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

DOI: 10.4236/jmp.2015.614218   PDF   HTML   XML   3,056 Downloads   3,400 Views   Citations


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.

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Chakeres, D. and Vento, R. (2015) The Association of the Neutron, and the Quantum Properties of Hydrogen, with the Prime Numbers 2, 3, 5, 7, 11. Journal of Modern Physics, 6, 2145-2157. doi: 10.4236/jmp.2015.614218.

Conflicts of Interest

The authors declare no conflicts of interest.


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