We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows for a new realization of the "one electron Universe" of Wheeler-Feynman (the so called "ensemble of duplicons") and leads to a radical concept of "dimerous" (consisting of two identical matter pre-elements, "duplicons") electron. Using this concept, together with an additional phase-like invariant (arising from the complex pre-geometry), we manage to give a visual classical explanation for quantum interference phenomena and, in particular, for the canonical two-slit experiment. Fundamental relativistic condition of quantum interference generalizing the de Broglie relationship is obtained, and an experimentally verifiable distinction in predictions of quantum theory and presented algebrodynamical scheme is established.
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows for a new realization of the "one electron Universe" of Wheeler-Feynman (the so called "ensemble of duplicons") and leads to a radical concept of "dimerous" (consisting of two identical matter pre-elements, "duplicons") electron. Using this concept, together with an additional phase-like invariant (arising from the complex pre-geometry), we manage to give a visual classical explanation for quantum interference phenomena and, in particular, for the canonical two-slit experiment. Fundamental relativistic condition of quantum interference generalizing the de Broglie relationship is obtained, and an experimentally verifiable distinction in predictions of quantum theory and presented algebrodynamical scheme is established.
This paper develops a phase-first reconstruction of quantum interference within standard quantum mechanics and wave optics. Its central idea is that interference patterns become conceptually clearer when the complex phase is treated as the organizing structure and probability or intensity density is treated as the visible statistical expression of that structure. The guiding principle is: the phase structures the pattern; the density renders it visible. The paper shows how this principle applies to single-slit diffraction, double-slit interference, Airy patterns, Fourier optics, Fresnel propagation, probability current, the Madelung representation, which-way marking, reduced coherence, and quantum eraser experiments. In each case, the observed density pattern is interpreted as the visible result of coherent phase relations among amplitudes. The reconstruction is strictly conservative. It does not modify quantum mechanics, the Born rule, unitary dynamics, or standard wave optics. It introduces no new postulates and makes no new empirical prediction. Its purpose is conceptual and pedagogical: to clarify the architecture of quantum interference by placing relative phase at the center of the analysis. This work is Part I of the series The Geometry of Phase. It establishes the phase-geometric foundation for later parts of the series, where the same perspective is extended to de Broglie matter waves, proper-time phase, relativistic action, and possible curvature-coupled phase extensions.
A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of self-amplified, essentially nonlinear squeeze of its extended part to a small volume around randomly chosen centre, followed by the reverse extension. The resulting spatially random pulsation, or "quantum beat", is observed as (massive) elementary particle such as the electron. The property of mass is then universally and consistently defined as temporal rate of such dynamically chaotic and essentially nonlinear quantum beat, without introduction of any additional entities. The obtained picture can be considered as complex-dynamical completion of the "double solution" concept of Louis de Broglie. The dynamically emerging wave-particle duality, quantum discreteness, indeterminacy, space, and time lead to the equations of special relativity and quantum mechanics, providing their causal explanation and explicit unification. The elementary particle structure, its intrinsic properties, quantum and relativistic behaviour are obtained thus all together, within the unified analysis of the unreduced interaction process leading to the universal concept of dynamic complexity. The same complex-dynamical process accounts for the universal gravitation and general relativity. The electromagnetic, weak, and strong types of interaction between particles also constitute integral, dynamically unified parts of quantum beat processes inside elementary particles. The classical, dynamically localised behaviour emerges in a closed system as a higher complexity level corresponding to formation of elementary bound systems (like atoms).
The double-slit experiment is commonly interpreted as evidence that a single electron must be described by a spatially extended wavefunction whose path amplitudes interfere. Here, we present an alternative geometric formulation within the Bivector Standard Model, in which the observed far-field interference pattern is reproduced while the phase is attributed to an internal bivector clock carried by the electron. In this approach, each electron remains localized and produces a single detection event, while the familiar fringe pattern emerges statistically from the accumulation of many impacts. Interference arises from the comparison of clock phases associated with geometrically distinct paths, rather than from the superposition of spatial waves. The resulting probability distribution recovers the standard two-slit interference factor, the single-slit diffraction envelope, and the usual fringe-spacing relation in the Fraunhofer regime. The de Broglie wavelength emerges as the spatial manifestation of this transported phase. This formulation provides a geometric account of the origin of phase in single-electron interference, consistent with standard results while offering a distinct physical interpretation.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
We perform an experimental test where we directly observe light-induced electron transitions with a macroscopic spatial discontinuity. The effect is related to the fundamental indivisibility of macroscopic orbit-like quantum states reminiscent of so-called extended states in the integer quantum Hall system. The test has become realizable due to the discovering of a quantum phase with spontaneous pervasive quantum ordering reminiscent of that of a single atom. The observed transitions may be regarded as a peculiar quantum dynamics beyond relativity, which implies that the current relativistic model of universe should be replaced by a deeper quantum model. It is the Bohm’s model of undivided universe which now should involve a deeper-than-classical concept of absolute simultaneity and a deeper-than-relativistic concept of space and time. Ultimately, our test thus establishes a new hierarchy of fundamental physical theories where the de Broglie-Bohm realistic quantum theory is the deepest theory which does not contradict either classical physics or relativity but rather is beyond both. This is because the fact that quantum theory is dealing with a deeper reality where physical objects are not self-sufficient entities and therefore they can transit discontinuously within an overall quantum system determined by their wavefunctions.
We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.