When a magnetic field is applied transverse to a sample, a transverse voltage is developed without current. This voltage is termed Hall's voltage. In the same manner the displacement current passes in a capacitor, may we suggest a magnetic current does the same in Hall effect? I have shown this is true if photons are massive. Could we produce a magnetic field from stationary electric charges?
No, there is no simple analogy between Hall effect and dielectric polarization. The Hall voltage is generated by displacement of the mobile charges and is a result of balance of forces between Lorentz force and electrostatic force. The displacement current in a capacitor is due to a (very small) displacement of immobile electrons (its a dielectric, hence an insulator).
For part 2: take an insulating single domain ferro- or ferrimagnet: magnetic field generated from stationary electric charges. that is of course, because these charges (electrons) carry spin and it is the alignment of the spins which gives rise to macroscopic magnetism.
Dear Fauth,
Thank you very much. Really very interesting and useful comments. It seems that the mass of the photon some how related to its spin magnetic moment.
Dear Fauth,
The system of equations are shown in the attached file. I trust that these modified Maxwell equations, when photons become massive, will have interesting applications in condensed matter physics. Your comments are appreciated.
I was not pondering the spin magnetic moment of a photon. I'd be very surprised if there was any, e.g. because photons carry no charge. Alternatively, we may go back to the very definition of what is a magnetic moment. An object is said to possess a magnetic moment whenever (\partial E)/(\partial B) is nonzero [E standing for the oject's energy and B for a static applied magnetic field]. I have never seen such a term for photons (but also have never searched for it). It would amount to a Zeeman energy of photons.
Semi-serious proposition: build a diffraction experiment in a strong magnetic field and see whether you can split the photon energies of a laser in two owing to a "photon Zeeman effect". I don't believe it will happen.
And what do you mean by "photons become massive" ? Nonzero rest mass? Then we would get a problem with them propagating at the speed of light, according to SRT. Is this what you imply? (have not read your document yet)
And concerning the quantity "Lambda" in your equations: any evidence for its relevance? Any prediction of your theory someone should bother testing? Why would that be important in solids?
I must also say that I find the definition of force strange. Why does it need a definition of this kind, where the well-known standard terms [2nd & third term in second parenthesis] are imaginary (and what would that mean).
What is the starting point of your derivations and what is the justification of the ansatz?
Dear Fauth,
These equations emerge from expressing Maxwell's equations in generalized complex numbers (Quaternions). In this format the force is expressed as a complex force embodying the force on the electric charge and a one on the magnetic charge. Hence, the complex force can be separated into two real forces. But the force on magnetic charge (qc) would vanish if B=vxE/c^2. Here Lambda could be related to the vacuum energy, a scalar magnetic energy. It also represents a longitudinal wave that accompanies the transverse one moving along the electric field direction. Tesla had once found longitudinal wave associated with the transverse wave of Maxwell but it was rejected. Stationary electric and magnetic fields satisfy the Poisson equation. The electromagnetic field and Lambda, for time varying fields, satisfy the telegraph equation that is known for transmission of signals across wires. Thus, the new Maxwell equations reduce to ordinary Maxwell equations when m=0 and Lambda=0. However, if it turned out that photons were massive, we would expect their equations to be those ones. In solid such electromagnetic effects will be prominent , where the main interactions are due to electromagnetic force. Therefore, one can test their existence.
Thanks for providing some insight.
If things were as you propose then you should write down what the "smoking gun" experiments would be, in your opinion. For example, you mention a quantitiy like the "magnetic current". If that were to exist, how would it reveal experimentally and be unequivocally identified?
And as for the extra term in the electric force part, wouldn't \Lambda being nonzero imply an exponential slowdown or acceleration of a free particle (depending on the sign of \Lambda)? I don't think that was ever observed. Or do I read your equation inadequately?
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