Derivation of Newton’s Law of Gravitation and Discovery of the Unique Normal Modes of the Universe

Abstract

The derivation of Newton’s law of gravitation is based on the concept that the universe is a pure wave system. Then, the elementary particles are shown to be the constructive interference peaks of the normal modes. For a normal mode originating at a mass particle, the force at another particle, r distant, is given by F = dE/dr = −sdI/dr where I is the intensity of a normal mode and s is the particle size. It was discovered that this force law leads to Newton’s law of gravitation only if the normal modes propagate circularly in a plane and are uniquely determined by the Bessel equation of half-order with l = 0. New results are: 1) Mass energy of particles due to gravitational intensity 2) Possible explanation of the spin 1/2 of elementary particles.