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Annalen der Physik

Addendum to the Elementary Process Theory

Marcoen J. T. F. Cabbolet

Published Nov 4, 2011• 9 citations
Publisher

Abstract

Abstract Recently, the Elementary Process Theory has been introduced as an axiomatic system with a potential application as a foundational framework for physics. This addendum clarifies the primitive concepts ‘phase quantum’ and ‘monad’ that play a central role in the physical picture that arises from the axiomatic system.
DOI
10.1002/andp.201100194

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Quantum physics consists of a formal core that is universally agreed upon (basically being a piece of mathematics with suggestive names for concepts matching related concepts of experimental culture) and an interpretational halo (trying to make this relation more precise) that remains highly disputed even after more than 90 years of modern quantum physics. The latter is the subject of the interpretation of quantum mechanics (see Part II), where many interpretations coexist and compete for the attention of those interested in what quantum physics really means. In this chapter, an axiomatic introduction to the undisputed formal core of quantum physics is given. The axioms described present nonrelativistic quantum statistical mechanics in the Schrödinger picture. The relativistic case is outside the scope of these axioms, as it must be treated by quantum field theory; see Chapter 7. As in any axiomatic setting (necessary for a formal discipline), there are a number of different but equivalent sets of axioms or postulates that can be used to define formal quantum physics. Since they are equivalent, their choice is a matter of convenience. The choice presented here is a formulation featuring three aspects: It emphasises the similarity of quantum mechanics and classical mechanics, gives most direct access to statistical mechanics, and is free from allusions to measurement. The reason for the first is that this similarity serves as a guide to meaning. From the axiomatic setting for quantum mechanics presented below, classical mechanics (in the Koopman setting discussed in Section 7.10) is obtained by simply restricting the operators to be diagonal, so that all operations happen pointwise on the diagonal elements. Thus, multiplication is commutative, and one can identify operators and functions. In particular, the density operator degenerates into a probability density. Therefore, the quantum case appears as a generalization of the classical case allowing for noncommutativity, so that both q-observables and the density operator are (usually infinite-dimensional) operators. The reason for the second is that statistical mechanics is the main tool for applications of quantum physics to the macroscopic systems we are familiar with. The reason for the third is that realistic measurements constitute a complex process involving macroscopic detectors, hence should be explained by quantum statistical mechanics rather than be part of the axiomatic foundations themselves. (This is in marked contrast to other foundations, and distinguishes the present system of axioms.)
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This work presents a unified generative framework for logic, computation, and physical theories, starting from a minimal recursive structure. Rather than assuming pre-existing logical axioms, computational primitives, or physical laws, the framework derives them as emergent features of a single generative process governed by stabilization and constraint propagation. Within this model, classical logic and computation arise as stabilized regimes of recursive structure, while quantum-mechanical phenomena are interpreted as pre-stabilization behavior—patterns that have not yet resolved into invariant records at the emergent spatial level. Superposition, interference, entanglement, and measurement are described structurally, without invoking parallel-world narratives or epistemic uncertainty. Measurement is treated as constraint coupling that forces refinement until a stable record forms. The framework emphasizes pattern persistence, invariance under refinement, and dynamic resolution as organizing principles. It provides a conceptual account of quantum behavior that is consistent with standard quantum mechanics while reframing it as a consequence of generative structure rather than an axiomatic starting point. This work is foundational and conceptual in nature. It does not propose new experimental predictions or modifications to established physical theory, but aims to clarify the structural relationship between computation, logic, and physics, and to offer a coherent ontological picture underlying these domains.Contact: arthur.nogman@gmail.com
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