Classical Electrodynamics without the Lorentz Condition: Extracting Energy from the Vacuum

It is shown that if the Lorentz condition is discarded, the Maxwell–Heaviside field equations become the Lehnert equations, indicating the presence of charge density and current density in the vacuum. The Lehnert equations are a subset of the O(3) Yang–Mills field equations. Charge and current density in the vacuum are defined straightforwardly in terms of the vector potential and scalar potential, and are conceptually similar to Maxwell's displacement current, which also occurs in the classical vacuum. A demonstration is made of the existence of a time dependent classical vacuum polarization which appears if the Lorentz condition is discarded. Vacuum charge and current appear phenomenologically in the Lehnert equations but fundamentally in the O(3) Yang–Mills theory of classical electrodynamics. The latter also allows for the possibility of the existence of vacuum topological magnetic charge density and topological magnetic current density. Both O(3) and Lehnert equations are superior to the Maxwell–Heaviside equations in being able to describe phenomena not amenable to the latter. In theory, devices can be made to extract the energy associated with vacuum charge and current.

[1]  John David Jackson,et al.  Classical Electrodynamics , 2020, Nature.

[2]  D. Chung,et al.  Apparent negative electrical resistance in carbon fiber composites , 1999 .

[3]  G. Schilling Watching the Universe's Second Biggest Bang , 1999, Science.

[4]  P. Leonard The Challenge of Gamma Ray Burst Observations , 1998, Science.

[5]  B. Lehnert Minimum electric charge of an extended electromagnetic field theory , 1996 .

[6]  V. Letokhov Laser Maxwell's demon , 1995 .

[7]  V. L’vov Wave Turbulence Under Parametric Excitation: Applications to Magnets , 1994 .

[8]  N. Lawandy,et al.  Laser action in strongly scattering media , 1994, Nature.

[9]  Paul Mandel,et al.  Lasing without inversion: A useful concept? , 1993 .

[10]  Cole,et al.  Extracting energy and heat from the vacuum. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  M. Evans On the experimental measurement of the photon's fundamental static magnetic field operator B̂Π: the optical Zeeman effect in atoms , 1992 .

[12]  M. Evans The elementary static magnetic field of the photon , 1992 .

[13]  Olga Kocharovskaya,et al.  Amplification and lasing without inversion , 1992 .

[14]  R. Fischer,et al.  Comment on ‘‘How can a particle absorb more than the light incident on it?’’ , 1983 .

[15]  Craig F. Bohren,et al.  How can a particle absorb more than the light incident on it , 1983 .

[16]  Gabriel Kron,et al.  Four Abstract Reference Frames of an Electric Network , 1968 .

[17]  B. Lehnert Total reflection process including waves of an extended electromagnetic theory , 1995 .

[18]  V. L’vov Wave Turbulence Under Parametric Excitation , 1994 .

[19]  H. Harmuth Information theory applied to space-time physics , 1992 .

[20]  Gabriel Kron,et al.  Electric Circuit Models of the Schrödinger Equation , 1945 .