The law of addition of probabilities by means of complex probability amplitudes with its powerful interference consequences, unique to quantum mechanics, is shown to apply elsewhere. The two parts of quantum mechanics: an unvisualizable dynamics and a visualizable concretization (the latter corresponding to reduction of the state vector when a measurement is made) are shown to have a correspondence in computation. Namely, a conceptual structure called a field (of the real numbers, say), its operations, and the concretization of that structure is done by means of a (digital) computer (the latter is interpreted as playing the role of a measuring apparatus). The probabilistic state-reduction operator of quantum mechanics is replaced by a deterministic operation, an extension of rounding. State, wave function, dynamics, observation, uncertainty, and nonlocality are shown to have their counterparts in the new model. The algorithmic counterpart of the double slit experiment to validate the existence of interference in the new framework is defined and performed. A notion of spin in computation is introduced. In an appendix, we comment on how this model impacts a speculative theory of the mind by Penrose.
The law of addition of probabilities by means of complex probability amplitudes with its powerful interference consequences, unique to quantum mechanics, is shown to apply elsewhere. The two parts of quantum mechanics: an unvisualizable dynamics and a visualizable concretization (the latter corresponding to reduction of the state vector when a measurement is made) are shown to have a correspondence in computation. Namely, a conceptual structure called a field (of the real numbers, say), its operations, and the concretization of that structure is done by means of a (digital) computer (the latter is interpreted as playing the role of a measuring apparatus). The probabilistic state-reduction operator of quantum mechanics is replaced by a deterministic operation, an extension of rounding. State, wave function, dynamics, observation, uncertainty, and nonlocality are shown to have their counterparts in the new model. The algorithmic counterpart of the double slit experiment to validate the existence of interference in the new framework is defined and performed. A notion of spin in computation is introduced. In an appendix, we comment on how this model impacts a speculative theory of the mind by Penrose.
Phase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalized probabilistic theories or the convex framework . The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekkens' toy model, quantum theory and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics.
We develop a statistical interpretation of quantum interference in which probabilities, rather than wave amplitudes as primitive objects, form the fundamental descriptive level of quantum phenomena. Interference effects are treated as structural relations between alternative probabilistic contributions, governed by a principle of global consistency (priority of the whole over parts). Within this framework, quantum probabilities are non-Kolmogorovian but remain objectively defined. We show that this interpretation naturally leads to the lattice-theoretic structure of quantum propositions introduced by Birkhoff and von Neumann. Quantum logic thus emerges not as an abstract postulate, but as a structural consequence of quantum probability itself. Finally, we illustrate how this viewpoint provides a clear conceptual reading of quantum algorithms. As an appendix, the Grover search algorithm is analyzed as an example where interference-based probability redistribution can be understood without invoking metaphysical superposition, but purely through statistical structure.
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.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.
GETT Resolves Young’s Double-Slit Experiment — J. E. Holland (2025)** This paper presents a complete physical resolution of Young’s double-slit experiment using the General Expanse Tension Theory (GETT) framework. GETT models all matter as localised excitations of a real, gauge-invariant scalar field Φ, and all wave-like behaviour as small propagating perturbations of this field, known as Expanse Tension Ripples (ETRs). These ripples are launched at the instant of particle emission and propagate at near-light speed. As two ETRs pass through the slits and interfere, they imprint a dynamic tension landscape into the Φ-field. The particle core does not superpose or interfere with itself; instead, it is continuously guided by the local tension gradient generated by the interference of the real δΦ waves. Note: The ETT / GETT framework and theory was developed to address macro-scale cosmic anomalies, galaxy rotations and late time accelerations, this paper simply applies the framework previously developed to this new application. The result is a deterministic, mechanistic explanation of the double-slit experiment that reproduces all key observations traditionally attributed to quantum wave–particle duality. The guidance mechanism emerges from the Φ-field’s density-dependent tension and operates smoothly across time: as the ETR interference pattern forms and sharpens, the particle experiences corresponding changes in the local tension slope, steering it toward regions of lowest tension. Across many single-particle events, this produces the observed statistical fringe pattern without invoking wavefunction collapse, superposition of particle trajectories, or any probabilistic interpretation of the particle itself. The paper includes: A full historical analysis from Hooke, Huygens, and Young to modern single-particle interferometry. A detailed explanation of Φ-field dynamics and the origin, propagation, and interference of ETRs. A time-resolved account of how the particle is guided by evolving tension gradients. A comprehensive 12-phase sequence describing the complete physical process from emission to detection. A mathematical core (Appendix N) giving the field Lagrangian, δΦ wave equation, tension structure, and force law. A simulation appendix (Appendix Q) demonstrating numerically that Fresnel-propagated ETRs, combined with tension-gradient guidance, reproduce the expected interference pattern without wavefunctions. A new visual appendix (Appendix R) illustrating the dynamic evolution of the interference landscape and real-time particle guidance. A predictions section (5.8) giving concrete, testable numerical signatures of GETT in modern interferometry, including expected fringe shifts, timing offsets, and modulation depths. This work shows that the double-slit experiment can be fully explained using only a single real field, its perturbations, and their tension gradients—without the conceptual difficulties of standard quantum mechanics. It provides a unified, physically transparent account that is consistent with all single-particle observations from Taylor (1909) to Tonomura (1989) and with modern weak-measurement and biprism experiments. By resolving the double-slit experiment using deterministic field physics, this paper strengthens the broader GETT programme, in which the Φ-field and its density dependency unify gravity, inertia, cosmology, and particle behaviour within a single theoretical structure. This study demonstrates that GETT naturally reproduces quantum interference and offers a clear, testable alternative to traditional quantum interpretations.
We discuss some seemingly paradoxical yet valid effects of quantum physics in information processing. Firstly, we argue that the act of ``doing nothing'' on part of an entangled quantum system is a highly non-trivial operation and that it is the essential ingredient underlying the computational speedup in the known quantum algorithms. Secondly, we show that the watched pot effect of quantum measurement theory gives the following novel computational possibility: suppose that we have a quantum computer with an on/off switch, programmed ready to solve a decision problem. Then (in certain circumstances) the mere fact that the computer would have given the answer if it were run, is enough for us to learn the answer, even though the computer is in fact not run.