An approach to quantum theory tailored for those students whose backgrounds include relative strength in classical electromagnetic field theory but less in classical mechanics is described. Rather than building quantum theory by following the historical steps, as is often done, the technique is to approach the subject directly from a background knowledge of electromagnetic field theory. The approach uses the postulates that the Maxwell equations are always valid for point charges, that a form of steady-state cosmology is correct, and that the superposition principle is applicable to statistical processes. The model permits a direct transition from electromagnetic field theory to quantum theory. It is self-consistent and based upon currently acceptable physical postulates. It meets the epistemological objections against the orthodox interpretation that Einstein raised and that have never been adequately answered. It does not fall into the class of proposed interpretations that Wigner showed to be inconsistent with the wave theory.
An approach to quantum theory tailored for those students whose backgrounds include relative strength in classical electromagnetic field theory but less in classical mechanics is described. Rather than building quantum theory by following the historical steps, as is often done, the technique is to approach the subject directly from a background knowledge of electromagnetic field theory. The approach uses the postulates that the Maxwell equations are always valid for point charges, that a form of steady-state cosmology is correct, and that the superposition principle is applicable to statistical processes. The model permits a direct transition from electromagnetic field theory to quantum theory. It is self-consistent and based upon currently acceptable physical postulates. It meets the epistemological objections against the orthodox interpretation that Einstein raised and that have never been adequately answered. It does not fall into the class of proposed interpretations that Wigner showed to be inconsistent with the wave theory.
Abstract It can easily be argued that a fully mature and complete knowledge of quantum mechanics should include historical, axiomatic, formal mathematical, and even philosophical background to the subject. However, for a student approaching quantum theory for the first time in a serious way, it can be the case that an approach utilizing his or her existing knowledge of, and intuition for, classical physics (including mechanics, wave physics, and electricity and magnetism) as well as emphasizing connections to experimental results can be the most pro- ductive. That, at least, is the point of view adopted in this text and can be illustrated by a focus on the following general topics:
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
Maxwell’s equations, formulated in 1865, preceded quantum mechanics by six decades. When the logical direction is reversed, however, the electromagnetic field structure can be interpreted as the form required for a quantum theory of charged matter once three standard ingredients are imposed: local gauge invariance, conserved electric current, and a dynamical electromagnetic field. Quantum mechanics supplies the charged-particle state, probability amplitudes, quantum currents, and—through the Dirac equation—a relativistically consistent description of electron charge and spin. Gauge symmetry then organizes the electromagnetic interaction, while current conservation constrains the admissible source structure. The homogeneous Maxwell identities follow naturally from expressing the field through a four-potential, whereas the sourced Maxwell equations require an additional electromagnetic field action or equivalent dynamical assumption. The resulting framework clarifies both the strength and the limit of a “Maxwell from quantum mechanics” program: quantum theory and gauge structure strongly constrain electromagnetism, but Maxwell field dynamics are not obtained from the electron wave equation alone.
Recent advances in quantum technology – from quantum computers and simulators to communication and metrology – have not only opened up a whole new world of applications but also changed the understanding of quantum theory itself. This text introduces quantum theory entirely from this new perspective. It does away with the traditional approach to quantum theory as a theory of microscopic matter, and focuses instead on quantum theory as a framework for information processing. Accordingly, the emphasis is on concepts like measurement, probability, statistical correlations, and transformations, rather than waves and particles. The text begins with experimental evidence that forces one to abandon the classical description and to re-examine such basic notions as measurement, probability, and state. Thorough investigation of these concepts leads to the alternative framework of quantum theory. The requisite mathematics is developed and linked to its operational meaning. This part of the text culminates in an exploration of some of the most vexing issues of quantum theory, regarding locality, non-contextuality, and realism. The second half of the text explains how the peculiar features of quantum theory are harnessed to tackle information processing tasks that are intractable or even impossible classically. It provides the tools for understanding and designing the pertinent protocols, and discusses a range of examples representative of current quantum technology.
Abstract 1. The procedure usually adopted in the Quantum Theory for the estimation of the intensities of a spectrum line includes two stages : (1) the electric moment, p, of the distribution responsible for the spectrum line is calculated by means of Schrodinger’s integrals or some equivalent method ; (2) the rate of loss of energy due to radiation is calculated by the classical formula due to H. Hertz, viz., 2p2/3c3, just as if the distribution were concentrated in a dipole of precisely the same moment p. The first stage involves no difficulties beyond those met with in the evaluation of the integrals or matrices with which we are concerned, the only principles needed being those of the particular quantum theory adopted. But the second stage is open to grave objections and can only be justified on the ground of necessity owing to the absence of any completely satisfactory quantum theory of the electromagnetic field. Sometimes an appeal is made to Bohr’s Correspondence Principle, but this itself involves a somewhat hazardous extrapolation from infinitely large down to small quantum numbers and cannot take the place of a rigorous calculation. A logically consistent method is possible, based on Maxwell’s theory as represented by his electromagnetic equations and their solutions in terms of the classical retarded potential integrals. It may be objected that we do not know how far Maxwell’s equations can be applied to the interiors of atoms, in particular to distributions like those of Schrodinger, but precisely the same objection applies to the customary use of the classical expression for the radiation from an oscillating dipole. Moreover, the attempts made by Heisenberg and Pauli, Dirac and others to formulate a quantum theory of the electromagnetic field have all been based on the assumption that such a theory must be consistent with Maxwell’s equations. The direct application of the methods of classical electromagnetic theory to Schrodinger’s distributions can be justified at least as a rigorous attempt to determine their electromagnetic field and the radiation from them, and the validity of the procedure will have to be judged by the agreement, or otherwise, of the results obtained with experience. In this way we avoid the assumption that a spatially extended distribution can be treated as if its electric moment were concentrated in a point; in fact, the results obtained in this paper for the more important spectrum line series show definitely that the assumption is false, because it leads to results in many cases quite inconsistent with a rigorous application of Maxwell’s theory.