Real Wave Quantum Mechanics (RWQM) seeks to demonstrate that standard Quantum Mechanics (QM) can be derived from first principles based entirely on the interactions of real waves in an underlying universal medium. This paper extends previous work on 1 and 2 dimensional applications which used discrete linear/grid structures of entities known as Field Rotators (FRs). It is shown that FRs can be extended continuously in the 3rd dimension to give threadlike forms named FReds. Although continuous, it is shown that the 3rd dimension can be discretized to simplify calculations. Results are similar to those from Schr\"odinger's equation and can be viewed interactively from within the document or directly from the Zenodo site by downloading the appropriate html file. The meaning and role of phase in standard QM is made clear and intuitive by the RWQM approach.
Real Wave Quantum Mechanics (RWQM) seeks to demonstrate that standard Quantum Mechanics (QM) can be derived from first principles based entirely on the interactions of real waves in an underlying universal medium. This paper extends previous work on 1 and 2 dimensional applications which used discrete linear/grid structures of entities known as Field Rotators (FRs). It is shown that FRs can be extended continuously in the 3rd dimension to give threadlike forms named FReds. Although continuous, it is shown that the 3rd dimension can be discretized to simplify calculations. Results are similar to those from Schr"odinger's equation and can be viewed interactively from within the document or directly from the Zenodo site by downloading the appropriate html file. The meaning and role of phase in standard QM is made clear and intuitive by the RWQM approach.
Abstract Real Wave Quantum Mechanics (RWQM) shows that quantum wave functions can arise naturally from the interaction of acoustic waves in an underlying medium, provided these exhibit a small degree of nonlinearity characterized by a dimensionless number, α. Small vortices called Field Rotators (FRs) containing angular momentum can form where there is a correlation between the phase of incoming waves and their direction of arrival. Interaction between FRs arranged in grids in a stochastic wave field can lead to self-sustaining structures which can be interpreted as charged leptons. FRs within the structures are described by their phase, amplitude and spin, thus mapping onto the wave functions of quantum mechanics. Calculations of small stationary state models in 1, 2 and 3 dimensions agree well with Schrödinger wave functions, except that the phases of neighbouring FRs alternate by π radians, a fact which is shown to be essential to the agreement and leads to the Pauli Exclusion Principle. Stable structures have internal phase variation not predicted by the Schrödinger equation, which is associated with internal energy flow and is lost when taking ψ∗ψ. It is hypothesized that orbital ’motion’ is a similar energy flow. Motion of whole structures through the medium leads directly to Special Relativity. The theory illuminates many ’difficult’ features of Quantum Mechanics. Quantitative confirmation of the theory is computationally difficult because of the huge number of interactions involved.
Self Interacting Wave Field (SIWF) theory replaces the ’probability wave’ interpretation of quantum mechanics with a mass-density one. It postulates the existence of a universal acoustic wave-bearing medium in Absolute Euclidian Space Time (AEST). Places where monochromatic waves arrive with phase and direction correlated have angular momentum and are called Field Rotators (FRs). Any non-linearity at FRs makes interaction between ’structures’ of FRs possible. Fundamental particles of nature arise from stable structures: where radiative losses are balanced against gains from resonance with a stochastic field within the medium. ’Phase Harmony’ within the structures has Special Relativity as a consequence. The de Broglie-Einstein equations hold if FRs rotate at the Compton frequency. Schrodinger’s wave function is shown to be a partial representation of the physical wave characterizing the motion of structures. Orbital and spin angular momenta are predicted to be ¯h and ¯h/2 respectively. The Pauli Exclusion principle is demonstrated. When applied to a 1-dimensional Simple Harmonic Oscillator and various square well potentials, the predicted eigenfunctions replicate those found via the Schrodinger equation. Eigenenergies also match if a dimensionless fractional parameter, α, is set to 1/π. In 3-D this could relate to the Fine Structure Constant.
An axiomatic approach to quantum mechanics that has, as a theorem, the Schrödinger equation may be of enormous value to cope with interpretation issues, since all the interpretation constructs must be present in the axioms, or directly derived by them from their mathematical unfolding. Thus, it is critical to show that this axiomatic derivation is reliable beyond any possible doubt. To show this, it is possible to make generalizations and extensions of the axioms to derive the Schrödinger equation in the underlying generalized or extended formats. In previous papers, we have shown that the axiomatic approach we propose can be used to derive the Schrödinger equation as a direct axiom. Since then, we have also shown that it was possible to generalize that derivation to coordinate systems other than the Cartesian, as well as its relativistic extensions that lead to the relativistic wave equations. An extension to dissipative systems was also performed, allowing us to mathematically derive the Caldirola–Kanai equation from first principles. All these derivations were performed using pure states and in the absence of the electromagnetic field. This means that we can further generalize the approach to embrace these two possibilities. Being an axiomatic approach, we show that we need only to slightly modify the axioms to derive the Schrödinger equation for these two contexts. Despite being quite direct, the algebraic complexity of these derivations should give the reader the desired confidence in the proposed axioms.
In the previous chapter, the postulates helped us to use the wave function to find the expected results of experimental measurements by letting a dynamical quantity F (x, p, t) → F (xˆ, pˆ, t) and integrating over space. In the examples, however, the wave functions were typically given and not derived from first principles. We now endeavor to find the appropriate wave functions for a variety of physical systems in one dimension by solving the Schro¨dinger equation where for time-independent cases, the total energy is an eigenvalue. In subsequent chapters, we will extend the method to three dimensions and develop the appropriate operators, eigenvalues, and eigenfunctions for angular momentum. We will also develop methods for examining time-dependent systems. The latter chapters address special systems of interest that may be referred to as applications of quantum mechanics.
Understanding whether the mathematical structure of quantum mechanics is fundamental or emergent remains a central question in the foundations of physics. In particular, the special role played by time in quantum theory, appearing as an external evolution parameter rather than a dynamical observable, suggests that the formalism itself may arise from deeper structural considerations. In this work, we investigate the emergence of quantum mechanical formalism from classical wave dynamics by adopting a dimensional framework in which time is treated as a +1 evolution parameter relative to the dimensions through which physical phenomena (fields or disturbances of a field) propagate and interact. Within this perspective, different fields may evolve with respect to different effective dimensions, while remaining embedded in a common higher-dimensional space, allowing time to acquire a relational and context-dependent role. This means that in our proposed model, time is not a fixed dimension which is experienced the same way for every field or field interaction of any dimensionality. In that sense, time for one physical phenomenon can behave as space for a higher dimensional physical phenomenon, whose time is a different +1 dimension. The central objective of this paper is to determine how a higher-dimensional deterministic field can be consistently represented by a lower-dimensional description that lacks direct access to its full set of evolution parameters and evolves through a spatial (for the higher-dimensional field) dimension. To this end, we introduce a general projection framework in which a higher-dimensional field is mapped to a reduced field through an interaction-based recording process. Crucially, we do not assume the form of this mapping a priori. Instead, we impose the requirement that it preserve the maximum amount of physically accessible information. In particular, we demand the faithful encoding of phase relations, interference structure, and spectral composition, including the relative contributions of different Fourier modes and their superposition. We first demonstrate, within a purely classical 3+1-dimensional wave framework that these constraints severely restrict the admissible form of the reduced description and naturally lead to complex amplitudes, linear superposition, Hilbert space structure, and canonical operator relations. This analysis provides an intuitive and mathematically explicit route to quantum-like descriptions without assuming quantum postulates. We then generalize the construction to a 4+1-dimensional framework, introducing an additional evolution parameter and showing that under the same information-preserving constraints, the Schrödinger equation appears as an effective low-energy description of the reduced dynamics, while a relativistic dispersion relation emerges simultaneously through the encoding of the hidden evolution parameter as an invariant frequency scale. In this way, both quantum mechanical and relativistic structures arise from the same underlying requirement: the consistent and information-preserving representation of higher-dimensional wave propagation in a lower-dimensional observational framework. The results suggest that the formal structure of quantum mechanics need not be postulated a priori, but may instead be understood as the unique mathematical language required to encode the observable remnant of a higher-dimensional deterministic dynamics under strict constraints of symmetry, invariance, and information preservation.