Emergent Quantum Mechanics (Em.QM) is defined here as the attempt to bridge the gap between quantum and classical mechanics, and to restore causality to the atomic world. An example described in the paper shows how a conspiracy of the classical laws produces a replica of the quantum harmonic oscillator. This is achieved using a droplet model of electrons, obeying Newton/Einstein dynamics in combination with Maxwell’s electromagnetic laws. A concise sketch of the droplet theory precedes the sections on the harmonic oscillator. This summary also briefly mentions other successes of the droplet theory, such as the derivation of the fundamental quantum laws \(p=\frac{h}{\lambda}\) and \(E=h.\nu\) with a practically correct numerical value of Planck’s constant h. Although these subjects were already addressed in earlier publications about Em.QM, recently simpler and more transparent derivations were found and are reported here. Finally, the achievements of Em.QM until now are reviewed. Em.QM does not compete with conventional QM: the latter will always be superior for performing actual calculations, whereas Em.QM is concerned with possible interpretations of quantum phenomena. An assessment is given of the present status of Em.QM in this perspective.
Emergent Quantum Mechanics (Em.QM) is defined here as the attempt to bridge the gap between quantum and classical mechanics, and to restore causality to the atomic world. An example described in the paper shows how a conspiracy of the classical laws produces a replica of the quantum harmonic oscillator. This is achieved using a droplet model of electrons, obeying Newton/Einstein dynamics in combination with Maxwell’s electromagnetic laws. A concise sketch of the droplet theory precedes the sections on the harmonic oscillator. This summary also briefly mentions other successes of the droplet theory, such as the derivation of the fundamental quantum laws (p=\frac{h}{\lambda}) and (E=h.\nu) with a practically correct numerical value of Planck’s constant h. Although these subjects were already addressed in earlier publications about Em.QM, recently simpler and more transparent derivations were found and are reported here. Finally, the achievements of Em.QM until now are reviewed. Em.QM does not compete with conventional QM: the latter will always be superior for performing actual calculations, whereas Em.QM is concerned with possible interpretations of quantum phenomena. An assessment is given of the present status of Em.QM in this perspective.
Emergent Quantum Mechanics (Em.QM) is defined here as the attempt to bridge the gap between quantum and classical mechanics, and to restore causality to the atomic world. An example described in the paper shows how a conspiracy of the classical laws produces a replica of the quantum harmonic oscillator. This is achieved using a droplet model of electrons, obeying Newton/Einstein dynamics in combination with Maxwell’s electromagnetic laws. A concise sketch of the droplet theory precedes the sections on the harmonic oscillator. This summary also briefly mentions other successes of the droplet theory, such as the derivation of the fundamental quantum laws p=λh and E=h.ν with a practically correct numerical value of Planck’s constant h. Although these subjects were already addressed in earlier publications about Em.QM, recently simpler and more transparent derivations were found and are reported here. Finally, the achievements of Em.QM until now are reviewed. Em.QM does not compete with conventional QM: the latter will always be superior for performing actual calculations, whereas Em.QM is concerned with possible interpretations of quantum phenomena. An assessment is given of the present status of Em.QM in this perspective.
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)].
In Feynman’s “Lectures on Physics” it is observed that close to an oscillating dipole the electromagnetic field is almost quasi-static, as if retardation is absent and the speed of transmission thus would approach infinity. Within the framework of Emergent Quantum Mechanics (Em.QM) non-singular electron models are being revisited, showing similar phenomena near a droplet of charge. In the literature, the matter has been called an as yet unsolved dilemma because – like the “spooky” non-local effects of Quantum Mechanics (QM) – it seems to be in conflict with relativity theory. In the present paper, an asymptotic expansion of the electromagnetic field around a moving and deforming droplet of charge is used to investigate the matter in detail. It is concluded that Feynman’s formulae are correct, be it _after_ initial conditions of the boundary value problem have been established by a field of normal travelling waves. When such a reset has been completed, the field of travelling waves can be written as a superposition of groups of standing waves. In each standing wave system, the variables belonging to it display synchronicity, which causes the illusion of non-retarded interactions. But in fact, there are no causal relations between the singularities (such as charges) and the other field variables (such as electromagnetic forces), even though the illusion may be given that superluminal signalling takes place. The conclusions are important for the theory of Em.QM, since they show that the classical laws are able to mimic non-local phenomena.
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear explanation was given for why everyday objects, which are merely collections of atoms, are observed to obey Newton's laws. It would seem that, if quantum mechanics explains all the properties of atoms accurately, they, too, should obey quantum mechanics. This reasoning led some scientists to believe in a distinct macroscopic, or ``big and complicated,'' world in which quantum mechanics fails and classical mechanics takes over, although there has never been experimental evidence for such a failure. Even those who insisted that Newtonian mechanics would somehow emerge from the underlying quantum mechanics as the system became increasingly macroscopic were hindered by the lack of adequate experimental and theoretical tools. In the last decade, however, this quantum-to-classical transition has become accessible to experimental study and quantitative description, and the resulting insights are the subject of this article.
Elements of quantum mechanics Quantum mechanics was discovered in 1925 through groping efforts to compromise two apparently contradictory pictures on the fundamental entities in nature. One was the wave picture for light which was later extended to matter by de Broglie, another was the corpuscular picture of matter which was later extended to light by Einstein. Schrödinger's wave equation came as a natural development of the first stream, while Heisenberg's matrix mechanics was presented as a unique proposal from the second stream. In spite of completely different appearances, the two theories proved, within a couple of years after their discoveries, to be equivalent. This is a most beautiful example that the physical reality exists independent of the mathematical framework formulated for its description. In this chapter, we will give a very brief review of the principles of quantum mechanics, 1–3 mainly with the harmonic oscillator as a model system for the following reasons. The first is historical: the electromagnetic wave, whose interaction with matter is the subject of this book, is a harmonic oscillator, a system which was for the first time subject to “quantization”, thus opening a way to the discovery of quantum mechanics. The second is technical: the harmonic oscillator is one of very few examples of analytically soluble problems in quantum mechanics. The third is pedagogical: the harmonic oscillator is a system best suited for realization of the equivalence of the two different pictures mentioned above and hence for a deeper understanding of the principles of quantum mechanics.
Following a short history of quantum mechanics, an outline of the contents of this book is given. A model of an electron is derived by time-averaging the motion of a “zittering” electromagnetic singularity, and by adding an apparent force in the form of surface tension in order to remove false electrostatic effects due to the model simplification. This model of a deformable droplet of charge is adopted as a working hypothesis, to see what are the consequences of such a model. The consequences are mathematically worked out and are shown to lead to a quantitatively correct replica of quantum behaviour. Matter waves are shown to correspond to trains of beats in the pulsation of the droplet, and the correct value of Planck's constant is derived. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.