1 A mass-without-mass model of protons and neutrons Jean Louis Van Belle, Drs, MAEc, BAEc, BPhil 8 February 2021 Contents Introduction .................................................................................................................................................. 1 The electron .................................................................................................................................................. 3 The muon-electron ....................................................................................................................................... 4 The proton .................................................................................................................................................... 5 The neutron .................................................................................................................................................. 7 Electron, proton, and neutron magnetic moments ...................................................................................... 9 Conclusion ................................................................................................................................................... 10 Introduction ‘Mass without mass’ models analyze elementary particles as harmonic oscillations whose total energy – at any moment (KE + PE) or over the cycle – is given by E = ma 2  2 . One can calculate the radius or amplitude of the oscillation directly from the mass-energy equivalence and Planck-Einstein relations, as well as the tangential velocity formula⎯interpreting c as a tangential or orbital (escape) velocity. E=m 2 E=ℏω }⇒m 2 =ℏω =ω⟺=  ω ⟺ω=   }⇒m 2 ω 2 =ℏω⟹m  2 ω 2 ω 2 =ℏ   ⟺= ℏ m Such models assume a centripetal force whose nature, in the absence of a charge at the center, can only be explained with a reference to the quantized energy levels we associate with atomic or molecular electron orbitals 1 , and the physical dimension of the oscillation in space and time may effectively be understood as a quantization of spacetime. 1 See, for example, Feynman’s analysis of quantized energy levels or his explanation of the size of an atom. As for the question why such elementary currents do not radiate their energy out, the answer is the same: persistent currents in a superconductor do not radiate their energy out either. The general idea is that of a perpetuum mobile (no external driving force or frictional/damping terms). For an easy mathematical introduction, see Feynman, Chapter 21 (the harmonic oscillator) and Chapter 23 (resonance).