Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Dual Quantum Mechanics and Its Electromagnetic Analog

Version 1 : Received: 18 September 2018 / Approved: 19 September 2018 / Online: 19 September 2018 (04:26:00 CEST)

How to cite: Arbab, A. Dual Quantum Mechanics and Its Electromagnetic Analog. Preprints 2018, 2018090363 (doi: 10.20944/preprints201809.0363.v1). Arbab, A. Dual Quantum Mechanics and Its Electromagnetic Analog. Preprints 2018, 2018090363 (doi: 10.20944/preprints201809.0363.v1).

## Abstract

An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation keeping the form of the particle fixed but decaying its amplitude. An analogy with Maxwellian equations is presented. Massive electromagnetic field will satisfy a quantum Telegraph equation instead of a pure wave equation. This equation resembles the motion of the electromagnetic field in a conducting medium. With a particular setting of the scalar and vector wavefunctions, the dual quantum equations are found to yield the quantized Maxwell's equations. The total energy of the particle is related to the phase velocity ($v_p$) of the wave representing it by $E=p\,|v_p|$, where $p$ is the matter wave momentum. A particular solution which describes the process under which the particle undergoes a creation and annihilation is derived. The force acting on the moving particle is expressed in a dual Lorentz-like form. If the particle moves like a fluid, a dissipative (drag) quantum force will arise.

## Subject Areas

relativistic quantum mechanics; Maxwell's electrodynamics; symmetrized Maxwell's equations; quaternionic quantum mechanics; telegraph equation; hall effect

Comment 1
Commenter: Mohamed Elmansour Hassani
The commenter has declared there is no conflict of interests.
Comment: Comment on “Dual Quantum Mechanics and Its Electromagnetic Analog” by Arbab Arbab
After an attentive reading, I found the paper highly questionable mathematically and physically. More precisely, the authors' basic equations, namely, Eqs.(3), (4), (5) and (6) are completely meaningless mathematically and physically since they are not dimensionally homogeneous. Consequently, contrary to the author's claim, Eq.(7) which is dimensionally homogeneous, cannot be deduced from the meaningless ones, i.e., Eqs.(3-6).
Recall, Dimensional Analysis (DA) is a robust tool and its main role and importance is to check the dimensional homogeneity of equations.

Now, let us rewrite the author's basic equations in DA.

Eq.(3): 1/L ‒ 1/L^2 T^‒1 = 1/L^2 T^‒1

Eq.(4): 1/L ‒ 1/L^2 T^1 = 1/L^2 T^1

Eq.(5): 1/L + 1/L ‒ 1/L^2 T^‒1 = 1/L

Eq.(6): 1/L ‒ 1/L + 1/L^2 T^‒1 = 1/L

It is clear, Eqs.(3-6) are not dimensionally homogeneous and for that reason ‒they are mathematically and physically meaningless and any equation that can be deduced from them must also be meaningless. Consequently, the totality of the paper is highly questionable.
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Response 1 to Comment 1
Commenter: A. I. Arbab (Click to see Publons profile: )
The commenter has declared there is no conflict of interests.
Comment: The dimensions of all equations are correct. If you can't see this please contact any of your student who can tell you this fact. If you can not find out I can make this for you by pen and paper. I also notice you have a trend of falsifying other works without having this right. Your critics is so weak. Please concentrate on your own work if you have.
Comment 2
Commenter: Mohamed E. Hassani
The commenter has declared there is no conflict of interests.
Comment: In his response to my comment on his paper “Dual Quantum Mechanics and Its Electromagnetic Analog”, Professor Arbab wrote: The dimensions of all equations are correct. This claim is incorrect since my comment was and is specifically focused on the equations (3-6) and their applications.

Like many, it seems that Professor Arbab has a BIG problem with dimensional analysis (DA) and its applications!
Questions:
1) What is the expression of "nabla operator" in DA?
2) What is the expression of (∂\∂t) in DA?
3) What is the expression of (Planck constant) h in DA?
4) What is the expression of (light speed in vacuum) c in DA?
5) What is the expression of (mass) m in DA?
6) What are the expressions of (the scalar and vector potentials) ϕ and ψ in DA?

1) [nabla operator] = 1/L = L^‒1

2) [∂\∂t] = 1/T = T^‒1

3) [h] = M L^2 T^‒2 T = M L^2 T^‒1

4) [c] = LT^‒1

5) [m] = M

6) [ϕ] = [ψ] = 1

‒ Now, with the help of the above DA-expressions, professor Arbab can check his Eqs.(3-6).

NB.: The intellectual duty of every good scientist is the protection of Science.
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