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The Generalized Pythagorean Comma Harmonic Powers of a Fundamental Frequency Are Equivalent the Standing Wave Harmonic Fraction System

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Advances in Pure Mathematics 2018年第7期8卷 652-665页

作者： donald chakeres The Ohio State University Columbus USA

Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the ha

关键词： Power Laws Harmonic Systems Standing Wave Harmonic Fractions Dimensional Analysis Buckingham Pi Theorem Pythagorean Comma

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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

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Journal of Modern Physics 2016年第13期7卷 1801-1810页

作者： donald William chakeres Department of Radiology The Ohio State University Columbus OH USA

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.

关键词： Fundamental Physical Constants Unification Models Hydrogen Electron Bohr Radius Rydberg Constant Fine Structure Constant

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Prediction and Derivation of the Higgs Boson from the Neutron and Properties of Hydrogen Demonstrating Relationships with Planck’s Time, the Down Quark, and the Fine Structure Constant

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Journal of Modern Physics 2014年第16期5卷 1670-1683页

作者： donald William chakeres Department of Radiology The Ohio State University Columbus OH USA

A high accuracy Higgs boson, H0, is an important physical constant. The Higgs boson is associated with the property of mass related to broken symmetry in the Standard Model. The H0 mass cannot be derived by the Standard Model. The goal of this work is to derive and predict the mass of H0 from the subatomic data of the frequency equivalents of the neutron, electron, Bohr radius, and the ionization energy of hydrogen. H0’s close relationships to the fine structure constant, α, the down quark, and Planck time, tP are demonstrated. The methods of the harmonic neutron hypothesis introduced in 2009 were utilized. It assumes that the fundamental constants as frequency equivalents represent a classic unified harmonic system where each physical constant is associated with a classic harmonic integer fraction. It has been demonstrated that the sum exponent of a harmonic integer fraction, and a small derived linear δ value of the annhilation frequency of the neutron, vn, 2.2718591 × 1023 Hz, (vns) as a dimensionless coupling constant represent many physical constants as frequency equivalents. This is a natural unit system. The harmonic integer fraction series is 1/±n, and 1 ± 1/n for n equals 1 to ∞. The H0 is empirically and logically is associated with harmonic fractions, 1/11 and 1 + 1/11. α-1 is associated with 11. α-1 is a free space scaling constant for the electromagnetic force so it is logical that 11 should also have a pair, but for a free space mass constant. Also there should be a harmonic faction pair for the down quark, 1 - 1/11, just as there is pairing of the up quark, 1 - 1/10, and top quark, 1 + 1/10. The harmonic neutron hypothesis has published a method deriving a high accuracy Planck time, tP from the same limited subatomic data. The δ line for H0 should be closely associated with tP since they both are related to mass. The preferred derived value related to tP2 is 125.596808 GeV/c2. A less attractive derived value is 125.120961 GeV/c2 from the weak force fa

关键词： Higgs Boson Neutron Unificaiton Model Down Quark Fine Structure Constant Planck Time Gravity

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The Derivation of the Cosmic Microwave Background Radiation Peak Spectral Radiance, Planck Time, and the Hubble Constant from the Neutron and Hydrogen

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Journal of Modern Physics 2016年第6期7卷 573-586页

作者： donald William chakeres Vola Andrianarijaona Department of Radiology The Ohio State University Columbus OH USA Department of Physics & Engineering Pacific Union College Angwin CA USA

Purpose: The cosmic microwave background radiation, CMB, is fundamental to observational cosmology, and is believed to be a remnant from the Big Bang. The CMB, Planck time, tP, and the Hubble constant, H0, are important cosmologic constants. The goal is to accurately derive and demonstrate the inter-relationships of the CMB peak spectral radiance frequency, tP, and H0 from neutron and hydrogen quantum data only. Methods: The harmonic neutron hypothesis, HNH, evaluates physical phenomena within a finite consecutive integer and exponential power law harmonic fraction series that are scaled by a fundamental frequency of the neutron as the exponent base. The CMB and the H0 are derived from a previously published method used to derive tP. Their associated integer exponents are respectively +1/2, −3/4, and −128/35. Results: Precise mathematical relationships of these three constants are demonstrated. All of the derived values are within their known observational values. The derived and known values are: νCMB, 160.041737 (06) × 109 Hz, ~160 × 109 Hz;2.72519 K, 2.72548 ± 0.00057 K, H0 2.29726666 (11) × 10−18 s−1, ~2.3 × 10−18 s−1;and tP 5.3911418 (3) × 10−44 s, 5.39106 (32) × 10−44 s. Conclusion: The cosmic fundamental constants tP, H0, and CMB are mathematically inter-related constants all defined by gravity. They are also directly derivable from the quantum properties of the neutron and hydrogen within a harmonic power law.

关键词： Cosmic Microwave Background Radiation Neutron Fundamental Physical Constants Unification Models Hydrogen Planck Time Hubble Constant

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A New Quantum Number Triangular Array That Defines the Internal Organization of Valence Quarks, the Hadron Quark Model, and the CKM Matrix

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Journal of Modern Physics 2016年第1期7卷 145-155页

作者： donald William chakeres Richard Vento Department of Radiology The Ohio State University Columbus Ohio USA Retired Columbus State Community College Columbus Ohio USA

Purpose: The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants, including the quarks, are associated with partial harmonic fractional exponents, , of a fundamental frequency, vF. The model has shown that the properties of the quarks are based on a progression of prime number composites. They also fall on three separate power law lines related to integer factors of the Y-intercept, , of a fundamental electromagnetic line which is scaled by the Rydberg constant, R and Planck’s constant. The quark lines are scaled by the quantum number factors {1, 2, 3}, and their Y-intercepts are referred to as nbem. The goal is to present a new proto-quark model in a six-quark inverted triangular array that defines the global organization of the valence quarks, which determines the hadronic quantum numbers, the standard hadron quark model, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Methods: The charm, bottom, top quarks are associated with power law line Y-intercept, nbem equal to 1;the strange and down quarks with nbem equal to 2;and the up quark with nbem equal to 3. An inverted equilateral triangular array with three rows arranged from upper row (triangle base) to bottom row (triangle vertex), is associated respectively with nbem numbers 1, 2, and 3. The novelty of our perspective thus defines a new global valence quark organization which supersedes the Standard hadron composite quark model. The quarks are ordered via relative mass, partial fractions, and nbem quantum number. The top row of our inverted triangle includes the c, b, and t quarks from left to right;the middle row depicts the d and s quarks;and the bottom row, the up quark. Results: Our array depicts a quantum generator of the global organization of the valence quarks defining the composite quark model. The vertices of the triangular array are the up quarks, the midpoints are the down quar

关键词： Quarks Quark Model Neutron Cabibbo-Kobayashi-Maskawa Matrix Fundamental Physical Constants Fundamental Particles Unification Models

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Quantum Neutron Unit Gravity

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Journal of High Energy Physics, Gravitation and Cosmology 2017年第2期3卷 267-276页

作者： donald chakeres Vola Andrianarijaona Department of Radiology The Ohio State University Columbus OH USA Department of Physics and Engineering Pacific Union College Angwin CA USA

Quantum gravity and the transformation of a neutron star or the merger of two neutron stars into a black hole are important topics in cosmology. According to the Schwarzschild radius relationship, a black hole arises when two times of the gravitational binding energy of the gravitational system, GBE, equal the annihilation energy of its total mass. From a quantum perspective, the integer number of neutrons defines the GBE and mass in the merger of binary pure neutron stars transforming to a black hole. Therefore, one can scale all gravitational binding energy relationships by using neutron mass, energy, distance, time, or frequency equivalents. We define ?of the neutron as the binding energy, 1.4188 × 10󔼹 J, of a virtual system of two neutrons separated by the neutron Compton wavelength. The??divided by a neutron’s rest mass energy represents a fundamental, dimensionless proportionality constant, 9.4252 × 10󔼰, . The square root of , αG, which we introduce here as a coupling constant, is identical in concept to the fine structure constant found in electromagnetic physics, but for gravity. Both αG and ?inter-relate the neutron, proton, electron, Bohr radius, speed of light, Planck’s constant, GBE of the electron in hydrogen, and Planck time. This paper demonstrates a direct conceptual and computational rationale of why the neutron and its negative beta decay quantum products accurately can represent a quantum gravitational natural unit system.

关键词： Quantum Gravity Neutron Black Holes Neutron Stars

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The Harmonic Neutron Hypothesis: Prime Number Factor Patterns and Their Relationship to the Hierarchy of the Fundamental Particles and Bosons

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Advances in Pure Mathematics 2015年第5期5卷 240-250页

作者： donald William chakeres Richard Vento Department of Radiology The Ohio State University Columbus USA Columbus State Community College Columbus USA

The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial harmonic fractional exponents, 1 ± (1/n), of a fundamental frequency, Vf. The goal is to evaluate the prime and composite factors associated with the neutron n0, the quarks, the kinetic energy of neutron beta decay, the Rydberg constant, R, e, a0, H0, h, α, W, Z, the muon, and the neutron gluon. Their pure number characteristics correspond and explain the hierarchy of the particles and bosons. The elements and black body radiation represent consecutive integer series. The relative scale of the constants cluster in a partial harmonic fraction pattern around the neutron. The global numerical organization is related to the only possible prime factor partial fractions of 2/3, or 3/2, as pairs of 3 physical entities with a total of 6 in each group. Many other progressively resonant prime number factor patterns are identified with increasing numbers of smaller factors, higher primes, or larger partial fractions associated with higher order particles or bosons.

关键词： Boson Fundamental Particles Prime Numbers Physical Constants Unification Models Neutron Quarks Lepton W Boson Z Boson Gluon

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Prediction and Derivation of the Hubble Constant from Subatomic Data Utilizing the Harmonic Neutron Hypothesis

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Journal of Modern Physics 2015年第3期6卷 283-302页

作者： donald William chakeres Richard Vento Department of Radiology The Ohio State University Columbus USA Columbus State Community College Columbus USA

Purpose: To accurately derive H0 from subatomic constants in abscence of any standard astronomy data. Methods: Recent astronomical data have determined a value of Hubble’s constant to range from 76.9+3.9-3.4+10.0-8.0 to 67.80 ± 0.77 (km/s)/Mpc. An innovative prediction of H0 is obtained from harmonic properties of the frequency equivalents of neutron, n0, in conjunction with the electron, e;the Bohr radius, α0;and the Rydberg constant, R. These represent integer natural unit sets. The neutron is converted from its frequency equivalent to a dimensionless constant,, where “h” = Planck’s constant, and “s” is measured in seconds. The fundamental frequency, Vf, is the first integer series set . All other atomic data are scaled to Vf as elements in a large, but a countable point set. The present value of H0 is derived and ΩM assumed to be 0. An accurate derivation of H0 is made using a unified power law. The integer set of the first twelve integers N12 {1,2,…,11,12}, and their harmonic fractions exponents of Vf represent the first generation of bosons and particles. Thepartial harmonic fraction, -3/4, is exponent of Vf which represents H0. The partial fraction 3/4 is associated with a component of neutron beta decay kinetic energy. Results: H0 is predicted utilizing a previously published line used to derive Planck time, tp. The power law line of the experimental H0 and tp conforms to the predicted line. Conclusions: H0 can be predicted from subatomic data related to the neutron and hydrogen.

关键词： Hubble Constant Neutron Unification Model Planck Time Quantum Gravity Neutron Beta Decay Neutrino

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The Association of the Neutron, and the Quantum Properties of Hydrogen, with the Prime Numbers 2, 3, 5, 7, 11

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Journal of Modern Physics 2015年第14期6卷 2145-2157页

作者： donald William chakeres Richard Vento Department of Radiology The Ohio State University Columbus USA Retired Columbus State Community College Columbus USA

The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants are associated with quantum integers, n, within a classic integer and partial harmonic fraction system, and follow a known two-dimensional, 2D, power law geometry. These are exponents of a fundamental frequency, vF, the basis of which is the annhilation frequency of the neutron, vn0. Our goal to a first approximation is to derive the frequency equivalents of the Rydberg constant, vR, the Bohr radius, va0, the electron, ve-, and the reciprocal fine structure constant, 1/α all from vn0, π, and a small set of prime integers only. The primes used in the derivations are respectively 2, 3, 5, 7, and 11. This is possible since it is known that the number 3 is associated with R, 5 with a0, 7 with e-, and 11 with 1/α. In addition, the interrelationships of the frequency ratio equivalents of these natural units with 2 and π are known, thus allowing for the derivation of any one from the others. Also the integer and partial fractions of a0, e-, and n0 define Planck time squared, tP2. An accurate estimate of tP2 from vF alone is also related to the integer 2 since gravity is a kinetic force. Planck time squared, tP2 scales the Y-axis, and vF scales the X-axis. In conclusion the quantum properties of hydrogen are derived from only the natural unit physical data of the neutron, to a relative precision ranging from 2.6 × 10-3 to 6.7 × 10-4. This supports the hypothesis that many of the fundamental constants are related to vn0.

关键词： Neutron Fundamental Physical Constants Unification Models Hydrogen Fine Structure Constant Bohr Radius Rydberg Constant Electron Quantum Harmonic Oscillators

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A Frequency-Equivalent Scale-Free Derivation of the Neutron, Hydrogen Quanta, Planck Time, and a Black Hole from 2 and π;and Harmonic Fraction Power Laws

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Journal of Applied Mathematics and Physics 2017年第5期5卷 1073-1091页

作者： donald chakeres Richard Vento Vola Andrianarijaona Department of Radiology the Ohio State University Columbus Ohio USA Department of Mathematics and Physics Columbus State Community College Columbus Ohio USA Retired Department of Physics and Engineering Pacific Union College Angwin California USA

We find that π represents dual attributes. One is within the purely mathematical domain and can be derived for example, from infinite series, among several other methods. The other is within a 2D geometric-physical domain. This paper analyzes several physical constants from an analogous perspective where they are defined solely by mathematical and 2D geometric properties independent of any actual physical scaling data. The constants are evaluated as natural unit frequency equivalents of the neutron, electron, Bohr radius, Rydberg constant, Planck’s constant, Planck time, a Black hole with a Schwarzschild radius, the distance light travels in one time unit;and the fine structure constant. These constants are defined within two inter-related harmonic domains. In the linear domain, the ratios of the frequency equivalents of the Rydberg constant, Bohr radius, electron;and the fine structure constant are related to products of 2 and π. In the power law domain, their partial harmonic fraction powers, and the integer fraction powers of the fundamental frequency for Planck time are known. All of the constants are then derived at the point where a single fundamental frequency simultaneously fulfills both domains independent of any direct physical scale data. The derived values relative errors from the known values range from 10-3 to 10-1 supporting the concept and method.

关键词： Fundamental Constants Neutron Black Hole Planck Time Computational Physics Mathematical Physics Hydrogen

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