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The Complex Gaussian Wave Packet as a Physical Primitive

F. Pat Eblen

Published Feb 5, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.18489791

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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.
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.
In my dissertation I analyze the structure of fundamental physical theories. I start with an analysis of what an adequate primitive ontology is, discussing the measurement problem in quantum mechanics and theirs solutions. It is commonly said that these theories have little in common. I argue instead that the moral of the measurement problem is that the wave function cannot represent physical objects and a common structure between these solutions can be recognized: each of them is about a clear three-dimensional primitive ontology that evolves according to a law determined by the wave function. The primitive ontology is what matter is made of while the wave function tells the matter how to move. One might think that what is important in the notion of primitive ontology is their three-dimensionality. If so, in a theory like classical electrodynamics electromagnetic fields would be part of the primitive ontology. I argue that, reflecting on what the purpose of a fundamental physical theory is, namely to explain the behavior of objects in three--dimensional space, one can recognize that a fundamental physical theory has a particular architecture. If so, electromagnetic fields play a different role in the theory than the particles and therefore should be considered, like the wave function, as part of the law.Therefore, we can characterize the general structure of a fundamental physical theory as a mathematical structure grounded on a primitive ontology. I explore this idea to better understand theories like classical mechanics and relativity, emphasizing that primitive ontology is crucial in the process of building new theories, being fundamental in identifying the symmetries. Finally, I analyze what it means to explain the word around us in terms of the notion of primitive ontology in the case of regularities of statistical character. Here is where the notion of typicality comes into play: we have explained a phenomenon if the typical histories of the primitive ontology give rise to the statistical regularities we observe.
Primitive ontology is a program which seeks to make explicit the ontological commitments of physical theories in terms of a distribution of matter in ordinary space-time. This program targets wave-function realism, which interprets the high-dimensional configuration space on which wave-functions are defined as our fundamental physical space. Wave-function realism allegedly fails to account for a correspondence between the ontology it postulates and the ‘manifest image’ of the world in which experimental tests of the theory are performed, and therefore the wave-function must be completed with an additional structure which describes what fundamentally exists in ordinary space-time: the ‘primitive ontol- ogy’. However primitive ontologies face some difficulties, in particular concerning the ontological status of the wave-function. In this paper, I defend a realist inter- pretation of the wave-function as describing objects in ordinary space-time, which does not require supplementing the theory with additional structure. The main dif- ference between this proposal and other primitive ontology proposals is that the fundamental constituents of reality are not conceived of as localised objects, but as primitive relations. This interpretation purports to share the advantages of both wave-function realism and primitive ontologies without facing the same difficulties. I argue that the need for an additional structure stems from a commitment to the locality of the fundamental constituents of reality, and that such commitment is unnecessary for recovering the manifest image of the world.
The aim of this paper is to summarize a particular approach of doing \nmetaphysics through physics - the primitive ontology approach. The idea is that any \nfundamental physical theory has a well-defined architecture, to the foundation of which \nthere is the primitive ontology, which represents matter. According to the framework \nprovided by this approach when applied to quantum mechanics, the wave function is not \nsuitable to represent matter. Rather, the wave function has a nomological character, given that its role in the theory is to implement the law of evolution for the primitive ontology.
The objective of this paper is to show that, instead of quantum probabilities, wave packets are physically real. First, Cartwright's recent argument for the reality of quantum probabilities is criticized. Then, the notion of ‘physically real’ is precisely defined and the difference between wave functions and quantum probabilities clarified. Being thus prepared, some strong reasons are discussed for considering the wave packet to be physically real. Finding the reasons inconclusive, I explain how the Aharonov—Bohm effect delivers the final punch. I conclude that wave packets are the quantum objects that underlie the indeterministic quantum processes and have the propensity of displaying probabilistic (or indeterministic) behavior.