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

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.

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

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.

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

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.

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

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 quarks. All weak transitions are from a corner to a midpoint or vice versa. The standard 3 by 3 CKM matrix is generated from the new quark triangle with each up type quark (u, c, and t) transforming to each down type (d, s, and b), with their experimental flavor transition magnitudes given. Conclusion: A new quark quantum number, nbem, is an important discovery that generates a new proto-valence quark triangle that secondarily generates the composite quark model and the CKM matrix.

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

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.