In continuation of some previous work published by this author in an open access journal [S. Koutandos, IOSR J. Appl. Phys. 10, 26 (2018); 10, 35 (2018); 9, 47 (2017); 11, 72 (2019)], he now derives the London equations from an expansion of the rotation of vorticity. Vorticity is a vector quantity described in fluid mechanics which characterizes the angular motion of a point particle as it moves. A small ball, for example, found in a field of vorticity would turn around itself. This is in accordance with the existence of the spin of a particle. We claim that due to the dipolar nature of the electric charge, its rotation vortex effects appear. It is found that the total time derivative of the radius possibly due to Brownian motion is different from the velocity but is used as a starting point in describing a fluid-like flow for the electron where all the quantities behave accordingly. Finally, we ascribe the relativistic radius of the electron to a curvature of spacetime from the mass energy equivalence for the electric energy. This paper may also be looked at as one more discussion about the hidden variables quest in quantum mechanics, offering some progress in understanding them.

In the present paper, we attempt to bring to light some of the hidden variables of quantum mechanics by continuing the work of others who introduced constant curvature to spacetime. The article is also a continuation of a previous one [S. Koutandos, Phys. Essays 33, 208 (2020)] published in this journal proving London equations. We find that there is dilation of volume and that mass may have a surface density. Unlike the case of superconductors, however these surfaces collapse to a point. This is where the difficulty in measurement comes from.

Conduction electron spin resonance is employed to study the interplay of the electronic and structural properties in the normal state of Mg1−xAlxB2 alloys as a function of Al-doping for 0 ≤ x ≤ 1. The x-dependence of the spin susceptibility reveals considerable reduction of the total density of states N (EF) with increasing Al concentration, complying with theoretical predictions for a predominant filling effect of the hole σ bands by electron doping. The CESR linewidth exhibits significant broadening, especially prominent in the high-Al-content region, indicative of the presence of enhanced structural disorder, consistent with the presence of compositional fluctuations.The recent discovery of superconductivity in magnesium diboride (MgB 2 ) with critical temperature T c ≈ 39 K [1] stimulated intensive experimental and theoretical studies of its distinctive electronic properties, mostly focusing on the incomplete filling of the in-plane σ bands due to predominantly covalent sp x p y -bonding within the B layers, in contrast with the metallic-type bonding between the Mg and B planes [2][3][4][5][6][7]. Holes at the top of the σ bands are localized within the honeycomb B layers and retain their two-dimensional (2D) character compared to three-dimensional (3D) delocalized electrons and holes in the π bands derived from the boron p z -orbitals. These 2D covalent and 3D metallic states provide comparable contributions to the total density of states N (E F ) at the Fermi level, while the strong interaction of the σ bands with the high-frequency E 2g stretching mode has been implicated to account for phonon-mediated superconductivity [7,8].Alloying MgB 2 and the doping dependence of its electronic properties currently attract much attention from both fundamental and applied perspective [9]. Among various substitutions, alloys of the form Mg 1−x Al x B 2 are of particular interest as the substitution of Al for Mg provides a continuous way of electron doping, attainable up to the structural prototype AlB 2 . However, recent experimental work revealed diverse structural and electronic phenomena for the latter system [10][11][12][13][14][15][16][17][18][19][20][21][22]. In particular, T c decreases with Al-doping at rates critically dependent on x, and vanishes rapidly at x ≈ 0.6. X-ray diffraction experiments have shown