not in Maxwell's equations, although they are covariant with SR...

But the differential form of the Maxwell's equations are right in the sense that they allow one to affirm that there is no source for the magnetic field B.

Going further, microscopically, including QM, the only "source" of magnetic fields B is the movement of charges. There are no monopoles.

If the charges are a total of zero, they can still exist (as + 1 and -1 in balance) and yet have a magnetic field by their movement. Movement, here, is relative -- even if the observer moves inertially, not at rest.

An observer at rest, relative to a classical (SR included, but not QM yet) constant velocity, moving, free electron, sees a magnetic field B. An observer on the free electron itself, classical (SR included, but not QM yet), is at rest therefore, and sees no magnetic field B. Where did B go?

Nowhere, that classical B is observer-dependent. The observer changed, inertially, and sees different things -- no more magnetic field B. It was not intrinsic to the situation, it was arbitrary.

Now, if one adds QM, a magnetic field may appear. But this is not classical electrodynamics anymore, and Maxwell's equations show further shortcomings when compared with reality, with experiments. In QM, an electron itself has a dipole moment, a B field -- but is an electron not a particle in QM? NO. It is called "spin" -- a quantum property intrinsic (not observer-dependent) to electrons.

Electrons are also not made up of quarks. They are in a separate "family" of particles known as leptons.

Matter and energy are also not forms of the same thing (as popular accounts say), where mass is not conserved in SR but is an invariant in SR, whereas energy is conserved in SR. There is no "energyless" mass, but there is massless energy.

Electrons have mass and so are considered matter and not massless energy. There are other considerations, even without QM, just SR, that distinguish electrons from photons.

This means that photons are part of a larger description that has consequences, not just "reduce the fields to particles which interact with their sources" -- even if one restricts to electrodynamics.

An observer on a free electron itself, following classical Maxwell's equations (SR included, but not QM yet), is at rest therefore, and sees no magnetic field B.

In the QM view, the Hamiltonian for such a system may not be separable, and there may seem to be no way to naturally change the spherical symmetry into cylindrical symmetry, adiabatically. However, experimental and theoretical results indicate that an "approximate symmetry" may exist. The scaling law is derived by us in Phys. Review Lett., in:

[1] Article Scaling Laws for Rydberg Atoms in Magnetic Fields

where we explore the dynamics of electronic motion along a plane perpendicular to the magnetic field.

Still, contrary to a common misconception, we do not have different kinds of photons for the magnetic and electric fields, as they (E and B) have the same units -- eg, gauss. It is important, to avoid confusion, to also remember, from SR, that E and B are not independent. The only observer-independent reality (SR included, but not QM yet) is the EM field, which has one kind of photon -- the EM photon.

Yes, one could ask, this is the magnetic field of just one charge, but it is vectorially added with time-shifts (for example, using phasors, as propagation is not instantaneous) in classical electrodynamics of Maxwell (CEM) (SR included, but not QM yet) to other like individual contributions to create, for example, the almost-rectilinear stationary magnetic field inside a solenoid. It could also create a rotating magnetic field, from three stationary coils, as used in AC motors. (The QM view is different, electrons are no longer isolated particles, and can influence even themselves.)

In CEM, the phasor addition manages, for example, to cancel locally away, the undesired spatial and temporal "noise" of the other electrons. For example, to generate an almost-rectilinear stationary, or circular, magnetic field -- going from spherical to circular symmetry "approximately," as in QM [1]. The same can happen in magnetic domains, in a material, even if the electrons move otherwise.

Now, we go even more microscopically, to atoms and particles. Still, there are no monopoles. As I summarized before, and may be easier to follow with [1], there is no "source" of magnetic fields B but the movement of charges, where spherical symmetry (of even a perfectly round B field) can change to cylindrical symmetry, or other, "approximately" as in [1], and and QM further introduces the spin of the electron.

I am going to present additional evidence, supporting the exclusion of Maxwell laws from EM. The pros and cons of such change in physics are discussed above, where historical reasons are path-dependent and considered not relevant to the physics.

If one changes "geometry" to "analytics" (because geometry implies an outside model) then it may be possible to expect to derive the EM forces without other assumptions, and without QM, using SR, with some developments as done geometrically by Prof. Melvin Schwartz in 1972, in his seminal book "Principles of Electrodynamics", published by McGraw-Hill, while at Stanford University.

Accordingly, Schwartz shows in "Principles of Electrodynamics" that electromagnetism is deeply affected by SR, E and B are not independent, and must have the same units (already have, in SI CGS).To repeat partly, because RG hides replies, read the review below:

"Unlike most textbooks on electromagnetic theory, which treat electricity, magnetism, Coulomb's law and Faraday's law as almost independent subjects within the framework of the theory, this well-written text takes a relativistic point of view in which electric and magnetic fields are really different aspects of the same physical quantity. Suitable for advanced undergraduates and graduate students, this volume offers a superb exposition of the essential unity of electromagnetism in its natural, relativistic framework while demonstrating the powerful constraint of relativistic invariance."

SR Minkowski is not disputable here, even Einstein agreed with it, which was humanly hard, in creating GR. But this is not relevant in physics -- the point of view may change many times, but our description of reality has to not change -- it has to agree with Nature.

It is well-known that SR Minkowski is valid for arbitrary motion, not just inertial. Any acceleration is included in such SR. See references above and online.

To agree with peoples' objection to treat time as a complex number in Minkowski SR, we recall that there is no situation where a complex number is necessary in a physical quantity, by definition -- a physics value (such as time) must be measurable, but complex numbers are not measurable. Time cannot be imaginary, or complex.

Complex numbers can be very helpful though, as in Minkowski SR, but are neither necessary nor truthful to the physics. It is just a bookkeeping model, it has no ontology. It is arbitrary. One may not use it.

What has ontology is the 4D model, as one may find in situations using tensors. One should not confuse complex numbers with a 4D model of spacetime, when encoding 4D in simple complex numbers for time, without tensors. For example, Cl(3,1) encodes 3D + 1D in multivectors, using reals, but keeps space apart from time, and is therefore useful but not covariant.

Tensors are covariant because if we write A = A in any coordinate system X using tensors, still A = A in any system with constant velocity relative to X. The principle here is physical -- stated first by Einstein, with Galileo applying approximately, to low speeds.

In a similar way, one should not confuse a complex reactance in electronic circuits with a single circuit element, such as a capacitor.

A capacitor can be represented also without any complex numbers, exists, is physical, it is a physical fact.

However, the use of a complex reactance brings the association of circuit elements to a ready calculation in lower frequency, simple algebra. However, it cannot represent that same circuit element, in higher or optical frequencies.

Also, we need to consider that the = sign has at least 5 meanings. When the = sign is used, care must be taken. Usually, there are different situations for each side, but in spacetime connected. Can also be otherwise. For example, in E = mc^2.

Further considerations to be added, below.

People often mentioned that is not easy to define the age of the universe.

Actually, it is now near zero time at the origin, that is what Physics can calculate to, and measure. It depends, however, where you are. On Earth, it is now about 13 billion years older.

Further, there is no "universal time", and people actually thought so because there is no way in Physics to instantaneously connect the clocks, and different strategies were considered. But it is not because people cannot know, it is arbitrary.

In SR, we already know there can be preferred frames (the lab frame is often used for v=0, or the CMB, etc.). We explain elsewhere that SR and GR do NOT work on the basis that there is no preferential or special inertial frame of reference. The CMB does not introduce newphysics, that is the point.

The principle in inertial motion, which is due as far back as Galileo, is NOT that there are no special or preferential frames, such as the CMB or other, but that there are no frames in inertial motion where the laws of physics are different to inertial observers.

So, there can be no absolute frame, a "universal time" does not exist. And, no one misses it -- this is not like ship navigation in medieval history, that had to synchronize clocks. Thus, a "universal time" is not even needed, nor possible. In spacetime, the separation into space and time is arbitrary. Seehttps://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html

This affirms, on mathematical elegance -- that is just human-defined. Elegance is for tailors, said the same Einstein. One should, rather, concentrate on the primacy of physical laws.

In maths elegance is OK, some defend them, but these are just mathematically-based structures, and constraints. Even the sign = has at least 5 meanings. We have to realize that they are not physically necessary, however, and may be a cause for nonphysical results. Further, every number in a set of data, if it is genuinely the result of a physical measurement process, is always a rational.

For example, we calculate a crystal lattice first, stationary, then perturb that matrix with a phonon. The phonon, however, was always there, but was NOT used to calculate the crystal lattice. The reason is the large differences in energy between the atoms' covalent bonds in the crystal, with the phonon. But make the phonon resonant, or too numerous, and one has to calculate the matrix with the phonon, separation of variables does not work anymore. This is not a mind's dream, it can change the lasing frequency of the crystal itself, and be calculated. See

Article Quantum well lasers tunable by long wavelength radiation

For the curious, the general principle behind the assertion that "the = sign has at least 5 meanings" is that "trust provides meaning to information." Information itself is just arbitrary, syntactic, data. If someone says they will send you a GIFT, they may send you a poison (GIFT in German). A symbol like "=" is no different than a symbol like "GIFT" --- the meaning depends on trust, outside the channel of information transfer. Some languages have no word for trust, just confidence, but they are not equivalent; so if you are reading this through automatic translation -- beware. Trust != confidence, where "!=" means, as usual, "not equal".

Specifically, "=", mathematically, may mean "exact equality", "congruence", "equality to the left", "equality to the right", "comparison", etc. For example, to a C compiler "2=2" is incorrect and it should balk, whereas it will accept "2==2" as an exact comparison test.

So much for physics equations with "=", like "E = mc^2".

Contrary to common lore, energy and mass are not equivalent. The m (for mass) is an invariant but is not conserved, but E (for energy) is conserved, while there is massless energy but not "energyless" mass, so the "=" sign has to be interpreted according to the physicist's beliefs (here, belief is the probability that the evidence supports the claim).

For another example, in the Einstein Equation in GR, Einstein introduced the cosmological constant as "deux ex machina" (no physical theory behind it, as an ansatz, quite teleological albeit not necessarily theological) to preserve the universe without expansion.

Time and space, however, are not isolated, they exist in fusion, as the word spacetime indicates. They cannot be uniquely divided, experiments show with zero contradiction of physical facts.

People, however, can use any formulation of SR they want, such as with "relativistic mass", Clifford Cl(3,1), and Minkowski spacetime, even no SR, with the experimental rule, based on physical facts:

Comoving observers NEVER measure time dilation or length contraction, whereas non-comoving ALWAYS do. It does not matter the acceleration, nor the velocity.

Comoving means same position and velocity, not necessarily identical objects; in cosmology comoving observers see the same wavefront, so it is coherent. Depending on the SR formulation one uses, even no SR, more or less "paradoxes" will result. The less "paradoxes" the better.

Therefore, "relativistic mass", even as used by Melvin Schwartz (op. cit), is a concept that is not a physical fact, but may be a platonic model, inaccessible, a bookkeeping method, a mathematical equation one uses, without ontology.

We should not be surprised to see the same in complex numbers -- where we can start and end with a real number, but go through the complex plane.

It is not that the complex number has real existence, but that hidden path allows us to consider singularities easily in a finite way, like the Residue Theorem does. Someone, not wishing to use complex numbers, can do the same thing -- without trusting the Residue Theorem.

It is not necessary to use complex numbers in Physics or Engineering, and all measurements of physical facts are real numbers (actually, rational), but they can greatly simplify the calculations.

Likewise, in solid state physics, there is a concept called hole, which can be seen as the absence of an electron, and has "negative mass". Again, though, is just a bookkeeping method.

Similar with configurations of SR. There is no "absolute truth" in the equations but they represent bookkeeping methods, with more or less "paradoxes" -- including the choice of no SR. The method with less "paradox" is, naturally, the method with stronger ontological value -- Nature, as we can see it.

Reality is observer-dependent, in QM and life. Reality also seems to support free-speech, valued since Greek times. This allows us to explain findings in apparent contradiction in GR, for example (see newer version of preprint).

Starting with the Heisenberg principle, observer and experiment cannot be dissociated. There is no objectivity in QM -- but there is a coherent abstract view one can pursue in QM. See Deleted research item The research item mentioned here has been deleted

New version, following the EMM work, with added references to help in general:

Deleted research item The research item mentioned here has been deleted

BTW, E and B are not independent and have the same unit (since 1881), before Schwartz's book in 1972 (op.cit.). The EMM is using that development, not creating it.

In the book, the unit question is treated right in the beginning, and that is why the book uses CGS, where the common unit to E and B is called "gauss" -- officially by SI. John Littlejohn at Berkeley writes,

"The main advantage of Gaussian units is that they make fundamental physical issues and theoretical relations involving electromagnetic phenomena more clear. For example, special relativity and quantum electrodynamics are simpler, more transparent and more elegant in Gaussian units than in SI [MKS] units, and generally the various formulas of electromagnetism are simpler and easier to remember in Gaussian units than in SI [MKS] units. Gaussian units are really the simpler system of units, and they would be better for pedagogical purposes were it not for the fact that students must deal with SI [MKS] units some day anyway".

At least, this may reduce conflicts and 'paradoxes", as the QM model (preprint linked above) says, and supports SR.

Two additional references, on E and B:

http://info.ee.surrey.ac.uk/Workshop/advice/coils/unit_systems/

https://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf

NONE OF THE MAXWELL'S EQUATIONS CAN BE EXCLUDED FROM CLASSICAL ELECTRODYNAMICS.

All: First, I suggest to see the video by Robbert Dijkgraaf in https://www.youtube.com/watch?v=6oWLIVNI6VA

For a metaphor, a finger may type D on a keyboard, but G was meant. The D was an illusion, but made real by the keyboard. Error-correcting codes may encode all possible futures as the one real possibility, e.g., forming a n-step circle of maximum probability around each letter on a QWERTY keyboard, so that for a 2-step circle if one types D then it is correctable to G, but if one types L it is NOT correctable to G.

This can prevent "microscopic" folding of past, present, and future from "macroscopically" affecting reality, and is represented in reverse by a large number of birds doing a macroscopic pattern in the sky, albeit microscopically avoiding it.

The B field in EM, is another example -- it is in all cases we could research generated by movements of charges, using SR as fundamental, so that macroscopically we do "see" an external magnetic field B, while there is no internal magnetic monopole or dipole, intrinsically.

Give the end result without mentioning the history?

Sure, it is possible, but pointless.

All: By requiring variations in all directions to equal zero (the variational principle), one can obtain the Euler-Lagrange equation both in SR and in the Schroedinger equation (non-SR QM), leading to RQM (SR + QM), and QFT. EM and GR will have to be extended likewise, one may conclude, following also the Euler-Lagrange equation. This extends, not contradicts, F = ma, Newton's law, which also obeys the Euler-Lagrange equation. So, the Euler-Lagrange equation is likely to explain whatever we may find, including dark-matter. Details at:

Preprint New Physics with the Euler-Lagrange Equation: Going Beyond Newton

No, the Lorentz invariance (SRT) must be excluded from both Maxwell's equations and electromagnetism.

In Einstein's 1905 paper, the "kinematical part", he uses information exchanges by light between reference frames, and concludes that light is deformed. When light is used to measure time (frequency) or length (wavelength), or when the mass is deduced via E=mc² with an assumed c = constant, then one calculates what the deformed signal is, and with the speed of the frame, one can calculate back the emitted values of length and tick rate, and the deduced mass.

Then we always find a retarded clock tick rate and a shortened length deformation.

However, the result is valid for every frame, even mutually! Hence, each frame will say that the other lengths are shortened and the other clock tick rates are retarded.

This mutual result is only possible if the measurements are optical deformations, not real physical values inside the frames themselves.

Conclusion: relativity is just an optical deformation, nothing fundamentally physical or anything else, spites many claims made by the mainstream science.

Yet, it is disputable that c = constant at all times, and that the same signal would be running at c on Earth, on the planet Serpo, and on any place between-in, as seen from either planet, when one assumes that there is a method to communicate much faster than light in order to check that, like it would be the case with waves in the oceans, when checked by light.

In the second part of his 1905 paper, the "electrodynamical part", he applies the former, "kinematical" result to the electric and the magnetic field of one of Maxwell's equations.

However, the electric and the magnetic field are not observable with light as he did in the former, "kinematical" part, so, it is unapplicable here!!!

The electric and the magnetic field are entities by themselves and propagate by themselves, hit other charges and are a real force field. They are no observable field (by light) as supposed by Einstein!!!

So, his theory is nonsense in electromagnetism and in Maxwell's equations!

Best regards,

Thierry De Mees

TDM, ad all: Do you think that SR only works for those who believe on it? SR gets potentially more effective for those who know its laws, such as in creating MRI, but objectively acts on all humans and non-humans alike. Even on inert matter, and fields with no matter -- and particles such as a photon, which can have mass in collective effects (two photons or more).

As CB said elsewhere, it is not SR that should be categorized as metaphysics, but the denial of SR.

Since SRT is proven to be logically erroneous from its very own theory, because it tries to "observe" electric and magnetic fields by using light communication, SRT is simply not applicable to electromagnetism.

SRT is fraud and the mainstream knows it. See my explanation in above post.

Electromagnetic experiments are influenced by the retardation of the fields, which cause altered Maxwell equations at a distance, as very well explained by Oliver Heaviside at the end of the 19th century, several years before Einstein (who didn't understand an yota of it), and Heaviside's work was further developed by Oleg Jefimenko at the end of the 20th century.

The resulting equations have a factor that resemble a bit the Lorentz factor, but that doesn't validate of course Einstein's totally wrong work.

Einstein's idiocy indeed didn't result in a Nobel prize because the Cabal wasn't yet controlling it.

Only under great pressure, Einstein got the Nobel prize for some other stuff, and the "genius" attribution was pure lobbywork.

Dear Thierry ,

In fact, your comments on the special theory of relativity in Electromagnetism (static electromagnetic fields)as well as the Lorentz invariance of Maxwell's Equations surprised me.

I would like to point out a short history regarding the special relativity, electromagnetism as well as the retardation of electromagnetic fields originated from a moving charge as follows:

Hereby, I would like to emphasize that Oliver Heaviside was the first physicist who introduced the Lorenz transformations, when he was working on some electrodynamical problems such as those involving a steady current passing through a conducting wire for which the velocity of the charged particle was constant. He demonstrated that for an observer moving with the same velocity, the coefficients of the space-time transformations were obtained with due attention to this fact that the electric resistance of the wire should be invariant in comparison with the value obtained from other approaches (such as solving the Laplace equation for the steady current potential). Heaviside never published his important results.

After Heaviside, the Lorenz transformations were also studied by Joseph Larmor in 1900.

Afterwards, Hendrik Lorentz worked on the transformations, and obtained the coefficients. He published his results in a paper in 1904.

Albert Einstein used the results obtained by Hendrik Lorentz in his works and studied them in more details. For instance, he concentrated on the special relativity applied to static electromagnetic fields such as electromagnetism of charged particles traveling with a constant velocity (as is the case for steady current problems).

I know the incorrect assumption that Einstein made in his paper, but the special theory of relativity (and equivalently the Lorentz transformations) and electromagnetism (i.e. static electromagnetic fields) are closely related to each other, and is independent of the mistake made by Einstein. Hence I frankly say that:

EXCLUSION OF THE LORENTZ INVARIANCE FROM MAXWELL'S EQUATIONS OR ELECTROMAGNETISM CAN NEVER BE STATED AND DISCUSSED.

Study of electromagnetism of a charged particle moving with a constant velocity requires special theory of relativity provided the observer moves with the same velocity. As a consequence, this is a fact in static electromagnetic fields, and cannot be ignored.

On the other hand, retardation of electromagnetic fields is also a fact, and in general it can be properly studied with the Jefimenko's Generalizations for time varying fields, which correspond the generalized Coulomb and Biot-Savart laws.

In the case that the charged particle moves with a velocity (not essentially constant), the retarded electric and magnetic components of the electromagnetic fields can be properly explained by the Lienard-Wichert formulation. It is evident that if the charged particle travels in a medium with a time varying velocity, the special theory of relativity is no longer valid. Hence, Lorentz invariance as well as the Lorentz transformations are not applicable; and thus, cannot be used due to the acceleration of the charged particle.

Best wishes,

Houshyar Noshad

Dear Houshyar,

Oliver Heaviside tells a totally different story than what you tell. Oliver Heaviside was NOT introducing the Lorenz transformations. What he did is shown on page 495 of his book Electrical Papers Volume II, p. 495, https://archive.org/details/electricalpapers02heavrich

He has shown that the continuous emission of electric fields from a charge results in retardation of these fields (by the speed of light) in a given point, which gives accumulation or dilatation of the field amplitudes depending from the measuring position and the charge's speed. Mathematically, it results in a Lorentz-like factor in his equation.

Totally different is Einstein's approach, which calculates the deformation of light from moving frames, not charges. So, he observes with light, and calculates the deformation of that light.

Then, he tries to apply this to electric and magnetic fields (1905 paper, Electrodynamical part), which is of course impossible, since electric and magnetic fields are no observables as frames are, as he did in the kinematical part. Electric and magnetic fields simply are themselves present and cannot be observed by light. Contrary to light, these fields are force fields between charges, and Heaviside's equations show the results of the force fields at a distance for a moving charge with constant velocity during an infinite time.

Best regards,

Thierry De Mees

The phenomenon of EM waves cannot be understood as separated from

SRT. Agree with Houshyar. The Lorenz transformation is inherent in this.

The theory is practically built around the propagation of EM waves.

Dear Juan,

I quite agree with you.

It is evident that the Lorentz transformation and consequently the special theory of relativity is the base and foundation for static electromagnetic field theory. Special relativity will never be excluded from the static electromagnetic field theory.

A physicist who is an expert in Electrodynamics will never think about exclusion of Lorentz transformation from Maxwell's Equations as well as electromagnetism (i.e. static fields).

In the case of non-static electromagnetic fields, namely for time varying fields, the special relativity cannot be applied due to the acceleration of charged particles.

Dear Thierry,

I have studied the articles you sent to me previously. By studying the articles, no one can conclude that the Lorentz transformations can be excluded from static electromagnetic field theory.

STATIC ELECTROMAGNETIC FIELD THEORY AND SPECIAL THEORY OF RELATIVITY (LORENTZ TRANSFORMATIONS) ARE STRONGLY CORRELATED WITH EACH OTHER. HENCE, THE LORENTZ TRANSFORMATIONS WILL NEVER BE EXCLUDED FROM THE STATIC THEORY OF ELECTROMAGNETISM.

All: Is reality something meaningful? And is natural science steadily coming closer to a true depiction of it? These two questions are obviously related and belong very much to the domain everyone here can contribute, qua mind-independent reality. But some people here insist in staying in a mind--dependent reality, also known as psychosis.

Dear Houshyar Noshad ,

I take notice of your unsubstantiated opinion.

Since Einstein didn't apparently understood his error of his "Electrodynamical part", just as you don't, maybe could you explain what Einstein is really doing when in his 1905 paper he wrote down a Maxwell equation and then wrote: "If we apply to these equations the transformation developed in § 3, by referring the electromagnetic processes to the system of co-ordinates there introduced, moving with the velocity v, we obtain the equations:..."

How would kinematical equations, which are resulting from the effect of observation by light between reference frames, which then result in a deformation of these light signals, possibly be applicable upon fields, i.e. electric and magnetic force fields? How would such fields possibly exist as separate, observable entities, by using light as is used in the "Kinematical part"?

Maybe Einstein, you and 50 million people don't see the absurdity of this, nevertheless, it remains an absurdity.

Best regards,

Thierry De Mees

Dear Thierry De Mees,

For the static electromagnetic fields, i.e. time independent fields, there are four fundamental equations for static fields, the so-called Static Maxwell's equations. They are fundamental equations in time independent electromagnetism. All the equations can be derived merely by one experiment, which is well-known as the Coulomb law.

By taking the divergence of the Coulomb law, one can obtain an equation as

"Divergence D = Ro".

Taking the curl of the Coulomb law, another equation is obtained, namely,

"Curl E = 0".

For an electric charge moving with a constant velocity, one can conclude the magnetic force exerted on a moving test charge. For this purpose, the Lorentz transformations are used in order to connect a reference frame to the moving charge. Thus, the electric charge will be static in this reference frame. At this step, one can obtain the electric force exerted by the static charge on the test charge. This force can be properly derived by the Coulomb Law in the moving reference frame. By applying the inverse Lorentz transformations, it can be shown that the force exerted by the moving electric charge on the test charge (in the laboratory frame) is obtained. A part of this force is named as the magnetic force exerted by the moving charge on the test charge (in the laboratory frame). Afterwards, the magnetic field produced by the moving electric charge (with a constant velocity), the so-called the Biot-Savart Law is concluded.

By taking the divergence of the Biot-Savart law, one can obtain the equation

"Divergence B = 0".

Alternatively, taking the curl of the Biot-Savart law, another equation is obtained, namely,

"Curl H = J".

Please note that all the four Maxwell's equations (time independent) are based on the Coulomb Law as well as the Lorentz transformations.

Hence, no one is allowed to exclude the Lorentz transformations from the Maxwell's equations (time independent).

I know what you mean from deformation of the light signals as well as the time dependent (time varying) electromagnetic fields between the reference frames of Special Relativity. Please be informed that light signals are the time dependent electromagnetic fields, not the static electromagnetic fields. It should be noted that the Lorentz transformations are valid only for the static Electromagnetic fields (i.e. time independent fields), not for the time dependent fields, such as light signals and time varying electromagnetic fields. The reason is that an acceleration can be attributed to the time varying electromagnetic fields (such as light signals); and hence, its behavior cannot be explained within the framework of special relativity (i.e. the Lorentz transformations).

Best regards,

Houshyar Noshad

Dear Houshyar Noshad ,

In the first place, Heaviside has reduced the 10 Maxwell equations to the 4 that are well-known, and that are independent. It is nonsense to pretend that they follow the one from te other.

Additionally, pretending that Maxwell's equations are related with Lorentz transformations is a flagrant anachronism.

Neither Maxwell nor Heaviside has ever pretended such a thing. So, your story doesn't hold for a meter and is utter nonsense.

Only due to the utter wrong SRT, which was invented several decades later, this absurd belief has been wrongly implemented.

It is untrue that "light signals are the time dependent electromagnetic fields". No, light are no fields. Light is a very specific case, far from general.

Neither has the Maxwell equation that Einstein has chosen in his "Electrodynamical part" in order to allegedly "prove" his utter wrong case, anything to do with light.

So, dear Houshyar, it would be better to really study the case from the historical books of Maxwell, Heaviside and others, as well as to study what SRT is really about, instead of relying on the remnants of the brainwashing that you have received in your university period.

When doing that, maybe you will have the insight that SRT is very limited in its power (only locally, exclusively for light, not for electromagnetism), and that the true time-dependent equations of electromagnetism are given in Heaviside's book his book "Electrical Papers, Volume II", p. 495, https://archive.org/details/electricalpapers02heavrich

Best regards,

Thierry

Facts

1) EM waves can be derived from Maxwell equations

2) The EM waves are consistent with the Lorenz transformations (form invariant under this)

3) Maxwell equations can be given covariant form (consistent with special relativity)

All three of these facts are well explained in countless sources, it is idocy to try to deny.

Dear Juan,

Facts:

Consistence with crap (SRT) is not relevant and does not matter.

The number of sources is even less relevant. Even if 50 million people claim something wrong (politics, religion, pseudo-science), it still is wrong!

Neither Maxwell or Heaviside has bought such crap. They were right!

Best regards,

Thierry De Mees

Even more interesting: https://www.researchgate.net/post/What_does_Einstein_do_in_the_Electrodynamical_Part_of_his_1905_SRT_paper

I agree with Juan and in conflict with Thierry. I wrote all the things should be told, and after this note, I will not write further comments regarding this matter.

I strongly recommend Thierry to study electrodynamics and concentrate on solving the problems as well as its mathematical features. All the notes that Juan and I have released are sufficiently informative.

Dear Thierry, concerning your advice to me to study electromagnetism, I would like to inform you that I have focused most of my life in the field of electrodynamics, mathematical physics and its history.

No one can find a nonsense comment in my notes. They are quite informative and acceptable for a physicist who has deep knowledge in electrodynamics.

Dear Houshyar Noshad ,

I am convinced that you did a tremendous work in the field of history.

However, not even Superman would be able to combine two jobs such as performing excellently in the history job, and performing perfectly in the job of doing a true, profound investigation of all the theories themselves, including electromagnetism from the geniuses Maxwell (many books), Heaviside (many books), Jefimenko (many books), as well as the full understanding of the meaning(lessness) of Einstein's 1905 paper, as well as discovering the bogus of Planck's unsubstantiated interpretation of Kaufmann's experiments and similar experiments with charges, versus the true Maxwell-Heavisidian interpretation.

Since the DS (C_A) caught the occasion to misinform humanity for a century while playing hidden games, and since numerous (bogus) papers followed on Einstein's and Planck's, a true historian would have his hands full for a long time, and be unable to truly, scientifically investigate all of it, don't you think?

Besides, I am still waiting to get from you the least of a scientifically substantiated objection to my analysis on Einstein's "Electrodynamical part" of his 1905 paper.

Best regards,

Thierry De Mees

There is nothing wrong with Max’s axial vector maths It is the conclusion that is illogical. He showed that lines of force behaved like vortex structures in a hypothetical fluid. then ignored the logical obvious that the magnetic lines of force are the eyes of the vortexes. Collectively they rotate magnetism in either clockwise or anticlockwise vortexes around the long axes of magnets and coils. Like spins attract......The force on conductor doesn't need an axial vector to describe its direction. To paraphrase Dylan; "You don't need a weatherman to show you where the wind blows".

Houshyar Noshad , Insightful analysis, fleshing out and rationalising much oversimplistic history, i.e. Maxwell's important orthogonal 'curl' is completely ignored in current physics, and I found using it as Poincare's Sphere even allows a classical reproduction of QM's data! i.e. https://fqxi.org/community/forum/topic/3012

You should also be interested in this, just published; www.isaacpub.org/images/PaperPDF/TP_100087_2019070910523565700.pdf

But I importantly disagree with your characterizations; " acceleration can be attributed to the time varying electromagnetic fields (such as light signals); and hence, its behavior cannot be explained within the framework of special relativity (i.e. the Lorentz transformations)" . Try the LT as the Maxwell near/far field TZ it came from, a 2-fluid plasma where the electrons always CHANGE THE SPEED of EN signals to the new LOCAL c. This actually consistently COMPLETES the StR as Einsteins 1952 conception, removing all the issues.

Do comment. On my RG paper blogs if you prefer.

Ed, Which of Maxwell's equations do you want to get rid of? Faraday's Law? The Lorentz force? Ampère’s Circuital Law? Gauss's Law? Ohm's Law? The Equation of Continuity? Curl A = B? Or do you want to get rid of displacement current?

FDT, and all: The totality, it is explained in the question text.

When nonsense as "the cross-product of two vectors is not a vector" is claimed, everything is possible, even what my cat told me last night: "I think we should get rid of Maxwell's equations in electromagnetism: too much static electricity!!!"

All : Thanks, but this medium in RG, as a simple question, is short and also lacks the proper controls for a scientific discussion, such as a moderator, but comments are welcome in the RG preprint:

Preprint A Quantum Mechanical View of Reality or, can the Maxwell equ...

which also solves the link for [3] in the question above, which was broken (was an old RG glitch, thanks RG!).

Dear all, I think that saying "There is no need to exclude Maxwell's equations from physics, because they are equivalent to the relativistic equations for the field strength tensor." (ref. K. Kassner ) is total claptrap.

The 1905 SRT paper mathematically applies in its "Electrodynamic part" a physically totally wrong concept, as explained in the question:

https://www.researchgate.net/post/What_does_Einstein_do_in_the_Electrodynamical_Part_of_his_1905_SRT_paper

Indeed, applying the results of the "kinematical part", which is the observation of moving frames, to fields, means that fields are allegedly observable by the same way as in the "kinematical part", namely by the observation/measurement by light, which becomes deformed by the Lorentz transformations.

However, fieds are not 'observables', they simply fully exist by themselves, and they have different properties (induction) compared with light.

So, since Maxwell's equations represent fields and not observables by light, it is nonsense to further observe these fields by light, which indeed would give deformed results by the Lorentz transformations.

Hence, Heaviside's results in his excellent book Electrical Papers volume II, page 495 are correct by not including any further Lorentz transformations.

https://archive.org/details/electricalpapers02heavrich

Best regards,

Thierry De Mees

In all their simplicity, compactness and elegance, Maxwell’s equations have linked electricity and magnetism with geometry, topology and physics and have redefined our perception of space and nature.

THE MIND OF SCIENCE (Book)

MS: The E and B fields are not independent. The B field is caused by charges in motion, exclusivelly. The cross product of two vectors is not a vector. The Maxwell's equations are rifled with errors.

Dear Ed Gerck ,

your statement “the B field is caused by charges in motion, exclusively” is in strange contradiction to the Maxwell equations in empty space, which say that the rotation of the B field corresponds to the time derivative of the electrical field E.

Your statement also implies that you seem to know the mechanism how elementary particles create magnetic moments. Are there really charges in motion involved, with a movement pattern which generates a B field but does not cause any radiation?

WK: What I said is well-known.

EG: May be, but not comprehensible.

Hello! Is it also possible to use 3D Smith's diagram for EM?

Dear Wolfgang Konle ,

You say: "the Maxwell equations in empty space, [ ] say that the rotation of the B field corresponds to the time derivative of the electrical field E."

Remind however that everything of Maxwell's (in fact, Heaviside's) equations is created by charges in the first place.

But I agree that Ed is plain wrong when saying "The cross product of two vectors is not a vector." and "The Maxwell's equations are rifled with errors." .

Dear Thierry De Mees ,

you are right, charges are involved in the creation of electromagnetic waves. But the creation can have been long ago and then has no influence on the ongoing process described by the Maxwell equations in empty space.

Dear Wolfgang Konle,

You wrote: "But the creation can have been long ago and then has no influence on the ongoing process described by the Maxwell equations in empty space."

I have never agreed with this point of view, however, I used similar reasoning to be able to perform a mathematically approximate calculation (this kinematic link could be established by an appropriate generalization of the Lorentz transformation) in order to perform a link between the study of the behavior of accelerated point source in a Galilean reference system and the behavior of non accelerated point sources in this same reference system. Excerpt (my last contribution in https://www.researchgate.net/post/Does_an_accelerated_charge_radiate_in_its_rest_frame) :

>

My point of view is correctly expressed by this excerpt (from https://en.m.wikipedia.org/wiki/Jefimenko%27s_equations) :

>

Dear Rommel Nana Dutchou ,

you were right, if the divergence of the electric field in the wave would not be zero.

All: Gravitoelectromagnetism (​proposed by Oliver Heaviside and further developed by Olev Jefimenko) is incorrect and not covariant (does not show Lorentz covariance).

The electromagnetic force only occurs between non-comoving (comoving is defined as same velocity and distance) electrically charged particles, otherwise electric force applies. Their (Heaviside and Jefimenko) ideal of electromagnetic theory also fall short by not accepting the rules of SR. This is well-known, time to accept it.

Wrong Ed, it is covariant, not invariant, as it should be.. Time to read Jefimenko's books.

Dear Wolfgang, yes it can have been long time ago that the field was created.

Rommel says it very well, when citing Jefimenko.

Jefimenko discovered that Maxwell's equations are equivalences, of which both sides of the equation were/can be created by charges.

Best regards,

Thierry

All: Citing Jefimenko or Heaviside in physics is similar to citing Batman or Superman. It does not work, and physics is not decided by quotes, unlike human humanities. Physics is decided by Nature, by experiments.

Dear Ed Gerck,

"All: Citing Jefimenko or Heaviside in physics is similar to citing Batman or Superman. It does not work, and physics is not decided by quotes, unlike human humanities. Physics is decided by Nature, by experiments."

I answered you in my last contribution of the following discussion:

https://www.researchgate.net/post/Can_we_formulate_Hubble_law_and_expansion_of_universe_in_the_context_of_special_relativity

All: As a reminder, it is easy to deal with fantasy and nonsense posters in this thread:

1. They talk against known physics, such as special relativity.

2. They add one or more of their own links, and call it referencing, but trying to get clicks while hiding self or fringe group advertising and false news, and repeat copying their own links under different titles, questions, etc.

3. When asked to stay on topic, they argue, instead of stopping.

4. When asked to correct their wrong citations by the authors themselves, they do not and continue to offend copyright.

5. One recognizes them, also, by talking about other posters, not about the subject (ad hominen attack). Then, they redefine terms in an effort to control the discussion. We do not do that as a recommended practice in science. So, they are already off-topic.

If this happens, you can treat these messages as they are, ads, and skip them, reducing noise with known fantasy or nonsense posters.

Dear Ed,

I prefer to let people express themselves as they like and let the others filter them out as they wish. There is no science without skepticism.

True scientists don't let themselves being put under pressure, neither by the mainstream, nor by the opinion of 10 million people.

MS and all: This not a general discussion, it is a physics topic on the issue of the title, with limits explained in the question above. It is not open to anything else, for the benefit of the question itself. It is also not proper for people to "express themselves as they like" but the RG ToS apply here. Please delete your entry.