Concept of Quaternion Mass for Wave-Particle Duality : A Novel Approach

Abstract

Mass is in the central theme everywhere from atom to galaxy. But what is mass ? Is it scalar or vector ? Apparently it appears that mass is scalar; but relativistic mass is velocity dependent and moving mass such as photon is vector boson. In the present paper a new concept is introduced that in general, mass is neither scalar nor vector rather, mass is a quaternion quantity (scalar + vector). The concept of quaternion mass suggests that the total mass M of a moving body is quaternion sum of : (i) the scalar(grain or rest mass) mass mg establishing its particle behavior and (ii) the vector(photonic) mass mp governing its wave properties. Mathematically, total quaternion mass as M = mg + mp, its magnitude being the Pythagorean sum as |M| = (mg2+mp2)1/2 . The theory proposed here explains the wave-particle duality more clearly & conceptually and gives a mathematical blend to de-Broglie hypothesis. It also explains successfully several effects such as Compton effect and refraction of light which could not be explained otherwise by a single theory of wave or particle. Also explained are: Doppler effect of light, Photo-electric effect, Uncertainty principle and Relativity. The quaternion mass concept proposed in this paper is novel & is of fundamental importance; this could prove to be a revolutionary concept in physics and possibly lead to new directions.