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.
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.
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.
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.
Standard quantum theory provides a probabilistic framework for elementary particles, and it is widely held that the underlying physical mechanisms are inherently non-classical. Here, we present a classical electrodynamic analogue model where particles are treated as tightly bound composites of oscillating charge distributions, establishing a classical analogy to pilot-wave-like dynamics. These internal oscillations transform the particle into a Hertzian dipole that emits high-frequency electromagnetic waves, which are reflected by the environmental boundaries back onto the source. We derive the resulting ponderomotive fields symbolically, providing a closed-form analytical expression for the self-force and its deterministic effect on the particle’s trajectory. By means of Monte Carlo simulations, we demonstrate that the interaction of individual particles with their own reflected wave fields in atomic configurations emulates interference and diffraction patterns reminiscent of double-slit experiments. This hybrid analytical-numerical framework recovers a trajectory-based behavior that shares qualitative features with de Broglie’s double-solution theory. While not a replacement for standard quantum mechanics, our findings explore the potential of high-frequency classical electrodynamics to emulate phenomena such as wave-particle duality and statistical uncertainty through purely deterministic matter-field interactions.
We present a new paradigm of quantum reality in which classical particles interact deterministically with quantized electromagnetic fields embedded in a causal lattice spacetime. These interactions induce discrete momentum transfers that account for the dot-like buildup of double-slit interference fringes, the bi-fringe outcomes of the Stern–Gerlach experiment, and the correlations observed in entanglement tests. Within this framework, which provides a non-local hidden variable mechanism, naturally leads to the emergence of Heisenberg uncertainty, de Broglie duality, and the Dirac equation as natural consequences of causal field dynamics, rather than as postulated axioms. The model further provides experimentally testable predictions—including momentum-transfer sidebands and the temperature dependence of the Casimir force—that distinguish it from both the Copenhagen interpretation and more recent alternatives. By grounding quantum phenomena in causal field–particle interactions, this paradigm reproduces the experimental dot-like features in double-slit interference and Stern-Gerlach fringes. Thus, it offers a transparent and physically consistent alternative to the Copenhagen interpretation, achieving the completeness that Einstein argued was missing from conventional theory.
Quantum Electrodynamics (QED) has been extremely successful inits predictive capability for atomic phenomena. Thus the greatest hope for any alternative view is solely to mimic the predictive capability of quantum mechanics (QM), and perhaps its usefulness will lie in gaining a better understanding of microscopic phenomena. Many “paradoxes” and problematic situations emerge in QED. To combat the QED problems, the field of Stochastics Electrodynamics (SE) emerged, wherein a random “zero point radiation” is assumed to fill all of space in an attmept to explain quantum phenomena, without some of the paradoxical concerns. SE, however, has greater failings. One is that the electromagnetic field energy must be infinit eto work. We have examined a deterministic side branch of SE, “self field” electrodynamics, which may overcome the probelms of SE. Self field electrodynamics (SFE) utilizes the chaotic nature of electromagnetic emissions, as charges lose energy near atomic dimensions, to try to understand and mimic quantum phenomena. These fields and charges can “interact with themselves” in a non-linear fashion, and may thereby explain many quantum phenomena from a semi-classical viewpoint. Referred to as self fields, they have gone by other names in the literature: “evanesccent radiation”, “virtual photons”, and “vacuum fluctuations”. Using self fields, we discuss the uncertainty principles, the Casimir effects, and the black-body radiation spectrum, diffraction and interference effects, Schrodinger's equation, Planck's constant, and the nature of the electron and how they might be understood in the present framework. No new theory could ever replace QED. The self field view (if correct) would, at best, only serve to provide some understanding of the processes by which strange quantum phenomena occur at the atomic level. We discuss possible areas where experiments might be employed to test SFE, and areas where future work may lie.