Quantum Mechanics Hypothesis of Solar System Structure: Quantum de Broglie Wavelength, LQG Similitude and Slow Bang Theory (SB)

This idea of quantifying the energy of bodies orbiting the Sun is not new. We have identified that quantization applies well if we use the true quantum number associated with the true energy state of rotating bodies. This quantum number is very high for the main bodies or planets (10~70 to 76). However, since quantum energy levels E are very high and ΔE very low we observe that bodies can in practice occupy all orbits. Thus, the current observed stable positions of the bodies are the results of the quantization and the sum of the effects of other perturbative phenomena. To find a quantum state starting with n = 1, we expressed the true integer quantum numbers as a function of that of the planet Mercury and we find an excellent correlation. However, the search for a correlation of prediction of the average orbital radius of bodies using the simple integer number n = 1, 2, 3, 4, 5, 6, 7, … is not excellent for bodies beyond the planet Pluto. Indeed, several trans-Neptunian bodies have similar integer quantum numbers, which poses a problem in the sequence of integer numbers beyond 10. Moreover, it appears that the trans-Neptunian bodies seem to be grouped for many of them according to relatively well-defined bands. The study made it possible to question the de Broglie wavelength of bodies (10~-58 to -65 m). Indeed, with the hypothesis of Planck quantities that would apply to the scale of the universe, it is difficult to conceive that de Broglie wavelengths are less than the Planck length lp. This led to an expression of the modified de Broglie wavelength λm that predicts an asymptotic lower limit value equal to πlp. This modified de Broglie wavelength makes it possible to obtain a better correlation for the prediction of the average orbital radius of bodies. Finally, this modified wavelength of de Broglie made it possible to put into perspective the concept of the quantification of space with the idea of the minimum wavelength associated with photon’s energies during the generation of the energy of the universe according to a model already presented in this review. This modified de Broglie wavelength also makes it possible to imagine that the quantification of the volume of space involves the geometry of the sphere and the cube.

De Broglie’s Velocity of Transition between Quantum Levels and the Quantum of the Magnetic Spin Moment Obtained from the Uncertainty Principle for Energy and Time

The De Broglie’s approach to the quantum theory, when combined with the conservation rule of momentum, allows one to calculate the velocity of the electron transition from a quantum state n to its neighbouring state as a function of n. The paper shows, for the case of the harmonic oscillator taken as an example, that the De Broglie’s dependence of the transition velocity on n is equal to the n-dependence of that velocity calculated with the aid of the uncertainty principle for the energy and time. In the next step the minimal distance parameter provided by the uncertainty principle is applied in calculating the magnetic moment of the electron which effectuates its orbital motion in the magnetic field. This application gives readily the electron spin magnetic moment as well as the quantum of the magnetic flux known in superconductors as its result.

SUPER NONLINEAR TOTAL ENERGY OF A PARTICLE AND THE THEORY OF DE BROGLIE WAVE

By using Laurent series, the veloci ty (～c) is expanded and then the total energy expression of a particle moving w ith high velocity is obtained. The total energy contains two parts: the rest e ne rgy and the kinetic energy. Also in this paper the theory of the de Broglie wave from the relation of the energy_momentum is obtained in which the phase velocit y is still less than the velocity of light c .

Theoretical Evidence for Wave Nature of Micro Particle and New Theory of Its Collective Motion in Material

Since a material is composed of micro particles, investigating behavior of those particles is essentially dominant for materials science. The diffusivity of diffusion equation is relevant to not only a collective motion of micro particles but also a motion of single particle. An elementary process of diffusion was thus theoretically investigated in a local space and time. As a result, the investigation concluded that the wave nature of micro particle results from denying the mathematical density theorem of a real time in the Newton mechanics. In other words, the basic theory of quantum mechanics is established in accordance with the cause-and-effect relationship in the Newton mechanics, for the first time, regardless of the de Broglie hypothesis. In relation to the collective motion of micro particles, the new diffusion theory was also reasonably established using the universal expression of diffusivity obtained here. In the present paper, the new findings indispensable for the fundamental knowledge in physics are thus systematically discussed in accordance with the theoretical frame in physics.

On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity

In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.

Physical interpretation of Planck's constant based on the Maxwell theory

The discovery of the Planck relation is generally regarded as the starting point of quantum physics.Planck＇s constant h is now regarded as one of the most important universal constants.The physical nature of h,however,has not been well understood.It was originally suggested as a fitting constant to explain the black-body radiation.Although Planck had proposed a theoretical justification of h,he was never satisfied with that.To solve this outstanding problem,we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet.We find that the energy of the wave packet is indeed proportional to its oscillation frequency.This allows us to derive the value of Planck＇s constant.Furthermore,we show that the emission and transmission of a photon follows the all-or-none principle.The ＂strength＂ of the wave packet can be characterized by ζ,which represents the integrated strength of the vector potential along a transverse axis.We reason that ζ should have a fixed cut-off value for all photons.Our results suggest that a wave packet can behave like a particle.This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck＇s law.

The Real Reason Why the Electron’s Bare g-Factor Is 2 Times Classical

When analyzing an Electron’s orbit’s and movements, a “classical” bare g-factor of “1” must be used, but when analyzing just the Electron itself, a bare g-factor and gyromagnetic ratio of twice the “classical” value is needed to fit reality. Nobody has fully explained this yet. By examining the electromagnetic wave nature of the electron, it is possible to show a simple reason why its bare g-factor must be 2, without resorting to superluminal velocities or dismissing it as mystically intrinsic. A simple charged electromagnetic wave loop (CEWL) model of the electron that maintains the same electromagnetic wave nature as the high-energy photons from which electron-positron pairs form, will have exactly half of its energy in the form of magnetic energy who’s field lines are perpendicular to the direction of the charge rotation, which leads to the conclusion that only half of the electron’s electromagnetic mass is rotational mass, from which it is easy to calculate a bare g-factor of 2 using Feynman’s equation for the electron’s g-factor.

A Topological Transformation of Quantum Dynamics

In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.

Primary Assumptions and Guidance Laws in Wave Mechanics

In an article written by Louis de Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg and Born Standard Quantum Mechanics (SQM) was pointed out in the renunciation to describe “a permanent localization in space, and therefore a well-defined trajectory” for any moving particle. This challenge is taken up in the present paper, showing that de Broglie’s Primary Assumption p=hk, predicting the wave-particle duality, does also allow to obtain from the energy-dependent form of the Schrödinger and/or Klein-Gordon equations the Guidance Laws piloting particles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise—both in SQM and in the Bohmian approach—to probabilistic descriptions, overshadowing the role of de Broglie’s matter waves in physical space.

The Dynamics of Wave-Particle Duality

Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. In the case of Wave Mechanics, de Broglie’s merging of Maupertuis’s and Fermat’s principles (see Section 3) provides, without resorting to the probability-based guidance-laws and flow-lines of the Bohmian theory, the simple law addressing particles along the Helmholtz rays of the relevant matter waves. The purpose of the present research was to derive the exact Hamiltonian ray-trajectory systems concerning, respectively, classical electromagnetic waves, non-relativistic matter waves and relativistic matter waves. We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to “dances a wave-mechanical dance” around its classical trajectory, to which it reduces when the ray-coupling is neglected. Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability. We finally compared our exact dynamical approach, running as close as possible to Classical Mechanics, with the hydrodynamic Bohmian theory, based on fluid-like “guidance laws”.

On the Quantization of Time, Space and Gravity

We combine the de Broglie Matter Wave Equation with the Heisenberg Uncertainty Principle to derive an equation for time as a wave. This happens to be the first time that these two statements have been combined in this manner to derive an equation for time. The result is astounding. Time turns out to be a minuscule blob of quantum electromagnetic energy in perpetual angular momentum. From this time equation, we derive an equation for space which turns out to also predict a string (like the string of string theory). We then combine the time equation with the space equation to derive an equation for the inverse of quantum gravity which is also surprisingly electromagnetic in nature. This last statement implies that space is multidimensional and gravity in multidimensional space is not quantized, but its inverse (which is single-dimensional) is.

A Brief Note on the Clock-Hypothesis

The clock-hypothesis is the fundamental assumption in the theories of relativity that duration, measured by clocks, is proportionate to the length of their respective world lines. Over the years, there have been contributions both, theoretical and experimental in nature, either confirming or questioning this hypothesis. We give an elementary model of two classes of clocks, which turn out to be relativistic clocks, and by doing so also offer a basis to see the limitations of the clock-hypothesis. At the same time, we find support for a hypothesis of L. de Broglie, regarding the existence of an internal clock of electrons. Our aim is to give a precise, yet accessible account of the subject.

Phase Velocity and Rest Energy of Schrödinger Equation Seen from Neutrino Oscillations

The phase velocity is discussed using de Broglie relations and Schrödinger equation. We argue that in non-relativistic quantum mechanics the Hamiltonian should be added by a rest-energy term when Schrödinger equation is used to study the interference between particles of different masses. From neutrino oscillation experiments, we find that the phase velocity can be related to a measurable quantity (the flavor transition probability), therefore, the phase factor originated from the rest energy can’t be omitted. Correspondingly, the energy in de Broglie relations should always be total energy rather than kinetic energy, contrary to some textbooks of quantum mechanics.