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Collective electrodynamics I (superconductoryquantum coherenceyvector potentialymagnetic interaction)

Carver Mead

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quan- tum systems; the only assumptions used are the Einstein- deBroglie relations, the discrete nature of charge, the Green's function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell's equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate.

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Collective electrodynamics I

Carver Mead

Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quantum systems; the only assumptions used are the Einstein-deBroglie relations, the discrete nature of charge, the Green's function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell's equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate.

Proceedings of the National Academy of Sciences•Jun 10, 1997•7 citations

Collective Electrodynamics I

Carver Mead

Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quantum systems; the only assumptions used are the Einstein-deBroglie relations, the discrete nature of charge, the Green’s function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell’s equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate. “But the real glory of science is that we can find a way of thinking such that the law is evident .” — R. P. Feynman

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•Mar 5, 2009•0 citations
Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quan- tum systems; the only assumptions used are the Einstein- deBroglie relations, the discrete nature of charge, the Green's function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell's equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate.
Standard results of electromagnetic theory are derived from the direct interaction of macroscopic quantum systems; the only assumptions used are the Einstein-deBroglie relations, the discrete nature of charge, the Green’s function for the vector potential, and the continuity of the wave function. No reference is needed to Maxwell’s equations or to traditional quantum formalism. Correspondence limits based on classical mechanics are shown to be inappropriate. “But the real glory of science is that we can find a way of thinking such that the law is evident .” — R. P. Feynman
An explicit physical interpretation of the electromagnetic vector potential is here pointed out—as field momentum available for exchange with kinetic momenta of charged matter. It is shown that the vector potential can be quite as directly measurable, without recourse to only quantum-mechanical effects, as are scalar potential differences and the force fields E, B. This suggests, in keeping with quantum electrodynamics, that the equations for potentials may be regarded as more ’’basic’’ than the Maxwell equations—but only because the potentials most directly represent interaction energy-momenta through which fields and charges become observable.
Preface. Introduction to the Conference. A Quantum of Light Shed on a Classical Problem C.K. Whitney. A Classical Photon Model R.J. Beil. Stationary Vacuum-Polarization 'P Fields': the Missing Element in Electromagnetism and Quantum Mechanics M.H. MacGregor. Electrons and Photons as Soliton-Waves G. Hunter. Topological Solitons in Non-Linear Electrodynamics G. Kalbermann. A Particle or a Photon in a Field T.W. Marshall, E. Santos. Could the Photon be Superfluous? M. Sachs. Fluctuation-Dissipation Quantum Electrodynamics G.F. Efremov, et al. Einstein-de-Broglie-Proca Theory of Light and Simultaneous Existence of Transverse and Longitudinal Photons S. Roy, M. Roy. Origin, Observation and Consequences of the B(3) Field M.W. Evans. Opto-Magnetic Effects in Non-Absorbing Media: Problems of Measurement and Interpretation S. Jeffers, et al. Generalized Equations of Electrodynamics of Continuous Media V.M. Dubovik, et al. Maxwellian Analysis of Reflection and Refraction R.D. Prosser, et al. Solutions of Maxwell Equations for a Hollow Curved Wave Conductor N. Bashkov, A. Tchernomorov. Maxwell's Equations Directly from the Dynamics of Point Particles G.N. Ord. Obtaining the Schrodinger and Dirac Equations from the Einstein/KAC Model of Brownian Motion by Projection G.N. Ord. Derivation of the Schrodinger Equation T.B. Andrews. An Appraisal of Stochastic Interpretations of Quantum Mechanics M. Baublitz, Jr. Compatible Statistical Interpretation of Quantum Beats M. Bozic. Stochastic Non-Markov Model of Quantum Mechanical Behaviour S.R. Vatsya. A Fundamental Force as the Deterministic Explanation of Quantum Mechanics B.J. Dalton. A Geometric Approach to the Quantum Mechanics of the Broglie and Vigier W.R. Wood, G. Papini. Stable Orbits as Limit Cycles S. Bergia. The Correspondence Principle: Periodic Orbits from Quantum Mechanics D. Provost. Neutron Interferometric Experiments on Quantum Mechanics G. Badurek. Enigmatic Neutrons V.K. Ignatovich. Experiments to Test the Reality of De Broglie Waves J.R. Croca. Preselected Quantum Optical Correlations M. Pavicic. Apparent Contradiction in EPR Correlations L.C. Ryff. The Wave- particle Duality E. Bitsakis. Quantum Mechanical Tunneling in a Causal Interpretation M. Clarkson. Quantum Uncertainty, Wave-particle Duality and Fundamental Symmetries P. Rowlands. On the Contradiction between Quantum Mechanics and Relativity: a Superluminal Quantum Morse Telegraph A. Garuccio. Incompatibility between Einstein's Relativity and Lorentz's Equations P. Marmet. On Self-Interaction and (Non-)Perturbative Quantum GRT H.-H. von Borzeszkowski. Classical Physics Foundations for Quantum Physics L. Motz, D.W. Kraft. Inertial Transformations: A Review F. Selleri. The Lorentz Invariance Revisited M. Surdin. A New Type of Massive Spin-One Boson: And Its Relation with Maxwell Equations D.V. Ahluwalia. Implications of Extended Models of the Electron for Particle Theory and Cosmology E.J. Sternglass. The Takabayasi Moving Frame, from the A Potential to the Z Boson R. Boudet. The Nature of the Cosmological Redshift M. Moles. A Quantum Digital Theory of Light N.V. Pope. Toward a Comprehensible Physical Theory: Gravity and Quantum Mechanics H. Yilmaz. Hidden Background Field and Quantum Non-Locality R. Ramanathan. Einstein-Podolsky-Rosen Correlations within Bell Region R. Horodecki. Electromagnetic Gauge as Integration Condi
We present a succinct way to quantize Maxwell's equations. We begin by discussing the random nature of quantum observables. Then we present the quantum Maxwell's equations and give their physical meanings. Due to the mathematical homomorphism between the classical and quantum cases [1], the derivation of quantum Maxwell's equations can be simplified. First, one needs only to verify that the classical equations of motion are derivable from a Hamiltonian by energy-conservation arguments. Then the quantum equations of motion follow due to homomorphism, which applies to sum-separable Hamiltonians. Hence, we first show the derivation of classical Maxwell's equations using Hamiltonian theory. Then the derivation of the quantum Maxwell's equations follows in an analogous fashion. Finally, we apply this quantization procedure to the dispersive medium case. (This article is written for the classical electromagnetic community assuming little knowledge of quantum theory, an introduction of which can be found in [2, Lecs. 38 and 39].)