J. P. Vigier

Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons “piloted” (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier,(1) Nelson,(2) de Broglie,(3) Guerra et al.(4)), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm(5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

Ampère forces considered as collective non-relativistic limit of the sum of all lorentz interactions acting on individual current elements : possible consequences for electromagnetic discharge stability and tokamak behaviour

Abstract The Ampere-Weber potential associated with the Ampere forces recently experimentally established between current elements is shown to be deductible, as non-relativistic approximation, from the sum of a particular relativistic representation of the Lienart-Wiechert four-vector potentials acting on a mixture of extended, individual, positively and negatively charged particle source components. Some consequences on the physical stability of e.m. currents both in solids, liquids and plasmas (tokamaks) are briefly discussed.

Explanation of the Motionless Electromagnetic Generator with O(3) Electrodynamics

Recently, Bearden el al. developed a device which is known as a motionless electromagnetic generator (MEG) and which produces a coefficient of performance (COP) far in excess of unity. The device has been independently replicated by Naudin. In this communication, the fundamental operational principle of the MEG is explained using a version of higher symmetry electrodynamics known as O(3) electrodynamics, which is based on the empirical existence of two circular polarization states of electromagnetic radiation, and which has been developed extensively in the literature. The theoretical explanation of the MEG with O(3) electrodynamics is straightforward: Magnetic energy is taken directly ex vacua and used to replenish the permanent magnets of the MEG device, which therefore produces a source of energy that, in theory, can be replenished indefinitely from the vacuum. Such a result is incomprehensible in U(1) Maxwell-Heaviside electrodynamics.

Variation of local heat energy and local temperatures under Lorentz transformations

Abstract If one defines in all inertial frames S the local heat energy Q and the local temperature T, in terms of specific collective variables which describe internal isotropic chaotic motions it is shown that they transform like Q = Q 0 (1 − β 2 ) 1 2 and T = T 0 (1 − β 2 ) 1 2 (with β = v c ) where the variables Q0 and T0 are defined in a physical local inertial frame average first introduced by Einstein. This calculation directly justifies (as a consequence of Hamiltons relativistic formalism) the purely heuristic transformations introduced on physical grounds by Planck, Einstein, Tolman and more recently by de Broglie.

Absolute space-time and realism in Lorentz invariant interpretations of quantum mechanics

Abstract The assertion that Lorentz invariance must necessarily be violated in models aimed at giving a realistic account of quantum theory is shown to be incorrect. Assuming that an absolute curved system ofaxes forms the envelope of Local inertial frames where the 2.7 K radiation field as the preferred frame is isotropic, we demonstrate that Lorentz invariance, as well as covariance, stil apply to quantum mechanics in all frames of reference whenever Einstein and de Broglies theory of light, recently revisited by Vigier [IEEE Trans. Plasma Sci. 18 (1990) 64; in: Proc. ISQM-SAT Conf.], is considered.

Self-Inconsistencies of the U(1) Theory of Electrodynamics: Michelson Interferometry

The Michelson interferogram from perfectly reflecting mirrors does not exist in the U(1) gauge theory of electrodynamics, which is therefore seriously flawed. The adoption of an O(3) internal gauge field symmetry allows these flaws to be remedied self-consistently and leads to several developments in electrodynamics, enriching the subject considerably.

Derivation of O(3) Electrodynamics from the Irreducible Representations of the Einstein Group

By considering the irreducible representations of the Einstein group (the Lie group of general relativity), Sachs [1] has shown that the electromagnetic field tensor can be developed in terms of a metric qμ, which is a set of four quaternion-valued components of four-vector. Using this method, it is shown that the electromagnetic field vanishes [1] in flat spacetime, and that electromagnetism in general is a non-Abelian field theory. In this paper the non-Abelian component of the field tensor is developed to show the presence of the B(3) field of the O(3) electrodynamics, and the basic structure of O(3) electrodynamics is shown to be a sub-structure of general relativity as developed by Sachs. The extensive empirical evidence for both theories is summarized.

Derivation of O(3) Electrodynamics from the Einstein–Sachs Theory of General Relativity

General relativity is reduced to O(3) electrodynamics by consideration of the irreducible representations of the Einstein group and through a particular choice of basis. The photon is shown always to possess a scalar curvature R, and so the origin of quantization is found in general relativity.

Anti-Gravity Effects in the Sachs Theory of Electrodynamics

It is demonstrated to a first approximation that anti-gravity effects can occur in the most general theory of electromagnetism, developed by Sachs [1] from the irreducible representations of the Einstein group.

Derivation of the B (3) Field and Concomitant Vacuum Energy Density from the Sachs Theory of Electrodynamics

The archetypical and phaseless vacuum magnetic flux density of O(3) electrodynamics, the B(3) field, is derived from the irreducible representation of the Einstein group and is shown to be accompanied by a vacuum energy density which depends directly on the square of the scalar curvature R of curved spacetime. The B(3) field and the vacuum energy density are obtained respectively from the non-Abelian part of the field tensor Fμν and the non-Abelian part of the metrical field equation. Both of these terms are given by Sachs [5].