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Does the Three Wave Hypothesis Imply a Hidden Structure

Mohammed I. Sanduk

Published Apr 1, 2007• 2 citations
OpenAlex

Abstract

The three wave hypothesis (TWH) is an attempt to relate the particle to an associated wave phenomenon. This hypothesis regards that the particle is associated with three waves: one transformed and two dispersive waves. Since the two dispersive waves are associated with a single particle, in this work we try to get a single representation for these two dispersions. The single representation exhibits similarities with those of a classical gear consisting of two perpendicular wheels. According to this similarity, the parameters of dispersive waves correspond to those of the wheels, and the transformed Compton wave corresponds to the system parameters (the combination). This similarity between the two models may possibly point to a hidden structure.

Related papers

Three Wave Hypothesis, Gear Model and the Rest Mass

Mohammed I. Sanduk

Three Wave Hypothesis (TWH) is of a relativistic quantum foundation. The formulation of TWH has perfect similarities with bevel gear model. The rest mass is considered within TWH and as a consequence of similarity, between TWH and the gear model, it is found that rest mass frequency is related the frequency of touch point of the gear in relative to the large wheel. In regarding this frequency instead of the small wheel frequency, the gear model leads to four-vector representation of a particle.

arXiv:0904.0790•Apr 5, 2009•0 citations

An Analogy for the Relativistic Quantum Mechanics through a Model of De Broglie Wave-covariant Ether

Mohammed I. Sanduk

Based on de Broglie’s wave hypothesis and the covariant ether, the Three Wave Hypothesis (TWH) has been proposed and developed in the last century. In 2007, the author found that the TWH may be attributed to a kinematical classical system of two perpendicular rolling circles. In 2012, the author showed that the position vector of a point in a model of two rolling circles in plane can be transformed to a complex vector under a proposed effect of partial observation. In the present project, this concept of transformation is developed to be a lab observation concept. Under this transformation of the lab observer, it is found that velocity equation of the motion of the point is transformed to an equation analogising the relativistic quantum mechanics equation (Dirac equation). Many other analogies has been found, and are listed in a comparison table. The analogy tries to explain the entanglement within the scope of the transformation. These analogies may suggest that both quantum mechanics and special relativity are emergent, both of them are unified, and of the same origin. The similarities suggest analogies and propose questions of interpretation for the standard quantum theory, without any possible causal claims.

•Jan 1, 2018•0 citations

The analogy of equation of rotation in complex plane with the Dirac equation, and its foundation

Mohammed I. Sanduk

The Three Wave Hypothesis (TWH) has been proposed by Horodecki in 1981. Sanduk attributed TWH to a classical kinematical model of two rolling circles in 2007. In a previous project in 2012, it is shown that the position vector of a point in a system of two rolling circles can be transformed to a complex vector under the effect of partial observation. The present work tries to develop this concept of transformation. Under this transformation, it is found that the kinematical equations of the motion of point can be transformed to equations analogise the relativistic quantum mechanics equations. Many analogies have been found and are listed in a comparison table. These analogies may sagest that both of the quantum mechanics and the special relativity are emergent, and are of the same origin.

EPJ Web of Conferences•Jan 1, 2018•3 citations

Walking Wave as a Model of Particle

Goryunov, A. V.

The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and Compton's wavelengths) and corpuscular characteristics (energy-momentum vector and the rest mass) of particle may be expressed through parameters of walking wave. By that the new view on a number concepts of physic related with wave-particle duality is suggested.

arXiv:1006.0016•Mar 16, 2010•0 citations

A kinematic model for a partially resolved dynamical system in a Euclidean plane

Mohammed I. Sanduk

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only.  The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function.

•Aug 8, 2012•1 citation

A Wave Interpretation of the Compton Effect

Ching-Chuan Su

Abstract – The Compton effect is commonly cited as a demonstration of the particle feature of light. In this investigation, we present an alternative interpretation of the Compton effect based on the postulates of de Broglie and on the wave scattering from a space- and timevarying medium, without explicit resort to the conservation of energy and momentum. PACS numbers: 13.60.Fz, 03.65.Ta, 03.75.-b 1.

•Jun 29, 2005•0 citations
The three wave hypothesis (TWH) is an attempt to relate the particle to an associated wave phenomenon. This hypothesis regards that the particle is associated with three waves: one transformed and two dispersive waves. Since the two dispersive waves are associated with a single particle, in this work we try to get a single representation for these two dispersions. The single representation exhibits similarities with those of a classical gear consisting of two perpendicular wheels. According to this similarity, the parameters of dispersive waves correspond to those of the wheels, and the transformed Compton wave corresponds to the system parameters (the combination). This similarity between the two models may possibly point to a hidden structure.
Based on de Broglie’s wave hypothesis and the covariant ether, the Three Wave Hypothesis (TWH) has been proposed and developed in the last century. In 2007, the author found that the TWH may be attributed to a kinematical classical system of two perpendicular rolling circles. In 2012, the author showed that the position vector of a point in a model of two rolling circles in plane can be transformed to a complex vector under a proposed effect of partial observation. In the present project, this concept of transformation is developed to be a lab observation concept. Under this transformation of the lab observer, it is found that velocity equation of the motion of the point is transformed to an equation analogising the relativistic quantum mechanics equation (Dirac equation). Many other analogies has been found, and are listed in a comparison table. The analogy tries to explain the entanglement within the scope of the transformation. These analogies may suggest that both quantum mechanics and special relativity are emergent, both of them are unified, and of the same origin. The similarities suggest analogies and propose questions of interpretation for the standard quantum theory, without any possible causal claims.
The Three Wave Hypothesis (TWH) has been proposed by Horodecki in 1981. Sanduk attributed TWH to a classical kinematical model of two rolling circles in 2007. In a previous project in 2012, it is shown that the position vector of a point in a system of two rolling circles can be transformed to a complex vector under the effect of partial observation. The present work tries to develop this concept of transformation. Under this transformation, it is found that the kinematical equations of the motion of point can be transformed to equations analogise the relativistic quantum mechanics equations. Many analogies have been found and are listed in a comparison table. These analogies may sagest that both of the quantum mechanics and the special relativity are emergent, and are of the same origin.
The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and Compton's wavelengths) and corpuscular characteristics (energy-momentum vector and the rest mass) of particle may be expressed through parameters of walking wave. By that the new view on a number concepts of physic related with wave-particle duality is suggested.
The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only.  The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function.