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

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, v F , the basis of which is the annhilation frequency of the neutron, v n 0 . Our goal to a first approximation is to derive the frequency equivalents of the Rydberg constant, v R , the Bohr radius, v a 0 , the electron, v e - , and the reciprocal fine structure constant, 1/ α all from v n 0 , 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 a 0 , 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 a 0 , e - , and n 0 define Planck time squared, t P 2 . An accurate estimate of t P 2 from v F alone is also related to the integer 2 since gravity is a kinetic force. Planck time squared, t P 2 scales the Y-axis, and v F 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 v n 0 .