Abstract
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.
Highlights
If the mass is that of the electron, the velocity is α × c ; the kinetic energy is equivalent to the ionization energy of hydrogen, in terms of R
We find that the physical constants must follow power law properties within a harmonic system with the four natural unit frequency equivalent values that scale the whole harmonic system, namely the neutron, n0 ; the electron, e− ; the Bohr radius, a0 ; and the Rydberg constant, R [22]
TP, is a unique fundamental constant in physics since it is the only one that unifies the electromagnetic with the speed of light, c; quantum phenomena through Planck’s constant, h; and the cosmologic, via the Newtonian gravitational constant, G, into a single composite scale
Summary
The directly observable properties of hydrogen, H, include the proton, p+, electron, e−; the Bohr radius, a0; and the ionization energy, developed with Rydberg’s constant, R These represent some of the most fundamental constants of mass, distance, and electromagnetic bosonic energy scaling factors in physics. They are not truly independent, but they represent a unique integrated quantum linear domain ratio system that is linked through classic Euclidean geometric scaling factors, 2 and π These constants correlate with different physical values, for mass; distance; frequency; and for electromagnetic energy which when normalized to a single Hertzian unit are unified. These same four constants are related to Coulomb’s law; the free space constants of permittivity and permeability; Planck’s constant, h, and the speed of light, c through computational definitions of a0. If the mass is that of the electron, the velocity is α × c ; the kinetic energy is equivalent to the ionization energy of hydrogen, in terms of R
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