From a Newtonian-Maxwellian solution for a perturbed vacuum with a physical structure constructed based on pivotal experimental observations, we have achieved a general scheme for the formation of basic material particles. A basic particle, which may be e.g. an electron, is composed of a tiny free aether-pole (a bare charge) and the mechanical wave disturbances -- identifying with electromagnetic waves -- generated by it in the medium. When in motion, as a result of a first kind source effect, this particle wave exhibits all of wave and dynamic properties known for a de Broglie wave, and is here called a Newton- de Broglie (NdB) particle wave. In a confined space, the Newtonian solution for the NdB particle wave is equivalent to that given by Schrodinger's quantum mechanics. Through this general scheme we have accomplished a basic task of the unification of the classical- and the quantum- mechanics, both in terms of the deduction of the latter from the former, and the convergence of the latter into the former at high velocities. Through completing the task, we unfold the origins of a series of phenomena including the electromagnetic waves, the electromagnetic radiation and absorption, atomic and thermal excitations, the inertial mass, the Schrodinger's wavefunction and de Broglie wave, the Heisenberg's uncertainty relation, the de Broglie relations, the simultaneous existence of electron and positron or generally of particles and their anti-particles, the (rest) mass-energy equivalence relation, etc. The general scheme facilitates also a Theory of Relative Motion which we present in a separate paper, II; a series of followed studies are planned. (An original report of the scheme with a Preface remarking on the changes in later publications.)
From a Newtonian-Maxwellian solution for a perturbed vacuum with a physical structure constructed based on pivotal experimental observations, we have achieved a general scheme for the formation of basic material particles. A basic particle, which may be e.g. an electron, is composed of a tiny free aether-pole (a bare charge) and the mechanical wave disturbances -- identifying with electromagnetic waves -- generated by it in the medium. When in motion, as a result of a first kind source effect, this particle wave exhibits all of wave and dynamic properties known for a de Broglie wave, and is here called a Newton- de Broglie (NdB) particle wave. In a confined space, the Newtonian solution for the NdB particle wave is equivalent to that given by Schrodinger's quantum mechanics. Through this general scheme we have accomplished a basic task of the unification of the classical- and the quantum- mechanics, both in terms of the deduction of the latter from the former, and the convergence of the latter into the former at high velocities. Through completing the task, we unfold the origins of a series of phenomena including the electromagnetic waves, the electromagnetic radiation and absorption, atomic and thermal excitations, the inertial mass, the Schrodinger's wavefunction and de Broglie wave, the Heisenberg's uncertainty relation, the de Broglie relations, the simultaneous existence of electron and positron or generally of particles and their anti-particles, the (rest) mass-energy equivalence relation, etc. The general scheme facilitates also a Theory of Relative Motion which we present in a separate paper, II; a series of followed studies are planned. (An original report of the scheme with a Preface remarking on the changes in later publications.)
We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field V in a susceptible vacuum. The waves are Doppler-displaced upon the source motion, and superpose into a total, traveling- and in turn a standing- beat wave, or de Broglie phase wave, described by a corresponding total classical wave equation. By back-substitution of the explicitly known total, standing beat wave function and upon appropriate reductions at classic-velocity limit, we separate out from the total a component wave equation describing the kinetic motion of particle, which is equivalent to the Schrödinger equation. The Schrödinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit.
Since the interest in the quantum phenomena started, there have been two main approaches to the quantum theory, the first approach investigates the motion of a wave-particle object by assuming the wave has the characteristics of a moving particle, momentum and energy, this approach was developed by physicists Max Planck, Albert Einstein, and others. The second approach investigates the motion of a particle-wave object by assuming the particle has the characteristics of a moving wave, wavelength, wave vector, and frequency, this approach was developed by physicists De Broglie, Schrodinger and others which led to the presence of quantum mechanics. This article focuses on the second approach and merging it with classical mechanics. An early mathematical formulation for the quantum theory was proposed by De Broglie’s relations and later on, another formulation was given by Schrodinger’s equation. A successful attempt to bridge the gap between classical mechanics with quantum theory implemented via a mathematical derivation for De Broglie’s relations and Schrodinger formulation, The derivation process overcame a main obstacle was the convergence of the deterministic nature of classical mechanics with the probabilistic nature of the quantum theory by adopting an innovative method based upon replacing constant values in a deterministic relation with probabilistic variables in the same relation, and this led to switch the relation from deterministic representation to probabilistic representation. Both classical and quantum explanation are given for the deduced formulas. An energy approach is instrumented. Since classical mechanics formulas are not sufficient to explain the quantum phenomena, a new concept of complementary energy introduced in order to connect the parameters of a moving particle with the parameters of an associated wave, the value of the complementary energy for each particle adjusted the total energy equation of N moving particles without changing the magnitude of the total energy of a system of N particles. In special cases, the value of the complementary energy for some particles equals the value of the total energy for the particles. The derivation process indicates that complementary energy corresponds to the potential energy on the surface of the material which prevents the particles to escape from the boundary of the matter to the outer space and maintains its coherence, complementary energy concept also manifest the impact of the moving particles on a single particle due to the energy conveyed during direct contact in case of collision or by the remote influence through an existing field in the space, so it represents an energy of dual nature for both matter and radiation wave combined. The complementary energy is not introduced as mathematical assumption in order to manipulate the total energy equation, it’s actually exists in the total energy equation and its validity has not been applied before. A general format for any potential energy is obtained regardless the nature of field it represents (a universal format for potential energy) that is by using mathematical manipulation for the equation of total energy of N moving particles. The derivation process led to a particle-wave formula. The substitution into the particle-wave formula with the speed of light, De Broglie’s relations, revealed. Some additional applications for the particle-wave formula are suggested, also as a well known energy quantization formula obtained by applying all of De Broglie’s relation, a general energy, and speed formulas resulting during the derivation process. Matching time independent equation called Schrodinger’s amplitude equation with classical mechanics formulation demonstrated by deducing both the wave function and the magnitude of the wave vector from the classical formulation after converting it to probabilistic formulation. A dedicated section for wave function solutions for Schrodinger’s time dependent equation was given in terms of the wave functions and the magnitude of the wave vectors obtained from the matching process of Schrodinger’s amplitude equation with classical mechanics.
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what the wave function represents. Besides the statistical meaning suggested by the Copenhagen interpretation, does the wave function represent any physical motion? For photon, we know it is an electro-magnetic wave. But what about particles with rest mass, such as an electron? To investigate the physical nature of matter wave, we propose that: (1) Like the photon, a particle is an excitation wave of a real physical field. (2) Different types of particles are different excitation modes of the same field. Based on this thinking, we show that the concept of quantum mechanics can be a natural extension of classical mechanics. By critically analyzing the transition from classical physics to quantum physics, we found a new physical meaning for the quantum wave function. This work suggests that various quantum wave equations, including the Klein-Gordon equation, the Dirac equation and the Schrodinger equation, could have a common base relating to the Basic Wave Equation of the matter wave. This work has some interesting implications. It suggests a possible way to explain the origin of visible matters and dark matters in our universe.
This article is a continuation of Part(I) to demonstrate more aspects for a successful merge of classical mechanics to the quantum theory. The article starts first with the deduction of the general form of the complimentary energy, next a robust firm mathematical proof is given indicates that the complimentary energy has a wave nature and it is a potential energy, then the radiation condition has been determined, a vector formula expresses the corresponding force was deduced and this force was called adhesion force. A mathematical convergence process has proved the duality of the electromagnetic wave parameters and particle parameters, which results in the existence of a “wave-particle” object. While finding the relationship between the electromagnetic wave parameters and particle parameters, a mathematical relationship was found indicating that not every moving charged mass generates a magnetic field. This relationship for the mass was linked to the effective mass tensor, The geometric representation of the constant energy surface and its relationship to the energy levels of both the orbital model (Bohr model) and the cloud model for different geometric 3D shapes were investigated as a sample of the possible geometric interpretations of the energy equation, that is by employing the triangle method, it is possible to create a geometric representation of the constant energy surfaces. The relation between the energy levels, quantum numbers, and band width is represented geometrically. As a result of proving the relationship between the motion of an electromagnetic wave and the motion of a particle associated with the wave, two new, unprecedented mathematical formulas were developed. The first formula specifies a moving charged mass and its relationship to the resulting wavelength. Thus, the radius of the charged mass is obtained in terms of its wavelength and mass density. The second formula specifies the kinetic energy of a photon. The grand potentials are the potential energy of the Newton’s Law of Universal Gravitation, Coulomb’s Law, and Inverse Square Law of Electromagnetic Waves Intensity. From the potential energy of Newton’s law of universal gravitation, the wavelength of the gravitational wave, as well as the wavelength of quantum gravity were deduced. A mathematical relationship was then deduced that determines the lengths of the functions of conic sections, and in particular the length of perimeter of ellipses. From the potential energy of Coulomb’s law of attraction, a mathematical formulation of the energy levels in general for any atom of an element was obtained. This mathematical formulation was compared with the results obtained by Bohr and Schrödinger for the hydrogen atom. As for the inverse square law of electromagnetic radiation intensity, several innovative mathematical equations have been deduced that link different parameters together. Following the contents of this article requires to be quite familiar with the contents of the first part with the same title, as well as a complete understanding of the concepts of intermediate parameters derived and used in the various equations. Otherwise, it will be extremely difficult to follow the contents of this article.
Abstract We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations of the particle path in Euclidean space are derived. The motion is marked by the relations basic for quantum mechanics: E=hν and Mv=h/λ (here, λ is the amplitude of spatial oscillations of the particle along the trajectory, i.e., the interval at which the velocity of the particle is periodically altered from v to 0 and then from 0 to v; ν is the frequency of these oscillations). Analysis is performed on the transition to wave mechanics where λ manifests itself as the de Broglie wavelength and ν is the distinctive frequency of the "particle-wave". A prerequisite for the wave solution to be Lorentz-invariant is treated. A hypothesis for a plausible hydrodynamic description of the relativistic particle motion is covered.