Preprint paper abstract: We develop the concept of a physical value primitive — the most fundamental mathematical representation of a single instance of any physical value — and argue that the complex Gaussian wave packet uniquely satisfies all physical constraints on such a primitive. We show that this primitive is forced by five independent lines of reasoning: physical realizability constraints, Fourier self-duality, minimum uncertainty saturation, maximum entropy under finite mean and variance, and basis-independence. We introduce the Shannon wave function as a novel extension of Shannon information theory to complex amplitudes, showing that it naturally assumes the form of a complex Gaussian wave packet with linear phase variation across symbols, by reasoning directly analogous to the emergence of a Gaussian amplitude spectrum in laser physics. We distinguish indefiniteness — an ontic property of the primitive — from uncertainty — an epistemic property of an observer — and argue that this distinction resolves foundational paradoxes in quantum mechanics, including the Bell test non-locality conclusion and the wave-particle duality of the double slit experiment. We argue that Shannon’s mathematical framework, extended by the Shannon wave function, has broader foundational application than currently acknowledged, providing a unified theory of indefiniteness resolution across physics and information theory.
Preprint paper abstract: We develop the concept of a physical value primitive — the most fundamental mathematical representation of a single instance of any physical value — and argue that the complex Gaussian wave packet uniquely satisfies all physical constraints on such a primitive. We show that this primitive is forced by five independent lines of reasoning: physical realizability constraints, Fourier self-duality, minimum uncertainty saturation, maximum entropy under finite mean and variance, and basis-independence. We introduce the Shannon wave function as a novel extension of Shannon information theory to complex amplitudes, showing that it naturally assumes the form of a complex Gaussian wave packet with linear phase variation across symbols, by reasoning directly analogous to the emergence of a Gaussian amplitude spectrum in laser physics. We distinguish indefiniteness — an ontic property of the primitive — from uncertainty — an epistemic property of an observer — and argue that this distinction resolves foundational paradoxes in quantum mechanics, including the Bell test non-locality conclusion and the wave-particle duality of the double slit experiment. We argue that Shannon’s mathematical framework, extended by the Shannon wave function, has broader foundational application than currently acknowledged, providing a unified theory of indefiniteness resolution across physics and information theory.
Preprint paper abstract: We propose and develop the thesis that every physically real primitive quantity is fundamentally an ontic distribution rather than single-valued in any observable domain. This is not an epistemic claim about measurement uncertainty or observer knowlwdge, but an ontological claim: single-valued physical primitives do not exist in nature. We argue that this view is not merely philosophically tenable but is in fact demanded by three independent pillars of established physics: the Heisenberg Uncertainty Principle (HUP), the impossibility of zero entropy in physical systems, and the Bekenstein bound on information density in finite regions of spacetime [23]. We further develop the implications of this framework for quantum measurement theory, the interpretation of Bell test results [1–3, 31, 32], and the concept of entanglement. In particular, we introduce the concept of a prominence function P(λ,θ) as an ontic measure of the capacity of a distribution’s constituents to physically interact with a given context, and propose that measurement outcomes arise from a distribution-valued product of source distributions and detector context distributions. We argue this framework suggests a reinterpretation of Bell’s theorem in which the assumption of single-valued hidden variables is not merely a simplification but a fundamental category error. This work extends prior analysis of Bell’s theorem in the interval-based framework of [28] and the ontological wave function model of [29].
Paper abstract: All physical theories rely—implicitly or explicitly—on foundational objects that are taken as irreducible. These objects, referred to here as physical primitives, define what the theory accepts as a single physically realizable instance. This paper examines the notion of a physical primitive from first principles and argues that many traditional primitives used in physics are physically unrealizable. We then show that a complex Gaussian wave packet uniquely satisfies the requirements for a physically realizable primitive capable of representing a single instance of any physical value.
Technical paper abstract: Significant open issues remain in conventional quantum theory that may need novel ideas to resolve. The usual model of a quantum wave function is an epistemic one in which the wave function encodes probabilities of future measurement outcomes. This model often falls short of adequately explaining certain basics, like the double slit experiment. We present here a new approach to modeling the wave function as a physical object, supported by analogies to the revolutionary theory of information conceived by Claude Shannon in the 1940’s. Our theory, we term Actualation Theory (AT), where actualation is a physical analog to information, provides a foundation for development of the physical, or ontic, wave function. We also provide some extension to Shannon Theory (ST) in developing comprehensive analogies to Actualation Theory (AT) in support of the physical wave function model.This paper does not represent a declaration that the concepts are valid and should be preferred, instead it is a proposal for consideration and further development.
Preprint paper abstract: We argue that Bell tests, while mathematically rigorous within their stated assumptions, operate in a regime that is fundamentally inconsistent with established physical principles including the Heisenberg Uncertainty Principle, the unattainability of zero entropy, and the Bekenstein bound. Specifically, we contend that the assumption of single-valued measurement outcomes—a cornerstone of Bell’s methodology—requires perfect localization of information that these principles forbid. We propose that physical measurements inherently produce multi-valued outcomes representable as sets of eigenvalues rather than single scalars. This multi-valued structure lacks a rigorously defined correlation product in current mathematics, analogous to the undefined product of kets |a⟩|b⟩. Consequently, Bell test conclusions regarding the incompatibility of locality and realism may be artifacts of imposing an inappropriate mathematical structure on physical reality. We outline the theoretical gap and suggest that experimental implementations using interference-based or other quantum hardware might physically realize the needed “set product” operations, enabling a new class of Bell-type experiments that probe correlations in the multi-valued regime. This work aims to stimulate discussion about whether current Bell tests address the correct mathematical framework for analyzing quantum correlations.
Abstract Wavefunctions are central to quantum mechanics, yet their ontological status remains one of the most debated questions in physics. This volume, within the Informational Constraints Quantum Event Realism (ICQER) framework, proposes a novel reinterpretation of wavefunctions as superpositions of informational constraint patterns distributed across quantum event networks. Moving beyond traditional views of the wavefunction as a mere probability amplitude or abstract mathematical tool, we develop a rigorous framework in which quantum states emerge from the coherent overlap and interplay of constraints that govern allowable event configurations. We establish the mathematical formalism for representing constraints as vectors in an event Hilbert space, constructing wavefunctions as linear combinations of constraint patterns with complex amplitude coefficients. Within this framework, measurement corresponds to the selective enforcement of constraints through projection operators, providing a natural, physical mechanism for wavefunction collapse that does not require observer intervention. Quantum dynamics, governed by the Schrödinger equation, is reinterpreted as the unitary propagation of constraint patterns through the event network, preserving coherence and enabling interference, entanglement, and other hallmark quantum phenomena. The constraint-based perspective resolves foundational puzzles including wave-particle duality, the measurement problem, and quantum nonlocality, while grounding the wavefunction in an objective, realist informational structure. We further explore the connection between quantum constraints and gravitational constraints within the Universal Constraint Gravity (UGC) framework, advancing a unified constraint-based foundation for physics across scales. This volume establishes wavefunctions as distributed informational structures that define quantum reality at its most fundamental level, opening new avenues for foundational research, quantum computation, and the unification of quantum mechanics with gravity.
The standard Copenhagen interpretation of quantum mechanics relies on a set of historically established, ad hoc postulates to describe particle-wave duality, measurement, and non-locality. In this paper, we propose a single foundational axiom that fully reproduces the standard mathematical formalism of quantum mechanics while eliminating the need for supplementary assumptions. From this singular postulate, we rigorously derive the fundamental origin of the wave function and the mathematical generator of the Schrödinger equation. Furthermore, we demonstrate via isomorfism that all seemingly inexplicable quantum phenomena—including wave-function collapse and quantum entanglement—are mathematically and conceptually reducible to the underlying dynamics of the double-slit experiment. By establishing a direct fundamental correlation between the double-slit interference mechanism and the Monty Hall phenomenon, we prove that these effects are distinct manifestations of the exact same principle. We framed the double-slit experiment as an interference of the space of possibilities affected by information and simetrys. Ultimately, by anchoring the existing quantum mathematical framework to this unique axiom, this work provides a coherent, paradox-free ontological foundation that resolves the interpretational crisis of quantum mechanics without altering its empirical predictive power.