Dear Arbab,

The hall effect could  be described qualitatively and quantitatively by the existing basic physical laws. The hall effect  results from applying vertical magnetic field on a current of mobile charges flowing in semiconductor. where a hall electric field will be formed perpendicular on the direction of the current and and the magnetic field. In this system there is no photons. Here one has moving charges with a velocity v with an applied magnetic induction B vertically on it. Such effect results in the so called Lorenz force FL given by FL= q v cross B where all quantities are vectors except q which has a sign.

Applying this equation together with the cu rent equation one can get the Hall electric field ans consequently the Hall voltage.

Please explain why do you speak of photons? what is the specific problem?

Best wishes

Dear Prof. Zekry,

Thank you for your reply showing how Hall effect is ordinarily understood. As you know, all electromagnetic phenomena should be explained within the framework of Maxwell equations. In particular Hall effect is explained from Lorentz force. You may also know that Maxwell equations are not invariant under duality, where electric and magnetic fields are interchanged, except in vacuum. Because of this no magnetic current is present in Maxwell's equation. To remedy this, we need to extend them to incorporate this current in some way. Maxwell's equations are so because they deal with massless photon. However, if photons are massive, several phenomena will arise. Of these are the magnetic current and magnetic charge. I made a minimal extension, different from the one done by Proca, in which Hall effect can be described by the new Maxwell's equations. What I wrote in my questions is how one measures that mass.

Okay Arbab. But still you did not describe how you would describe the hall effect using new formulation of the Maxwell equations in spite of there is no existence to photons in the problem?

    Dear Arbab,

    Perhaps you must think in Integer Quantum Hall Effect or in Fractional Quantum Hall Effect. In such special cases the photons can play an important role and the massive photons with longitudinal components would give a new scope for the usual one.

    More sophisticated is if you go directly to topological fields where the Chern-Simons terms (equivalent to massive photons under some conditions) in Anomalous Hall Effect or to the Quantum Spin Hall Effect which are nowadays under development for topological insulators and topological superconductivity.

    In ordinary Hall Effect you don't need to use photons but the ordinary classical electromagnetism as it was said.

Dear Profs. 

This is the new set of equations... where Lambda is an additional scalar function that gives rise to longitudinal wave besides the existing transverse one.

Dear Daniel,

Thank you for your kind reply. In fact, the quantum Hall effect comes from the supposition that the flux encapsulated by the sample is quantized.

Dear Remi,

These equation are  dimensionally correct. Please check you work. Here Lambda has a dimension of Tesla. These are equations in vacuum where charge density and current density are zero. They do obey energy conservation. If you like I can send you this equation. These are new to you and you never see before. You can think of them instead of giving a false unjustified opinion. Don't rely your discussion on the ordinary Maxwell equations.

Arbab,

The colleagues have raised some objections against your extensions on Maxwell equations especially Remi. I agree with him. Your modifications must be based on physical insight or logical reasoning. That is they must be based on strong physical foundations and when applied the modified equations must give results which are conforming with the experimental observations. In addition you have understand deeply the existing formulations. All these may lead that you will be convincing.

From the conceptual point of view, the electric field is generated by electric charges and by the time rate if change of the magnetic flux. The magnetic field is is generated by electric current, which is the flow of electric charges and not a flow of magnetic charges. It is generated also by the time rate of change of the electric field which is the displacement current. So, the electric field is the primary field of the electric charges and the magnetic field is also due to moving or displacing electric charges. This is my understanding to the electric and magnetic field and their interactions.

A similar question was previously asked on the researchgate and you can follow it in the link:https://www.researchgate.net/post/Has_a_divergent_electric_field_ever_been_detected_that_is_induced_by_dynamic_currents

However, i answer your question from the point of view of applied electrical engineer. There may be some trials to extend the theory of electromagnetic.

wish you success

Dear all colleagues,

have you tried any form of nonlinear electrodynamics Lagrangians? Perhaps the Born-Infeld or Heisenberg-Euler forms of the theory can give youa better understanding on the mass of the photon ... Some of you quoted to refer to variations of the theory electromagnetic ... I think that NLED can provide to you the key piece of understanding about the photon mass ... regards,

Dear Colleagues,

Thank you for your comments. The theory I provided is based on physical and logical grounds. I here only provide the resulting equations for you to think rather differently and seek some possible applications. I also made some viable application that worth investigation. This is related to the origin of  magnetic field detected at galactic level. This is shown to be due to the aftermath of the inflation and what it did to the magnetic field present in the universe at that time. 

As we know, some particles such as photons are never seen at rest in any reference frame. So, there are two kinds of particles in physics;

A. Some particles like the photon move only with the speed of light c, in all inertial reference frames. Let’s call these kinds of particles the NR-particles or Never at Rest condition particles.

B. Other particles like the electron always move with the speed v

    Dear Arbab,

    Your equations are dimensionally right, but there are some difficulties to interpret them physically.

1. You have two magnetic fields: lambda (scalar) and B (vector). How are they related?

2. Obviously they are not equivalent to Maxwell equations, because they have an additional source for the electric field E which physically meaningless for me (substituting Gauss law). Could you explain it?

3. You add also one equivalent term in "Faraday's law", but now substituting lambda by B. Notice that this means that you could have an extra energy to the electromotive usual force. Why?

4. In the equivalent Ampere's-Maxwell equation, you substitute again the density of currents by two term which are physically meaningless : one proportional to the electric field E and the another to the gradient of lambda.

    Let me to finish saying that Maxwell equations are well tested and in principle they must work in any place, although they can appear in different contexts as London equations of the superconductivity where the photons get to be massive thanks to a spontaneous breaking of symmetry. This doesn't prevent to have Maxwell equations to be true! 

Dear Prof. Arbab I. Arbab

Peace be upon you

I strongly concur with Prof. Daniel Baldomir. Maxwell equations are valid everywhere and anytime and can be applied for any medium.

But on the other side, I hope for you all the best and the sucess.

Go ahead to the forward

Good luck

   Dear Ahmed,

   I strongly agree with your last sentence" go ahead to the forward". And even I would add that it is full of value that there are people able to face difficult new points of views within so stablished and tested theories as classical electrodynamics. My best wishes for Arbab and my remarks only try to help in thinking on weak points of his equations.

Dear Colleagues,

Thank you very much for your critical points you raised against the new extension of Maxwell equations. I would like to remind you that in quantum electrodynamics, the vacuum fluctuation (or  charge polarization) can give rise to physical phenomena like the Casimir effect where two uncharged plates are found to be attracted when a strong field is applied. The question is from where these charges appear. It is from the vacuum. This is culminated in the right hand side of modified Gauss equation where Lambda and its time derivative are present. In this sense Lambda could represent the decay rate of the vacuum. Hence, Lambda could be associated with  the measure of how much charge can be borrowed from the vacuum. This gives a plausible interpretation of the modified Gauss equation. The additional term in the right hand side of the modified Faraday's equation could account for the Hall effect where a potential difference is developed between the sides of the sample when a magnetic field is applied. We could explain this if we assume that a magnetic current is developed that passes in the transverse direction of the sample, unlike the ordinary current that goes along the longitudinal direction. The existence of this current is a matter of experimental verification. The presence of a voltage would customarily presume a current. No mention of such a current in such an effect. If we are open minded, we could accept the idea and try to work it out. If afterwards it does not agree with experiment we then reject it. All new ideas are rejected in the beginning and afterwards they are accepted. Imagine that Planck idea of energy quantization was firstly reject!

     Dear Arbab,

     If you add Hall effect (electron-hole interaction of some eV) with Casimir effect (electron-positron with some MeV) and you put in difficulties Maxwell equations, I think that you need to justify the things deepler. This is not enough because notice that the above effects agrees perfectly with classical electrodynamics while your equations don't do it.

Dear colleague Prof. Dr.  Arbab I. Arbab

Have a nice time and good day.

It is a very interesting question and good discussion from our best colleagues.

Wishing you all best.

Yours

A. El-Denglawey

Dear Colleagues,

The extended Maxwell's equations I am proposing are necessary when the background in which the electromagnetic field is not uniform and homogenous (non-isothermal, non-isobaric, etc). Such a background will have its imprints on the fields and the currents (charges)

associated with it.

The question is senseless !!!!

Please learn physics a little bit !!!