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.
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.
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.
Part 1: the need for the quantum mechanics quantization of radiation the special theory of relativity wave-particle duality the nature of matter waves the uncertainty principle the Bohr atom. Part 2 Schrodinger's equation: the postulates of quantum mechanics the wave equation the wave equation in three dimensions the time-independent Schrodinger equation stationary states normalisation probability flux physical constraints on the wave-function wave packets Gaussian wave-packets and the uncertainty principle. Part 3 One-dimensional potential wells: potential wells the one-dimensional infinite square well discussion of infinite square-well results eigenvalue equations the finite square well finite square well eigenfunctions the control of the wave-function by the wave equation numerical integration of Schrodinger's equation continuum solutions of the square-well potential interpretation of unbound-particle wave functions the double potential well the quantum bouncer electric fields and the tilted well the harmonic oscillator - introduction the quantum oscillator discussion of harmonic oscillator eigenvalues and eigenfunctions the classical probability density more potential wells. Part 4 Schrodinger's equation in three dimensions: particle in a three dimensional box degeneracy Schrodingers equation in spherical polar coordinates - the hydrogen atom normalisation. Part 5 Formal development of quantum mechanics: eigenvalues equations, operators and measurements the momentum operator, eigenvalues and eigenfunctions the position operator and its eigenfunctions Hermitian operators orthogonality of eigenfunctions the expansion postulate example - the b-decay of tritium expectation values compatibility of observables - commutators non-commuting operators time-dependence of expectation values - Ehrenfest's theorem abstract operators - the parity operator, matrix mechanics. Part 6 Angular momentum: angular momentum operators angular momentum commutators angular momentum eigenvalues and eigenfunctions interpretation of angular momentum eigenvalues interpretation of angular momentum eigenfunctions the Stern-Gerlach apparatus and electron spin spin operators - the Pauli Spin matrices the Zeeman effect measurements in quantum mechanics. Part 7 Spherically symmetric potential wells: the rigid rotator the radial equation the hydrogen atom and hydrogen like ions the isotropic harmonic oscillator molecular vibrations - the Morse potential the spherical square well general properties of spherically symmetric potential wells. (Part contents)
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.
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time‐divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self‐interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self‐interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and it also implies that the de Broglie‐Bohm theory and many‐worlds interpretation are wrong and the dynamical collapse theories are in the right direction by admitting wavefunction collapse.
Till 1925 the idea of what the quantum theory would be was unknown. During 1925 three different but equivalent versions of quantum theory were proposed – Schrödinger-proposed wave mechanics; Heisenberg-developed matrix mechanics and Dirac-introduced operator theory. Considering the de Broglie’s matter waves Erwin Schrödinger, an Austrian physicist, argued that if a particle like an electron behaves as a wave then the equation of wave motion could be successfully applied to it. He postulated a function varying in both space and time in a wave-like manner (hence called wave function and denoted it as ψ). This function is generally complex and assumed to contain information about a system. Schrödinger set up a linear and time-dependent wave-like equation, called Schrödinger wave equation, to describe the wave aspect of a particle taking account of de Broglie’s relation for wavelength. Physically, |ψ(X, t)|2, where ψ(X, t) is the solution of the Schrödinger equation, is interpreted as position probability density. That is, |ψ(X, t)|2 is the probability density of observing a particle at position X at time t. ψ does not give exact outcomes of observations but helps us to know all possible events and their probabilities . Further, the probability interpretation allows us to find the average or expected result of a set of measurements on a quantum system.
Through studying we investigate the sense of the wave function of the mass and charge the density distributions of the quantum system. According to the protective calculation, a charged quantum system has effective distribution of mass and charging density in space, proportional to the square of the absolute value of its wave function. In a practical interpretation a wave function of the quantum system can be taken as a definition of either a physical field or the ergodic motion of a particle. The main distinction among the ergodic movement of a sphere and a cell lies in the concurrent property a sphere occurs simultaneously in space, while the agosic movement of a cell is spatially separated in time. If the wave function is a physical force, then the mass and charging density are simultaneously distributed in space to the charged quantum system and thus to the gravitational and electrostatic self-interactions of its wave function. This not only contradicts the superposition principle of quantum mechanics but also contradicts the findings of the experiments. Therefore, wave function is not a definition of a physical area, but rather a transient phase of a material.Each moment has a single localized particle with mass and charge, so the wave function is not auto-introduced. Therefore, it has been argued that the classical ergodic model may not correspond to quantum mechanics for determining constant motion of the particles. Based on the negative result, we say the wave function is a random and unsatisfactory explanation of the particles' quantum motion in nature.In this view, the square of the absolute value of the wave function not only gives the particles' potential in certain locations but also the potential where the cell is. The proposed Latest wave-function description offers a natural practical other than orthodox interpretation, and also suggests that the Broglie-Bohm theory and the interpretation of many worlds are incorrect, and the theories of dynamic collapse They are heading in the right direction by accepting collapse of wave function.