On the Fine Structure and the Other Coupling Constants at the Planck Scale

It is shown that the fine structure constant at Planck times tends to one as well as those of the weak and strong interactions. This results by constraining them at the Planck force. That seems to provide interesting new results which confirm that at the beginning of space time (Planck scale) all fundamental forces converge to the same unit value.

Determination of hyperfine structure constants of 5D_(5/2) and 7S_(1/2) states of rubidium in cascade atomic system

We present a method to precisely determine the hyperfine structure constants of the rubidium 5D（5/2） and 7S（1/2） states in a cascade atomic system. The probe laser is coupled to the 5S（1/2）→ 5P（3/2） hyperfine transition, while the coupling laser is scanned over the 5P（3/2）→ 5D（5/2）（7S（1/2）） transition. The high-resolution double-resonance optical pumping spectra are obtained with two counter-propagating laser beams acting on rubidium vapor. The hyperfine splitting structures are accurately measured by an optical frequency ruler based on the acousto-optic modulator, thus, the magnetic dipole hyperfine coupling constant A and quadrupole coupling constant B are determined. It is of great significance for the atomic hyperfine structure and fundamental physics research.

TOPOLOGICAL STRUCTURE OF RENORM ALIZATION CONSTANTS I N QUANTUM FIELD THEORY AT SHORT DISTANCE KUNMING COLLABRATION OF MULTIHADRON DYNAMIOS

The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.

An Electron Model Based on the Fine Structure Constant

In previous publications, the author has proposed a model of the electron’s internal structure, wherein a positively-charged negative mass outer shell and a negatively-charged positive mass central core are proposed to resolve the electron’s charge and mass inconsistencies. That model is modified in this document by assuming the electron’s radius is exactly equal to the classical electron radius. The attributes of the internal components of the electron’s structure have been recalculated accordingly. The shape of the electron is also predicted, and found to be slightly aspherical on the order of an oblate ellipsoid. This shape is attributed to centrifugal force and compliant outer shell material. It is interesting to note that all of the electron’s attributes, both external and internal, with the exception of mass and angular moment, are functions of the fine structure constant a, and can be calculated from just three additional constants: electron mass, Planck’s constant, and speed of light. In particular, the ratios of the outer shell charge and mass to the electron charge and mass, respectively, are 3/2a. The ratios of the central core charge and mass to the electron charge and mass, respectively, are 1-(3/2a). Attributes of the electron are compared with those of the muon. Charge and spin angular momentum are the same, while mass, magnetic moment, and radius appear to be related by the fine structure constant. The mass of the electron outer shell is nearly equal to the mass of the muon. The muon internal structure can be modeled exactly the same as for the electron, with exactly the same attribute relationships.

A Conceptual Model of Our Universe Derived from the Fine Structure Constant (α)

The Fine Structure Constant (α) is a dimensionless value that guides much of quantum physics but with no scientific insight into why this specific number. The number defines the coupling constant for the strength of the electromagnetic force and is precisely tuned to make our universe functional. This study introduces a novel approach to understanding a conceptual model for how this critical number is part of a larger design rather than a random accident of nature. The Fine Structure Constant (FSC) model employs a Python program to calculate n-dimensional property sets for prime number universes where α equals the whole number values 137 and 139, representing twin prime universes without a fractional constant. Each property is defined by theoretical prime number sets that represent focal points of matter and wave energy in their respective universes. This work aims to determine if these prime number sets can reproduce the observed α value, giving it a definable structure. The result of the FSC model produces a α value equal to 137.036, an almost exact match. Furthermore, the model indicates that other twin prime pairs also have a role in our functional universe, providing a hierarchy for atomic orbital energy levels and alignment with the principal and azimuthal quantum numbers. In addition, it construes stable matter as property sets with the highest ratio of twin prime elements. These results provide a new perspective on a mathematical structure that shapes our universe and, if valid, has the structural complexity to guide future research.

Calculation of <i>G</i>Gravity Constant from the Mass and Electron Charge, and Fine Structure Constant

This study proposes, from the theoretical point of view, the calculation of the gravitational constant G, made starting from the charge and the electron mass, taking the constant of the Fine Structure into examination. In the empty space, couples of virtual positron electrons dematerialize, giving virtual photon origin. They, at their time, will become electrons, positrons and so on. These transformations are made keeping the board of their “amount of movement” and when they meet the matter, these couples come, reissued depending on the field and on the matter mass. The matter is the change of the trend of their gyromagnetic movement relationship which puts under pressure. In presence of two masses, this gyromagnetic movement relationship is already partially oriented towards the other mass. From here a force is established between these two masses that give as calculated constant equal to 6.678532. This value of G, obtained leaving from the charge and the electron mass, is very near the experimental values estimated in these last decades regard the value of the gravitational constant of G.

Evaluation of the Fine Structure Constant

An equation is given for analytically defining the value of the fine structure constant, whose derivation follows two main steps, relative to the generation of electric charges and to the polarizability of vacuum due to virtual dipoles. The obtained value matches the experimental one by a factor lower than the relative standard uncertainty produced by the National Institute of Standards and Technology (NIST).

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

Fundamental Harmonic Power Laws Relating the Frequency Equivalents of the Electron, Bohr Radius, Rydberg Constant with the Fine Structure, Planck’s Constant, 2 and π

We evaluate three of the quantum constants of hydrogen, the electron, e-, the Bohr radius, a0, and the Rydberg constants, , as natural unit frequency equivalents, v. This is equivalent to Planck’s constant, h, the speed of light, c, and the electron charge, e, all scaled to 1 similar in concept to the Hartree atomic, and Planck units. These frequency ratios are analyzed as fundamental coupling constants. We recognize that the ratio of the product of 8π2, the ve- times the vR divided by va0 squared equals 1. This is a power law defining Planck’s constant in a dimensionless domain as 1. We also find that all of the possible dimensionless and dimensioned ratios correspond to other constants or classic relationships, and are systematically inter-related by multiple power laws to the fine structure constant, α;and the geometric factors 2, and π. One is related to an angular momentum scaled by Planck’s constant, and another is the kinetic energy law. There are harmonic sinusoidal relationships based on 2π circle geometry. In the dimensionless domain, α is equivalent to the free space constant of permeability, and its reciprocal to permittivity. If any two quanta are known, all of the others can be derived within power laws. This demonstrates that 8π2 represents the logical geometric conversion factor that links the Euclid geometric factors/three dimensional space, and the quantum domain. We conclude that the relative scale and organization of many of the fundamental constants even beyond hydrogen are related to a unified power law system defined by only three physical quanta of ve-, vR, and va0.

Fine Structure Constant Model Demonstrates the Electron Elementary Charge of Having an Intrinsic Manifold

Using our recently published electron’s charge electromagnetic flux manifold fiber model of the electron, described by analytical method and numerical simulations, we show how the fine structure constant is embedded as a geometrical proportionality constant in three dimensional space of its charge manifold and how this dictates the first QED term one-loop contribution of its anomalous magnetic moment making for the first time a connection of its intrinsic characteristics with physical geometrical dimensions and therefore demonstrating that the physical electron charge cannot be dimensionless. We show that the fine structure constant (FSC) α, and anomalous magnetic moment αμ of the electron is related to the sphericity of its charge distribution which is not perfectly spherical and thus has a shape, and therefore its self-confined charge possesses measurable physical dimensions. We also explain why these are not yet able to be measured by past and current experiments and how possible we could succeed.

Exceedingly Small Quantum of Time Kshana Explains the Structure of an Electron

In this study, an effort is made to find the attributes of an electron based on Maharishi Vyasa’s definition of kshana or moment. Kshana or moment is a very small quanta of time defined by Maharishi Vyasa. It is the time taken by an elementary particle to change the direction from east to north. It is found that the value of a kshana in the case of pair production is approximately 2 × 10-21 sec, and the radius of the spinning electron or positron is equal to the reduced Compton wavelength. The mass of the electron is equal to the codata recommended value of electron mass and time required in pair production is about four kshanas equal to spinning period of an electron. During validation, in case of the photoelectric effect, spectral series of hydrogen atoms, Compton scattering, and the statistical concept of motion of electron, the value of the number of kshanas in a second is the same as that found in pair production.

A New Theory on the Origin and Nature of the Fine Structure Constant

The nature and the origin of the fine structure are described. Based on the vortex model and hydrodynamics, a comprehensible interpretation of the fine structure constant is developed. The vacuum considered to have superfluid characteristics and elementary particles such as the electron and Hydrogen molecule are irrotational vortices of this superfluid. In such a vortex, the angular rotation ω is maintained, and the larger the radius, the slower the rotational speed. The fine structure value is derived from the ratio of the rotational speed of the boundaries of the vortex to the speed of the vortex eye in its center. Since the angular rotation is constant, the same value was derived from the ratio between the radius of the constant vortex core and the radius of the hall vortex. Therefore, the constancy of alpha is an expression of the constancy relation in the vortex structure.

Highly Accurate Relations between the Fine Structure Constant and Particle Masses, with Application to Its Cosmological Measurement

Highly accurate algebraic relations between the fine structure constant a and a wide range of particle masses are given, ranging from Δa/a = (2.1 ±0.1)×10-7 to Δa/a = (-2.7 ±0.3 ±0.6)×10-8, and with a very large standard deviation, ranging to Δa/a = -5.5×10-9. The analysis is based on empirical relations that exist among some particle masses, and also on several theoretical assumptions, of which the most significant is that the electromagnetic contribution to the electron’s mass is finite, and given by f ameb, where f is a dimensionless parameter that is shown to be equal to 1.032409810 (63), and where meb is the electron’s “bare mass.” The relations for a and f are homogeneous degree zero in the particle masses. The relations for f in terms of particle masses are found by trial and error. A quadratic equation is given relating a to f and me/mp. This equation is used in the application to cosmological measurements of a, and , where it is shown that, to a few percent accuracy, δa/a ≈ -δμ/μ. This relation can serve to test the validity of measurements of a and μ.

Electron Shape Calculated for the Dual-Charge Dual-Mass Model

A model for the internal structure of the electron using classical physics equations has been previously published by the author. The model employs both positive and negative charges and positive and negative masses. The internal attributes of the electron structure were calculated for both ring and spherical shapes. Further examination of the model reveals an instability for the ring shape. The spherical shape appears to be stable, but relies on tensile or compressive forces of the electron material for stability. The model is modified in this document to eliminate the dependency on material forces. Uniform stability is provided solely by balancing electrical and centrifugal forces. This stability is achieved by slightly elongating the sphere along the spin axis to create a prolate ellipsoid. The semi-major axis of the ellipsoid is the spin axis of the electron, and is calculated to be 1.20% longer than the semi-minor axis, which is the radius of the equator. Although the shape deviates slightly from a perfect sphere, the electric dipole moment is zero. In the author’s previously published document, the attributes of the internal components of the electron, such as charge and mass, were calculated and expressed as ratios to the classically measured values for the composite electron. It is interesting to note that all of these ratios are nearly the same as the inverse of the Fine Structure Constant, with differences of less than 15%. The electron model assumed that the outer surface charge was fixed and uniform. By allowing the charge to be mobile and the shape to have a particular ellipticity, it is shown that the calculated charge and mass ratios for the model can be exactly equal to the Fine Structure Constant and the Constant plus one. The electron radius predicted by the model is 15% greater than the Classical Electron Radius.

How to Achieve a Warp Drive

In this paper, we delve into the intrinsic nature of mass and gravity, as per the amplitude modulation interpretation of the quantum theory. We explore the idea that the elementary constituent is an electromagnetic configuration that interacts with the quantum field, leading to the emergence of inertia and gravity as a reaction to the exchange with the quantum field. While these two phenomena have a common origin, they are distinct. Our proposal suggests manipulating the connection between the quantum field and the particle using high-frequency electromagnetic fields, thereby making a warp drive possible.

On the Charges and Currents in the Quantum Field Theory

This paper is concerned with the determination of currents and charges in hypercomplex extensions of the Feynman-Dyson derivation of the Maxwell-Faraday equations. We analyze the appearance of charges and currents in non-Abelian versions of that approach: SU(2), SU(3) and G2. The structure constants of G2 Lie algebra are computed explicitly. Finally, we suggest a seven-dimensional treatment of color.

LIE GROUPS ADMITTED BY AUTONOMOUSSYSTEM WITH GIVEN STRUCTURECONSTANTS

This paper study the Lie groups admitted by differential equations. It is proved in this paper that for any n-th order autonomous system and any given structure constants Ckij, the system admits n-1 local one parameter Lie groups, and the 'non-trivial' structure constants of the Lie module generated by infinitesimal generators of these Lie groups are just Ckij. This result shows that integrable system may admit unsolvable local Lie group.

Application of Lambert <i>W</i>Function to Planck Spectral Radiance Frequencies

Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert W function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert W function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.

Structural,electronic and elastic properties of YCu from first principles

The structural, electronic and elastic properties of YCu compound in the B2 （CsCl） phase were investigated using the density functional theory （DFT） within the generalized gradient approximation （GGA）. The electronic density of states （DOS） obtained in this way accorded weU with the results of a recent study utilizing the full-potential linearized augmented plane wave （FLAPW） method. We also found that the density of d-states at the Fermi energy was low. The calculated equilibrium properties such as lattice constant, bulk modulus and its first derivative, and the elastic constants were in good agreement with experimental and theoretical results.

A Realistic Interpretation of Quantum Wavefunctions as Temperature Dependent Vacuum Polarization Waves

We discuss in this paper a novel interpretation of Born rule as an approximated thermodynamic law which emerges from the interaction of a quantum system with a non-stationary thermal bath associated to vacuum fluctuations induced by external environment radiation. In particular we assume that vacuum polarization is a real non relativistic phenomena caused by hidden vacuum charge oscillations which diffuses heat energy in a dispersive and dissipative dielectric medium with a temperature dependent speed of propagation. We propose a model which couples vacuum wavefunctions to vacuum charge fluctuations and we deduce a temperature dependent running fine structure constant function proportional, at first approximation, to the squared of the effective electron charge and compatible with known experimental data. We interpret the vacuum symmetry breaking energy fluctuations induced in scattering experiments of particle physics and in laser assisted nuclear reactions as thermal quasi-monochromatic beams produced by the decay of hidden non equilibrium massive photons propagating with a variable light speed. We suggest, exploiting an old analogy between plasmons and pseudo Goldstone bosons, to interpret heat diffusion of this non relativistic polarized vacuum as a real De Broglie electromagnetic scalar wave associated to the radiation emitted by the hidden massive photons with acceleration proportional to vacuum Unruh like temperature. We predict a temperature dependent deviation from Coulomb law and a generalized dispersive law of these hidden unstable photons that could be revealed as not stationary coloured noise in experiments on anomalous heat diffusions associated to the decay of unstable accelerated pairs produced in nuclear physics experiments. We discuss then how our proposal of a temperature dependent non relativistic vacuum polarization might be applied to deduce a dynamic generalization of Born rule based on a realistic interpretation of quantum wavefunctions as averaged electromagnetic waves of hidden massive photons. Finally we suggest to test our time asymmetric model looking for very fast oscillating polarization thermal waves emitted during the not instantaneous wavefunction collapse and revealed as not stationary bulk heating effects in experiments on accelerated conductors and nanoconductors.