Interference in the far-field radiation pattern emitted from a classical current distribution implies near-field work between different spatial portions of the distribution. We examine this relationship and the essential role of system geometry for the case of two oscillating dipoles and for a Gaussian current distribution. This analysis offers a compelling argument as to why the radiation from a large single-electron quantum wave packet should not exhibit the same destructive interference as that associated with a comparable classical charge density. Our discussion draws attention to the ad hoc heuristics motivating the original derivation of a quantum electron's radiation profile.
Interference in the far-field radiation pattern emitted from a classical current distribution implies near-field work between different spatial portions of the distribution. We examine this relationship and the essential role of system geometry for the case of two oscillating dipoles and for a Gaussian current distribution. This analysis offers a compelling argument as to why the radiation from a large single-electron quantum wave packet should not exhibit the same destructive interference as that associated with a comparable classical charge density. Our discussion draws attention to the ad hoc heuristics motivating the original derivation of a quantum electron's radiation profile.
We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.
In the early 1900s more and more experimental evidence was accumulated indicating that microscopic particles show wave-like properties in certain situations. These particle-wave features are very evident, e.g., in measurements where electrons are diffracted from a double slit to propagate toward a screen where they are detected. Based on the classical averaging of particles discussed in Section 1.2.2, one expects that the double slit only modulates the overall intensity, not the spatial distribution. Experimentally, however, one observes a nearly perfect interference pattern at the screen implying that the electrons exhibit wave averaging features such as discussed in Section 2.1.2. This behavior, originally unexpected for particle beams, persists even if the experiment is repeated such that only one electron at a time passes the double slit before it propagates to the detection screen. Thus, the wave aspect must be an inherent property of individual electrons and not an ensemble effect. Another, independent argument for the failure of classical physics is that the electromagnetic analysis of atoms leads to the conclusion that the negatively charged electron(s) should collapse into the positively charged ion because the electron–ion system loses its energy due to the emission of radiation. As we will see, this problem can be solved by including the wave aspects of particles into the analysis. In particular, as discussed in Section 2.3.3, waves can never be localized to a point without increasing their momentum and energy beyond bounds.
This article investigates the consequences of assuming that elementary particles, such as electrons, are internally composed of two very large charge distributions that almost completely neutralize each other externally and can be displaced relative to one another over a distance on the order of the Planck length. Owing to this internal structure, elementary particles would be excited into oscillation during acceleration in a particle accelerator and would therefore emit very weak but extremely high-frequency, coherent, classical electromagnetic waves. In the immediate vicinity of atoms, these waves would be reflected and subsequently act back on the electron in the form of classical forces. This feedback is analyzed in detail. Starting from the electromagnetic field of a Hertzian dipole, a formalism is derived that enables the calculation of the ponderomotive field exerted on the electron by its environment. The physical implications of this mechanism are then studied using numerical simulations. The obtained results are consistent with those of real diffraction and interference experiments with electrons. These findings suggest that, contrary to the prevailing view, key aspects of quantum mechanics-such as wave-particle duality, the measurement problem, and the uncertainty principle-may be explicable within a classical framework.
It is in accordance with such experiments as single photon self-interference that a photon, conveying one radiation energy quantum " h × frequency", is spatially extensive and stretches an electromagnetic wave train. A wave train, hence an energy quantum, can only be emitted (or absorbed) by its source (or absorber) gradually. In both two processes the wave and "particle" attributes of the radiation field are simultaneously prominent, where an overall satisfactory theory has been lacking; for the latter process no known theoretical description currently exists. This paper presents a first principles treatment, in a unified framework of the classical and quantum mechanics, of the latter process, the emission (similarly absorption) of a single radiation quantum based on the dynamics of the radiation-emitting source, a charged oscillator, which is itself extensive across the potential well in which it oscillates. During the emission of one single radiation quantum, the extensive charged oscillator undergoes a continuous radiation damping and is non-stationary. This process is in this work treated using a quasi stationary approach, whereby the classical equation of motion, which directly facilitates the correspondence principle for a particle oscillator, and the quantum wave equation are established for each sufficiently brief time interval. As an inevitable consequence of the division of the total time for emitting one single quantum, a fractional Planck constant h is introduced. The solutions to the two simultaneous equations yield for the charged oscillator a continuously exponentially decaying Hamiltonian that is at the same time quantised with respect to the fractional- h at any instant of time; and the radiation wave field emitted over time stretches a wave train of finite length. The total system of the source and radiation field maintains at any time (integer n times) one whole energy quantum, ( n × ) h × frequency, in complete accordance with the standard notion of quantum mechanics and experiment.
The classical electrodynamic conclusion that an accelerating point charge mustradiate has long been regarded as an iron law, yet the electron in the hydrogen atom does notradiate and fall into the nucleus. This paper points out that the root of this contradiction is not inclassical electromagnetic theory itself, but in the untested hidden assumption that “the electronis a point particle”. Compton scattering experiments have already shown that the electron, whencolliding with a photon, behaves as a particle with a finite size, and its intrinsic geometric radius isgiven by the reduced Compton wavelength: re = ℏ/(mec) . Based on this physical fact, andconsidering that while the electron revolves around the nucleus (orbital motion) it also has anintrinsic spin, the electron itself generates two homologous electromagnetic radiation fields:orbital radiation and spin radiation. These two real electromagnetic waves always superpose andinterfere in space. Under specific conditions (frequencies forming an integer ratio, oppositephases, and matching amplitudes), the two waves completely interfere destructively, resulting inzero net external radiation and forming a stable standing wave inside the system– this is thestationary state of the hydrogen atom. The destructive interference condition naturally leads toωs = nΩ (n integer) and re/R = α/n2 , where α is the fine-structure constant. Combined withthe Coulomb force (centripetal force) equation, one uniquely obtains the quantized orbital radiiRn = n2a0 (a0 is the Bohr radius) and the angular momentum quantization Ln = nℏ . Thefine-structure constant thus acquires a geometric meaning: α = re/a0 .This paper further reveals the classical nature of wave-particle duality: the electron is always aparticle (with a definite trajectory), and its wave-like behavior comes from the superposition andinterference of the electromagnetic waves of spin and orbital radiation. The “particle-like”behavior observed in experiments is essentially the point-like signal produced when the photonradiated by the electron is absorbed, while the wave-particle duality of the photon itself is an1intrinsic property of it being an electromagnetic wave packet. Based on this picture, the paperprovides a classical causal explanation for the electron double-slit experiment– the electron asa particle barely passes through the slits; the interference fringes originate from theself-interference of the radiation wave packet (photon) generated by the electron interactingwith the slit plate, and the bright spots on the screen come from the discrete absorption eventsof photons, with the accumulation of many events forming the fringes. Observation inevitablydisturbs the electron because any measurement disrupts the destructive interference condition,thereby eliminating the mystery of “wavefunction collapse”.The paper also systematically expounds the electromagnetic nature of the photon: the photon isan electromagnetic wave packet radiated when the electron transitions between stationarystates due to the imbalance of interference; its energy E = hλ is determined solely by thefrequency, with constant amplitude; the photon is born at the speed of light because it originatesfrom a pre-existing electromagnetic wave. Finally, the paper discusses the essence of theelectromagnetic field: the electromagnetic field is not matter but energy; the vacuum is theground state electromagnetic field (filled with photons), and the cosmic microwave backgroundradiation is its observational evidence. Macroscopic electromagnetic fields (such as radio waves,visible light) are perturbations superimposed on the ground state field, acting as carriers ofenergy and information. The paper also links the background photon field to the cosmicmicrowave background radiation, providing a new causal picture for the interaction mechanismof charged particles and the inverse-square law of forces.This model is completely based on classical electromagnetism and the physical fact that theelectron has a finite size, providing a causally clear and physically intuitive unified picture for thestability of the hydrogen atom, quantized orbits, wave-particle duality, the nature of the photon,the double-slit experiment, the measurement problem, and the energy origin of theelectromagnetic field.The model further suggests that the proton may also be a similar self-sustaining electromagneticbound state, and the origin of cosmic matter can be attributed to the process of energy lockingby the condensation of electrons and positrons, offering a unified perspective for physicalphenomena from the atom tothe cosmos.
The deterministic origin of quantum mechanics remains one of the most enduring challenges in modern physics. While standard quantum theory provides a probabilistic framework for elementary particles, its underlying physical mechanism is often considered non-classical. Here we show that central features of quantum phenomena can emerge from a classical electrodynamic model where particles are treated as tightly bound composites of oscillating charge distributions. These internal oscillations transform the particle into a Hertzian dipole that emits high-frequency, coherent, classical electromagnetic waves. We demonstrate that these waves, when reflected by surrounding matter, generate ponderomotive fields that act back on the particle’s trajectory. Our simulations of electron trajectories in atomic configurations reproduce the interference and diffraction patterns characteristic of double-slit experiments, realizing a pilot-wave-like dynamics reminiscent of de Broglie’s double-solution theory. These findings suggest that wave-particle duality, the measurement problem, and the uncertainty principle may not be irreducible quantum axioms, but rather emergent properties of deterministic, classical interactions between matter and high-frequency electromagnetic fields.