According to Teplitz, “The state of the classical electromagnetic theory reminds one of a house under construction that was abandoned by its working workmen upon receiving news of an approaching plague. The plague was in this case, of course, quantum theory.”
As cited in Electromagnetism: Paths to Research, by Doris Teplitz. Springer Verlag.
With thanks to everyone, please see Preprint at:
Preprint Maxwell Equations Excluded From Electromagnetism By Quantum Mechanics
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".
@ 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
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.
Dear Ed, you wrote: "SR has difficulties today".
Could you briefly indicate what those supposed difficulties are?
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.
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.
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
No, Maxwell's Equations can never be excluded from Electromagnetism. These are principles of Electromagnetism, and cannot be excluded.
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.
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?
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.
“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
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.
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
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.
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.
NONE OF THE MAXWELL'S EQUATIONS CAN BE EXCLUDED FROM CLASSICAL ELECTRODYNAMICS.
Give the end result without mentioning the history?
Sure, it is possible, but pointless.
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
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.
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?
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!!!"
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)
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?
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.
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
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
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.
As the name says, an electromagnetic field is a dual entity always having an electric and a magnetic component. The magnetic component has an influence on moving charges. Jefimenko’s analogy then simply means that a gravitational influence on moving masses exists.
Hi Ed Gerck ,
you say that magnetic fields and electric fields do not cause each other but are different appearances of the same source, moving charges. You also say that the Lorentz transformation expresses this circumstance.
I can follow this argumentation, but then your additional argument, the Maxwell equations would express a causal relation between electric and magnetic fields is not comprehensible.
Differential equations only express relations and do not contain any information about cause and effect.
If we consider the Maxwell equations, we could say “time variant electric fields cause magnetic fields” and “time variant magnetic fields cause electric fields”.
But assigning cause and effect to differential equations is an interpretation problem. It is not intrinsically expressed in differential equations.
Dear all,
A theory (SR) can erroneously/falsely "explain" an experiment (Kaufman, CERN), assuming that the theory itself would be consistent/correct. However, SR is wrong on many aspects, and moreover explains nothing correctly about charges or electromagnetic fields.
Also, the existence of a "photon", as a physical particle, is impossible, since light is a wave, and propagates by the grace of a medium, the ether.
Only when light is trapped within a confined space, as Louis de Broglie represented particles, then we have matter and elementary particles.
So, you see that the SR utopia, in which Einstein denies the existence of ether, comes to the situation that the propagation of waves in a medium is denied, which is impossible by definition, and consequently, the erroneous and anti-physical concept of a Photon-particle is created.
Indeed, when from a far star, an alleged "photon" is sent, why do we always measure it as velocity "c", whatever the stars relative speed to us is?
I explain in length why the mainstream concepts are indeed chimeras in:
Preprint Which Physical Process Regulates the Constant Speed of Light?
Best regards,
Thierry De Mees
Dear Thierry De Mees ,
To your comment “the existence of a photon”:
Mathematically, waves and particles are related by Fourier transform and both only exist in our imagination. We need a view beyond waves and particles.
Dear Ed Gerck ,
a slit experiment describes the behaviour of complete emissions from specific sources and allows the observation of interference effects and nothing else. Conclusions concerning specific quantized elementary parts of emissions (photons/electrons), based upon slit experiment results, are not possible.
Dear Wolfgang, mathematics *are* imagination, waves and particles are not.
The double slit experiment only shows that electrons are in fact "(self-)trapped light in a confined space", as the genius Louis de Broglie understood well, and they can be destroyed into light again when they hit a double slit.
Dear Thierry,
the double slit experiment only shows, that electrons emitted by a point source show an interference pattern. It does not give any hint, how we can interpret this result.
This does not mean that I prefer an other interpretation as de Broglie, but my point is that it is only an interpretation of the result.
By the way, considering electrons and protons as trapped light is something which could be possible (and useful in a theory beyond waves and particles).
Dear Ed Gerck ,
the (impressive) experiment in the YouTube video clearly shows that we need a concept beyond waves and particles.
Dear all, in this Fermilab video https://www.youtube.com/watch?v=LTJauaefTZM&t=13s
it is stated (by a public relativist) that mass doesn't increase with velocity. (This is only the very first step of the SRT destruction.)
The guy's "Mea Culpa" is FAR too little, by the way.
Of course mass doesn't increase with speed!!! This hoax has been lasting for more than a century.
Indeed, it follows that Planck's paper "The Principle of Relativity and the Fundamental Equations of Mechanics", written in 1906, and which include the alleged increasing mass with speed, is also crap and rubbish, and so, Planck didn't explain Kaufmann's experiment (with charges) by SRT at all!
It follows that Kaufmann's experiments are indeed only explained by electromagnetism, as follows from Heaviside's material: "Electrical Papers, Volume II, p 495".
Therefore, the conclusion is that charges get higher transverse electric fields due to motion, which fully explain the behavior (reduced deviations) of the charges with speed.
Dear Thierry De Mees ,
the only statement in the ( journalistically very good) YouTube video, you are referencing, is that there is no gamma correction in the gravitational interaction of masses moving with high speed relative to each other.
But an alternative expression has not been presented. The alternative expression should take into account gravitomagnetism. But it seems that concerning gravitomagnetism, physics has a gap.
No increasing gravity mass with speed = no increasing inertial mass with speed.
Reasons: 1) Equivalence principle. 2) Velocity value is non-absolute, but arbitrary/relative (Newton's inertia principle).
No increasing inertial mass with speed = no Planck interpretation for Kaufmann's experiment.
SRT is dead (again).
And, no, dear Wolfgang Konle , the guy also says that there is only one mass: the rest mass. This refers of course to inertial mass.
Dear Thierry De Mees ,
"no gamma correction" is synonym to "there is only one mass".
"p=gamma*m*v" still supports SRT(!)
Only "inertial mass" = "gravitational mass" is disproved.
Dear Wolfgang,
No! I repeat: the Fermilab guy also says that there is only one mass: the rest mass. This refers of course to inertial mass. He also says that gravitational mass doesn't increase.
Hence, no increasing inertial mass, no increasing gravity mass.
You wrote: " "p=gamma*m*v" still supports SRT "
No, not as generally pretended by the mainstream. Since the gamma is allegedly a physical entity as claimed by the mainstream, it should come from somewhere, either the "m", or the "v".
We know now that it is not so: neither physical entity can contain the gamma factor.
Moreover, since according to relativity, "v" is only conventional, depending from the observer, "p=gamma*m*v" can only be fictive/relative, not physically intrinsic.
You wrote: "Only "inertial mass" = "gravitational mass" is disproved."
No, it is part of the equivalence principle, and there is only one mass.
Dear Thierry
p=gamma*m*v means increasing inertia. (I do not say increasing inertial mass)
Well dear Wolfgang, in your equation, which of the physical entities allegedly brings up this gamma factor in order to get an increased inertia? Velocity or mass? Or what else?
"The use of "relativistic mass" should be restricted to historical references, not used to explain physical phenomena."
Yes, indeed. This falsifiés the explanation given by Planck to Kaufmann's experiments, and confirms that charges are to be treated by Heaviside's electromagnetism instead of SRT.
Thank you.
Well, Thierry, the gamma factor applies to the momentum p and informs us that we need a lot more energy to increase the velocity closer to the speed of light.
No, Wolfgang, if the gamma neither applies to "m" nor to "v" of which "p" is constituted, it cannot apply to "p".
And we *know* now that gamma applies to neither of them.
In the present case, the gamma in "p" is *calculated* to come from "m", because SRT *observes* such a deformed light information from a distance for a distant moving frame.
So, what is the conclusion?
The gamma factor only refers to the deformation of light, optically, when an inertial frame is *observed * by light from another frame.
It refers to optics, hence, not to intrinsic values.
Hence, the conclusion is that "p" represents the "optical deformation" of the real intrinsic momentum.
Best,
Thierry
Thierry, the LHC guys "feel" this gamma factor with its influence on inertia during acceleration of their particles. Would they belief you, if you tell them that they only need to adpat their coils to "optical deformations"?
Wikipedia seems to think that the cross product of two vectors is a vector - https://en.wikipedia.org/wiki/Cross_product - is that incorrect?
Dear Wolfgang Konle ,
You wrote: "the LHC guys "feel" this gamma factor with its influence on inertia during acceleration of their particles"
If a wrong theory explains such a thing, is the theory then correct?
Or should we then look at the theory of electromagnetism that explains such a gamma due to the acceleration (or velocity) of charges, and resulting in a gamma?
Best,
Thierry
Dear Thierry De Mees ,
many details of the current theories of electromagnetism and special relativity may be wrong, but "p=gamma*m*v" is correct and obviously describes a velocity dependent inertial mass.
The only thing in the momentum/mass context, which may be wrong is "inertial mass=gravitational mass" for masses in different reference systems.
Dear Wolfgang Konle ,
You wrote: " "p=gamma*m*v" is correct and obviously describes a velocity dependent inertial mass "
However, you don't have the beginning of a proof for that, neither has the mainstream. I proved you the opposite, and you didn't argue about my evidence in detail. Nobody does. I only see some relativistic sandwich men hanging around here at RG, pretending "this is correct" or "that is incorrect" on their signboard or poster.
What you believe is only the result of the brainwashing with false beliefs.
It is a result of harassment of those who question SRT. It is a scam, just as SRT is a scam for the "Electrodynamical Part" of the 1905 paper, and the 'modern' mainstream interpretations of SRT with their alleged increasing mass (FALSE), delayed time (FALSE) and shortened rulers (FALSE).
And when they finally agree that mass doesn't augment, they forget that the house of cards is totally collapsing: Kaufmann's experiments aren't explained any more, so the whole SRT with charges collapses.
As clearly follows from the "Kinematical Part" in the 1905 paper, SRT is ONLY optics of what is seen by light from a moving frame, when observing another moving frame.
Plenty of evidence for that. Since velocity is not absolutely defined in SRT, and since different observers see different values of 'm', 't' and 'l' for the SAME events, it CANNOT be intrinsic, only fictive.
Hence, even the equations of momentum, energy are only optical/fictional equations as a result of observation of moving frames, combined with a calculus when assuming that "c" is constant always and everywhere.
Best,
Thierry
Dear Thierry De Mees ,
It is obvious that controlling of high energy protons in the LHC ring with radius R is possible. Controlling means that the magnetic field B, which keeps protons with charge e on track are well known. The energy E of the protons is also known.
We therefore know evB=mv²/R or eRB=mv and mv²/2 =E.
We then get v=2E/eRB and m=(eRB)²/2E.
The control dynamics then show relations between E and B which are accurately compliant with velocities very close to c and also to m=gamma * m0. How would you interpret these experimental results?
Dear Wolfgang, is it possible to come to a workable result with a wrong theory? YES!
Does it make that theory correct? NO!
SRT is about *observation *, by light, of a kinematical event (moving frame).
Electromagnetic fields are not *observable* by light.
Their behavior is fully explained by the retardation of these fields as detected from a distance, because of the limited propagation speed of light.
This gives a Lorentz-like formulation of the electric field (see Heaviside, Electric papers volume II, p. 495), giving an increase of the fields in the direction perpendicular to the speed of the charge.
This increased field augments the own magnetic field as well.
So, it *appears* that you get thousands more charges in the transverse direction.
This also results in the creation of virtual electrons in accelerators, as observed. On the other hand, the electric field in the direction of motion is decreased.
So, in that direction, it appears that steadily less charge exist with speed. How would one be able to accelerate indefinitely a particle with no charge in the direction of motion?
Best regards,
Thierry
Dear Wolfgang, first question: please read back my last post.
"you then would doubt charge conservation?" No! Remember, E-M energy input is given by charge accelerators!
"you then would doubt the energy value achieved in all accelerator devices with a known voltage?"
Not to the point. If you try to accelerate a supersonic jet by using sound waves, driven externally from the ground, would the supersonic jet ever reach the speed of sound, regardless the quantity of sound energy involved?
Dear Wolfgang,
"indeed, wrong/incomplete theories can explain experimental results. But as long as no better theory exists, the match with experimental results counts for the theory."
Twice incorrect.
"No, passing an electrical potential difference with a given charge, always leads to the according energy gain, regardless of the velocity. The sound wave example is not applicable in that situation."
Not to the point.
"In fact, I am on your side concerning severe deficiencies in the current mainstream theories. But using arguments, quite close to conspiracy theories is not helpful."
You don't know/understand what I was talking about, so much is clear.
Dear Wolfgang, since politicians of the opposition understand nothing of straight science, what's the point to continue explaining you things?
Dear Wolfgang, you prove that I was right in my last post. Nothing of what you said in your replies had any sense of logic or scientific value.
"But from my point of view, you currently prefer unproved conspiracy theories instead of arguments based on the current state of knowledge."
Some people think they are shrinks and they can judge and treat other people alike, according to their inspiration of the moment.
They base their "knowledge" on what the LameStream science is telling them, but in reality, they are merely telling idioties and they try projecting their ignorance upon others.
@thierry
Yes the gamma factor refers to light deformation and nothing else. I was searching this line for few months,, even it is directly related to the refractive index of the medium. I got direct proof of it in few steps. Thank you for sharing this line.
Thiery
"EM fields are not observable by light"
Light is an EM field.
YOU CANNOT SEE LIGHT?
2
I think em field is not same as described for light it is something else. there are two basic differences between light and EM field.
1) Light can be explained by oscillatory theory including all its properties and always make reference to a feed source means require external energy.
2) EM is not explainable by oscillatory theory and no external energy is needed e.g. magnet. It is a kind of a peculiar closed system !
No correct reasoning, Juan Weisz ! The "Kinematical Part" in Einstein's 1905 paper used an observer. An observer observes by using incoming light. In the "Electrodynamical Part", Einstein allegedly applies the very result of that observation by light upon the fields of a Maxwell equation!!!
How would you possibly make electric fields of a Maxwell equation, emitted by an object that is travelling at speed v, become visible/observable by using a light beam between that field and an observer?
It is only possible to see the OBJECT by it, not the field!
Hence, the OBJECT can be seen by an observer by using the Lorentz Transformations, which is an optical deformation. NOT the field.
Hence, the "Electrodynamical Part" in Einstein's 1905 paper is not applicable to the Maxwell equations, ONLY to the object itself.
The Lorentz invariance is wrong.
The fields are detectable by themselves, and obey...., exactly, Maxwell's, Heaviside's and Jefimenko's equations, NO Special Relativity.
Light in the visible range is a mixture of different wavelengths of EM radiation from about 500 to 900 nm
Dont see why anyone should have a problem with this.
Its a fact.
Maybe revise what is meant by the EM spectrum. All the radiation from radio waves to gamma rays.
Dear All, I wrote previously:
>
We can make an analogy with the theory of the Thomas precession, where one wants to give a physical interpretation to the mathematical reality according to which the composition of two special transformations of Lorentz, when they are non-collinear, is not directly equivalent to a special transformation of Lorentz since it must be combined with a rotation. My thought has always been that it may be a mistake to want to use a sequence of uniform motion to follow a material point whose motion is accelerated. This can be illustrated by this attached image taken on the internet.
Exorcising Oersted and Maxwell
Since the ancients magnetism has been tinged with an inexplicable mystical strangeness which verged on spooky and sometimes even embraced the paranormal. Perhaps this is why cosmologists still sheer away from it, or if anything hold magnetism incidental to gravity.
They seem to have taken a lead from Newton who when asked what magnetism is replied “I make no hypothesis.” but peculiarly thought it inversely proportional to the cube of distance.
Oersted though had no qualms about defining it. It encircled its conductor as his magnet/compass attested. The counter-intuitiveness of this was unheeded. Does an arrow have a wind rotating around its shaft? Clearly not but a current in a conductor has a magnetic wind that does!****
If, in the absence of the magnet conjuring on his desk, Oersted had observed that two co-parallel currents attract, then he would have logically (and correctly) concluded that the co-parallel magnetic wind from each conductor lowered the pressure between them, therefore attraction…opposite currents increase pressure and repel.
A current coil then has an axial vortex of magnetism within and surrounding it. Aligned coils with like spin attract….. North poles are anticlockwise poles A-poles and south poles are clockwise C-poles.
Forty years later Maxwell compounded the counter-intuitiveness with: “An event (a current) in the ‘x’ direction encountering an event (magnetism) in the ‘y’ direction causes an event (a force) in the ‘z’ direction?” Clearly logically it does not, so the direction of one of the parameters is wrong!****
When we see that magnetism rationally flows co-parallel with its current, logical reasons manifest for electromagnetic phenomena.
A conductor through the diameter of a magnetic vortex is attracted by the co-parallel vortex wind on one side reducing pressure and repelled by the anti-parallel wind on the other side increasing pressure. Reverse the current reverses the force. The right hand screw rule is terminated. The perpendicularitis is cured.
Amidst the restructure of magnetism we loose Maxwell’s convoluted interpretation of a polarized electromagnetic wave and its lunatic butterfly graphic image, because all the wave is now one plane polarized.
Moreover, since both the electric and magnetic transverse vectors are aligned, then one can be redundant, and that turns out to be the electric vector.
After a few wavelengths the wave becomes purely magnetic.
For the cosmos to be au fait with magnetism it must exorcise the Oersted Illusion and Maxwell’s extrapolations.
With magnetism out of its spooky box, and since current coils and magnets operate in space, we can reasonably ask;
“What are they spinning?”
and “Is gravity incident to electromagnetism?” which it is.
All this plays havoc with Einstein and counter-intuitive electromagnetic tensors.
Blake Taylor, author of ‘Bi-verse, The Cosmic Split’
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