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CRC Press eBooks

Axiomatic Structure of Quantum Mechanics

Şaki̇r Erkoç

Published Jul 28, 2006• 0 citations
Publisher

Abstract

Classical mechanics (CM) is applied to a wide range of dynamical systems, including the EM field of interaction with matter. On the other hand, quantum mechanics (QM) is more suitable for the description of phenomena on the atomic scale.
DOI
10.1201/9781584887331-2

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Quantum mechanics (or simply quantum physics) is the branch of physics that applies to particles and systems of particles, such as atoms and molecules. In that realm the laws of classical mechanics and classical electromagnetism break down, and only quantum mechanics provides the concepts and computational methods that explain observed phenomena. Quantum mechanics uses specially developed tools, such as wave functions, that contain all of the relevant information about particles and systems. is approach is needed to understand the true nature of electromagnetic radiation and how that radiation interacts with matter. e mathematics used in quantum mechanics is highly specialized and often complex. In this chapter we’ll address some of the key questions that require quantum mechanics without presenting the full mathematical formalism. e important questions we’ll address all deal with observable physical phenomena. We’ll discuss how quantum mechanics is used to answer these questions but will omit the advanced mathematical details.
This work presents a unified, realistic, and mechanically grounded interpretation of fundamental physics across all scales, from quarks and elementary particles to atoms, macroscopic bodies, planetary motion, and black holes. The proposed framework provides a single coherent physical description capable of reproducing and explaining, within a common dynamical structure, the full range of phenomena traditionally treated separately by general relativity, quantum mechanics, and quantum electrodynamics. Within this approach, long-standing conceptual problems such as wave–particle duality, quantum interference, entanglement, and wavefunction collapse are not postulated as fundamental features of nature, but emerge naturally as dynamical properties of a physically real medium. The apparent dual behavior of matter and radiation, as well as nonlocal quantum correlations, arise from coherent and topologically constrained excitations of this medium, without invoking probabilistic ontologies or nonphysical abstractions. The theory is based on a revised physical concept of space, treated as a real superfluid medium endowed with density, elasticity, viscosity, permittivity, permeability, and a very small but non-zero electrical conductivity. In this model, space is no longer a passive geometric background, but an active physical system capable of storing, transmitting, and dissipating energy.Mass is interpreted as an isotropic compression of the superfluid, electric charge as an oriented torsional configuration, and fields as elastic stress and vorticity distributions of the medium itself. Electromagnetic and gravitational waves are described as propagating perturbations of the superfluid, while particles correspond to stable solitonic configurations sustained by the medium dynamics.At the microscopic level, starting from classical fluid equations (continuity and Euler equations) and applying the Madelung transformation, the Schrödinger equation is shown to emerge as a compact complex representation of the underlying real fluid dynamics, rather than as a fundamental postulate. Quantum phenomena such as quantization, tunneling, spin, and exclusion principles follow from stability, coherence, and topological constraints of solitonic wave structures. On cosmological scales, the same framework provides a unified interpretation of redshift, large-scale expansion phenomena, and the cosmic microwave background as cumulative dynamical and dissipative effects of wave propagation within the superfluid medium, rather than as consequences of metric expansion alone. Effects commonly attributed to dark matter and dark energy are reinterpreted as emergent manifestations of spatial density gradients, elastic stresses, and dissipative properties of the superfluid, without introducing additional unknown components. A wide range of experimentally verified phenomena—including the photoelectric effect, Compton scattering, Zeeman–Stark effects, the Aharonov–Bohm effect, Casimir effect, Unruh radiation, and cosmological attenuation effects—are consistently described within this unified framework. The proposed model offers an alternative foundational paradigm for physics, in which space, matter, and interactions emerge from a single physically intelligible dynamical system, restoring a continuous and causal description of nature from microscopic to cosmological scales.
We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization. 1 The neccessity of quantum mechanics (QM) was a result of experimental data for the energy spectrum of atoms which could not be explained in accord with the laws of classical mechanics. Nevertheless in the axiomatic basis of QM there are axioms which are not supported by the experimental results, since the whole system of axioms (1) is introduced only as a ”plausible generalization ” of the first axiom [1]:
Cognitional Mechanics (CM) is an axiomatic framework in which computations are performed as determinate sequences of non-commutative matrix operations. In its original formulation, CM guarantees logical finality: given the same inputs and operational ordering, the outcome is uniquely determined. While this ensures rigor and eliminates ambiguity, it also renders the internal computational process opaque, hiding the sequence of transformations that produce the result. This opacity has historically led to superficial analogies with Quantum Mechanics (QM), where wave and matrix formulations coexist. However, unlike QM, CM’s dual descriptions are purely representational: they do not introduce probability, superposition, or measurement postulates. Instead, representation choice affects only the visibility of the computational process, not the outcome. To address the explanatory limitations of the algebraic description, this work introduces a wave-representational layer for CM. This formulation maps discrete matrix operations onto continuous trajectories in an abstract state space. The resulting “wave” picture provides process visibility while preserving determinacy, making internal computation transparent without changing the axiomatic conclusions. By making operational trajectories explicit, this approach clarifies the structural distinction between CM and QM, formally invalidates the common CM = QM analogy, and provides a general framework for visualizing computation in axiomatic systems. The wave-representational layer is not a physical theory; it is an internal descriptive extension that enhances conceptual understanding of CM’s deterministic and non-commutative nature.
Quantum mechanics is commonly formulated through a set of postulates inferred from experimental observations. In the present work we investigate whether parts of this axiomatic structure can arise from classical dynamics in a stochastic non-inertial background. We show that two key elements of the conventional formulation—the existence of a fundamental action scale and the Schr¨odinger dynamics—can emerge from a stability condition applied to classical motion in the presence of non-inertial fluctuations. The stability condition implies a balance between the work of non-inertial forces and the emission of electromagnetic energy in the ground state. Within this framework stochastic non-inertial fluctuations generate an effective statistical description that reproduces the structure of quantum mechanics while reducing the number of fundamental assumptions. The theory predicts a previously unexplored Z5 scaling of non-inertial corrections to bound-state energies in hydrogen-like atoms.