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].
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].
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.
Draft preprint paper abstract: Bell tests have occupied a central role in the interpretation of quantum mechanics for over sixty years, widely regarded as definitive evidence for quantum nonlocality and the impossibility of local hidden-variable theories. We argue that this centrality is methodologically misplaced. Bell test outcome functionals are many-to-one maps that collapse a physically rich quantum state into a single binary value per trial, discarding the overwhelming majority of the physical information and actualities present. Conclusions about quantum reality drawn from such maximally coarse-grained outputs cannot be regarded as definitive descriptions of the underlying ontic state. By contrast, three independent and universal physical constraints — the Heisenberg Uncertainty Principle (HUP), the thermodynamic requirement of strictly nonzero entropy, and the Bekenstein entropy bound — each mandate irreducible dispersion in every physical process without exception. We propose that these pervasive, filter-free, and theoretically convergent constraints constitute stronger foundational evidence about quantum reality than Bell test statistics, and we examine the implications for the nonlocality interpretation. We do not claim Bell’s theorem is mathematically incorrect; we claim its physical regime is too narrow to support the sweeping ontological conclusions commonly attributed to it.
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 This paper develops a metaphysical interpretation of quantum probability under the title Distributed Presence (DP). The central claim is that quantum probabilities should not be understood as measures of ignorance, nor merely as formal devices for predicting measurement outcomes, but as expressions of an objective mode of being: a system’s structured distribution of presence across mutually available channels of realization. On this view, a quantum system prior to measurement is neither fully actual in one determinate outcome nor reducible to a set of hidden definite properties. Rather, it exists in a non-binary mode, articulated by normalized presence fractions associated with the possible outcomes defined by a given interaction context. The Born rule is accordingly not replaced, but reinterpreted: the standard probability assignment is read as the operational expression of an underlying ontological distribution. The paper argues that this framework provides a unified reading of several familiar quantum features. Superposition is understood as a real distribution of presence rather than as epistemic indeterminacy; measurement is interpreted as single-channel actualization rather than as the physical destruction of alternatives; wave-particle duality is recast as the relation between distributed structure and localized realization; and quantum randomness is treated as intrinsic yet structurally constrained. The proposal remains fully compatible with the standard Hilbert-space formalism and introduces no hidden variables, additional collapse dynamics, or many-world branching. Its aim is interpretive rather than revisionary. Beyond its relevance to the foundations of quantum theory, DP is advanced as a contribution to the ontology of probability more broadly. It seeks to show how probability may be objective, physically meaningful, and ontologically basic without collapsing into determinism on the one hand or epistemicism on the other. In that sense, the paper offers a realist, single-world, structurally articulated account of quantum chance.
The standard interpretation of quantum measurement on entangled systems holds that measuring one particle nonlocally collapses the wavefunction of its spacelike-separated partner. We argue that this conclusion rests on a false presupposition: that subsystems of entangled systems possess independent ontic states. If the global wavefunction is the sole ontic object (ψ-ontic holism), then for entangled systems there is no “state of B” to be affected by measurement at A. The reduced density matrix of a subsystem, while operationally useful, is not ontologically real for non-factorizable states. Measurement is a local dynamical process — concretely modeled by continuous spontaneous localization (CSL) — that destroys one local wavefunction component at the measurement site. The global state factorizes as a consequence, and subsystem ontology emerges for the first time. The transition of the distant particle’s reduced density matrix from mixed to pure reflects this emergence of separability, not a physical change at the distant location. We show that this framework is consistent with no-signaling, with the contextuality required by the Kochen–Specker and GHZ theorems, and with the local measurement axiom (Postulate M) proposed in a companion paper. Bell’s theorem does not force nonlocality upon our framework because it presupposes outcome determinism — the assignment of definite values to observables prior to measurement — which several quantum mechanical theorems and our ψ-ontic ontology explicitly deny. Decoherence, which is ubiquitous in nature, provides the mechanism by which the global wavefunction factorizes and classical separability emerges. The apparent nonlocality of quantum mechanics is thus reinterpreted as nonseparability: the fundamental ontology is holistic, but the dynamics are local.
We present a new psi-ontology theorem demonstrating that the quantum wave function is ontic (real) rather than epistemic (representing knowledge) in single-world unitary quantum theories (SUQTs). By leveraging a protocol of repeated reversible measurements on a single quantum system, we show that any two distinct quantum states produce different statistical distributions of (erased) measurement outcomes. This theoretical distinguishability implies that different quantum states correspond to different physical realities, supporting the ontic nature of the quantum state. Unlike previous psi-ontology theorems, such as the Pusey-Barrett-Rudolph theorem, our proof relies solely on the unitary evolution and Born rule of SUQTs, without additional assumptions like preparation independence. This strengthens its implications for quantum foundations, particularly in restricting non-psi-ontic interpretations like QBism without assuming an underlying ontic state and its dynamics. The theorem applies to any pair of distinct states in a finite-dimensional Hilbert space, with extensions to infinite-dimensional systems, offering a robust and general argument for the reality of the quantum state.