A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for whic...A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.展开更多
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 su...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.展开更多
This study proposes, from the theoretical point of view, the calculation of the gravitational constant <em>G</em>, made starting from the charge and the electron mass, taking the constant of the Fine Struc...This study proposes, from the theoretical point of view, the calculation of the gravitational constant <em>G</em>, 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 <em>G</em>, 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 <em>G</em>.展开更多
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 ...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).展开更多
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 ...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.展开更多
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 ...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 α<sub>μ</sub> 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.展开更多
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 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.展开更多
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<sup>-7</sup> to &Del...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<sup>-7</sup> to Δa/a = (-2.7 ±0.3 ±0.6)×10<sup>-8</sup>, and with a very large standard deviation, ranging to Δa/a = -5.5×10<sup>-9</sup>. 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 am<sub>eb</sub>, where f is a dimensionless parameter that is shown to be equal to 1.032409810 (63), and where meb</sub> 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 m<sub>e</sub>/m<sub>p</sub>. 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.展开更多
Random fluctuations of turbulence bring random fluctuations of the refractive index, making the atmosphere a random fluctuation medium that destroys the coherence of light-waves. Research in atmospheric turbulence is ...Random fluctuations of turbulence bring random fluctuations of the refractive index, making the atmosphere a random fluctuation medium that destroys the coherence of light-waves. Research in atmospheric turbulence is actually the investigation of the atmospheric refractive index. The atmospheric structure constant of refractive index, C n 2 , is an important parameter denoting atmospheric turbulence. In this paper, C n 2 is measured during the day and at night and in all four seasons using a high sensitivity micro-thermal meter QHTP-2. The vertical profile of C n 2 in Hefei (0-30 km) is investigated by the analysis of experimental data. The average profile of C n 2 in Hefei exhibits conspicuous day and night differences with increased altitude. The distribution of log(C n 2 ) is nearly normal and has conspicuous seasonal differences.展开更多
We evaluate three of the quantum constants of hydrogen, the electron, e<sup>-</sup>, the Bohr radius, a<sub>0</sub>, and the Rydberg constants, , as natural unit frequency equivalents, v. This ...We evaluate three of the quantum constants of hydrogen, the electron, e<sup>-</sup>, the Bohr radius, a<sub>0</sub>, 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 8π<sup>2</sup>, the v<sub>e</sub><sub>-</sub> times the v<sub>R</sub> divided by v<sub>a</sub><sub>0</sub> 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 v<sub>e</sub><sub>-</sub>, v<sub>R</sub>, and v<sub>a</sub><sub>0</sub>.展开更多
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...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.展开更多
The possible variation of the electromagnetic fine structure constant, αe, at cosmological scales has aroused great interest in recent years. Strongly lensed gravitational waves（GWs） and their electromagnetic count...The possible variation of the electromagnetic fine structure constant, αe, at cosmological scales has aroused great interest in recent years. Strongly lensed gravitational waves（GWs） and their electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of a photon can be modified,whereas the speed of a GW is the same as predicted by general relativity, and they both propagate in a flat FriedmanRobertson-Walker universe, we investigated the difference in time delays of the images and derived the upper bound of the variation of αe. For a typical lensing system in the standard cosmological models, we obtained B cosθ 1.85×10^（-5）,where B is the dipolar amplitude and θ is the angle between observation and the preferred direction. Our result is consistent with the most up-to-date observations on αe. In addition, the observations of strongly lensed GWs and their electromagnetic counterparts could be used to test which types of alternative theories of gravity can account for the variation of α_e.展开更多
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 ...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.展开更多
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 Minkowsk...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.展开更多
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 ...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<sup>-21</sup> 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.展开更多
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 c...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.展开更多
The Fine Structure Constant (eFSC) Model attempts to give a classical definition to a magical number that underlies much of quantum physics. The Fine Structure Constant (α) value equal to 137.03599206 represents a di...The Fine Structure Constant (eFSC) Model attempts to give a classical definition to a magical number that underlies much of quantum physics. The Fine Structure Constant (α) value equal to 137.03599206 represents a dimensionless constant that characterizes the strength of the electromagnetic (EM) interaction between subatomic charged particles. Python-generated property counts for the twin prime force F{139/137} show that the adjusted ratio gives a value of α = 137.036. This implies a mathematical framework underlying this constant is based on twin prime numbers and set theory. This study attempts to demonstrate a proof of concept that a hierarchy of fractional twin prime (αII) forces replicates the quantum nature of the universe and is aligned with the Standard Model of Particle Physics. An expanded eFSC Model demonstrates that twin prime forces and their property sets are mathematically viable substitutes for nuclear reactions, as demonstrated for the Beta-minus decay of neutrons into protons. Most significantly, the positive and negative prime numbers define these nuclear reactants and products as positive or negatively charged ions. Furthermore, the eFSC Model provides new insights regarding the hierarchy of EM forces underlying the quantum nature of the universe.展开更多
This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139...This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.展开更多
Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among...Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation can be explained numerically in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. Furthermore, every equation can also be explained in terms of the Avogadro number and the number of electrons at 1 C. We show that every equation can be described in terms of the Planck constant. Then, the ratio of the gravitational force to the electric force can be uniquely determined with the assumption of minimum mass. In this report, we describe the algorithms used to explain these equations in detail. Thus, there are no dimension mismatch problems.展开更多
This paper presents the development of a conceptual model of the universe,grounded in the Fine Structure Constant(α≈137.036).The Extended Fine Structure Constant(eFSC)Model exploresαas a function of twin prime mi-c...This paper presents the development of a conceptual model of the universe,grounded in the Fine Structure Constant(α≈137.036).The Extended Fine Structure Constant(eFSC)Model exploresαas a function of twin prime mi-croverses(U{137},whereα=137,and U{139},whereα=139),each defined by n-dimensional sets of prime numbers.Property counts for U{137}and U{139}are used in a modified Difference over Sum(DoS)calculation to ap-proximate the fractional component ofα,yielding a Relative Electromagnetic Force(EMF)value ofαII=0.036.Applying this method to additional twin prime pairs produces a distribution of EMF values that reflect the energy pro-files of known Standard Model forces,identifying the strong force as a triad of overlapping EM interactions,and linking the weak force to particle transitions involving neutrons,protons,electrons,and neutrinos.The model provides a conceptual framework for investigating the Higgs mechanism,quantum or-bital structures,quantum entanglement,and potential explanations for grav-ity,dark matter,dark energy,and time dilation.While not intended to supplant any existing physics,the eFSC Model offers a novel,prime-number-based archi-tecture for interpreting the quantum universe through a classical lens.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10471139
文摘A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.
文摘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.
文摘This study proposes, from the theoretical point of view, the calculation of the gravitational constant <em>G</em>, 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 <em>G</em>, 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 <em>G</em>.
文摘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).
文摘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.
文摘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 α<sub>μ</sub> 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.
文摘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.
文摘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<sup>-7</sup> to Δa/a = (-2.7 ±0.3 ±0.6)×10<sup>-8</sup>, and with a very large standard deviation, ranging to Δa/a = -5.5×10<sup>-9</sup>. 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 am<sub>eb</sub>, where f is a dimensionless parameter that is shown to be equal to 1.032409810 (63), and where meb</sub> 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 m<sub>e</sub>/m<sub>p</sub>. 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.
基金supported by the National High Technology Research and Development Program of China (GrantNo. 2011AA8061007)
文摘Random fluctuations of turbulence bring random fluctuations of the refractive index, making the atmosphere a random fluctuation medium that destroys the coherence of light-waves. Research in atmospheric turbulence is actually the investigation of the atmospheric refractive index. The atmospheric structure constant of refractive index, C n 2 , is an important parameter denoting atmospheric turbulence. In this paper, C n 2 is measured during the day and at night and in all four seasons using a high sensitivity micro-thermal meter QHTP-2. The vertical profile of C n 2 in Hefei (0-30 km) is investigated by the analysis of experimental data. The average profile of C n 2 in Hefei exhibits conspicuous day and night differences with increased altitude. The distribution of log(C n 2 ) is nearly normal and has conspicuous seasonal differences.
文摘We evaluate three of the quantum constants of hydrogen, the electron, e<sup>-</sup>, the Bohr radius, a<sub>0</sub>, 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 8π<sup>2</sup>, the v<sub>e</sub><sub>-</sub> times the v<sub>R</sub> divided by v<sub>a</sub><sub>0</sub> 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 v<sub>e</sub><sub>-</sub>, v<sub>R</sub>, and v<sub>a</sub><sub>0</sub>.
基金supported by the National Key R&D Program of China(No.2017YFA0304203)the National Natural Science Foundation of China(Nos.61575116,61705122,61728502,91736209,and 11434007)+3 种基金the Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China(No.IRT13076)the Program for Sanjin Scholars of Shanxi Provincethe Applied Basic Research Project of Shanxi Province(No.201701D221004)the Fund for Shanxi‘1331 Project’Key Subjects Construction
文摘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.
基金Supported by the National Natural Science Fund of China(11775038,11603005,11647307)
文摘The possible variation of the electromagnetic fine structure constant, αe, at cosmological scales has aroused great interest in recent years. Strongly lensed gravitational waves（GWs） and their electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of a photon can be modified,whereas the speed of a GW is the same as predicted by general relativity, and they both propagate in a flat FriedmanRobertson-Walker universe, we investigated the difference in time delays of the images and derived the upper bound of the variation of αe. For a typical lensing system in the standard cosmological models, we obtained B cosθ 1.85×10^（-5）,where B is the dipolar amplitude and θ is the angle between observation and the preferred direction. Our result is consistent with the most up-to-date observations on αe. In addition, the observations of strongly lensed GWs and their electromagnetic counterparts could be used to test which types of alternative theories of gravity can account for the variation of α_e.
文摘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.
文摘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.
文摘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<sup>-21</sup> 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.
基金Project supported by the National Natural Science Foundations of China(Grant No.61275047)the Research Project of Chinese Ministry of Education(Grant No.213009A)the Scientific and Technological Development Foundation of Jilin Province,China(Grant No.20130101031JC)
文摘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.
文摘The Fine Structure Constant (eFSC) Model attempts to give a classical definition to a magical number that underlies much of quantum physics. The Fine Structure Constant (α) value equal to 137.03599206 represents a dimensionless constant that characterizes the strength of the electromagnetic (EM) interaction between subatomic charged particles. Python-generated property counts for the twin prime force F{139/137} show that the adjusted ratio gives a value of α = 137.036. This implies a mathematical framework underlying this constant is based on twin prime numbers and set theory. This study attempts to demonstrate a proof of concept that a hierarchy of fractional twin prime (αII) forces replicates the quantum nature of the universe and is aligned with the Standard Model of Particle Physics. An expanded eFSC Model demonstrates that twin prime forces and their property sets are mathematically viable substitutes for nuclear reactions, as demonstrated for the Beta-minus decay of neutrons into protons. Most significantly, the positive and negative prime numbers define these nuclear reactants and products as positive or negatively charged ions. Furthermore, the eFSC Model provides new insights regarding the hierarchy of EM forces underlying the quantum nature of the universe.
文摘This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.
文摘Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation can be explained numerically in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. Furthermore, every equation can also be explained in terms of the Avogadro number and the number of electrons at 1 C. We show that every equation can be described in terms of the Planck constant. Then, the ratio of the gravitational force to the electric force can be uniquely determined with the assumption of minimum mass. In this report, we describe the algorithms used to explain these equations in detail. Thus, there are no dimension mismatch problems.
文摘This paper presents the development of a conceptual model of the universe,grounded in the Fine Structure Constant(α≈137.036).The Extended Fine Structure Constant(eFSC)Model exploresαas a function of twin prime mi-croverses(U{137},whereα=137,and U{139},whereα=139),each defined by n-dimensional sets of prime numbers.Property counts for U{137}and U{139}are used in a modified Difference over Sum(DoS)calculation to ap-proximate the fractional component ofα,yielding a Relative Electromagnetic Force(EMF)value ofαII=0.036.Applying this method to additional twin prime pairs produces a distribution of EMF values that reflect the energy pro-files of known Standard Model forces,identifying the strong force as a triad of overlapping EM interactions,and linking the weak force to particle transitions involving neutrons,protons,electrons,and neutrinos.The model provides a conceptual framework for investigating the Higgs mechanism,quantum or-bital structures,quantum entanglement,and potential explanations for grav-ity,dark matter,dark energy,and time dilation.While not intended to supplant any existing physics,the eFSC Model offers a novel,prime-number-based archi-tecture for interpreting the quantum universe through a classical lens.
