Rotating fields and particle-like states of electron-positron systems

Abstract

It is argued that the field of a charge in a stationary orbit co-rotates with the charge about the centre of mass. Such a field has no radiation term. It is obtained by transformation from the co-rotating frame of reference; direct calculation would require that the constitutional properties of the medium be known, these being such as to curve light rays. For rotating reference system Corum's tetrad field is employed, the object of anholonomity affecting the derivation of fields from potentials. The force between the charge *e of positronium is found to be (1 -p2)'/' e2/ri2 when the charges follow with velocity o x r (= pc) a stationary circular orbit of diameter r12 (= 2r). Stationary orbits are selected by Bohr quantisation of canonical angular momentum. A quadratic equation is obtained for yp and for r12, where y = (1 -p2)-1/2. One solution gives the well-known 'atom-like' states. The other gives 'particle-like' states for which orbital motion is ultrarelativistic (yp = n/a, where a = 1/137), orbital diameters are small compared with eZ/mc2 (zd), m being the electron mass, and energies are 2amc2/n, small compared with mc2. In such a state positronium is termed a 'positronium unit'. The unit has a very long lifetime for radiative transitions, and should possess a weak magnetic moment (p = cued/2n). If it is assigned half-integral orbital angular momentum (hence imaginary parity) it might be identified with the neutrino. A system in which two units orbit around a stationary charge has the properties of the muon, and a system with one orbiting unit has the properties of the charged pion. Spin, charge, rest energy and decay mode are explained in each case. The very different reactivities also can be explained. A system, 'trionium', in which two charges of one sign orbit about a central stationary charge of the opposite sign is explored. Again ultrarela- tivistic states emerge, but the energies differ inappreciably from the rest energy mc2 of the central charge. However, if one adds further pairs of charges in orbits of increasing radius, the magnetic coupling between orbital currents provides energies of order mc2/a. It is speculated that such a system may afford a model for the proton. 1. Introduction and general philosophy In the early years of this century physicists were confronted with an empirical classification of atoms based on their chemical reactivity -the periodic table of the elements. In addition, there was some spectroscopic evidence to be explained, chiefly the spectrum of the hydrogen atom and Moseley's law for x-ray lines. The key for the unravelling of this situation was provided by Rutherford when he proposed his electrodynamical model of the atom, and further crucial steps were taken by Bohr when he introduced the concept of stable orbits and thereby found at least a first-order explanation for the hydrogen atom spectrum. One wonders how long progress might have been delayed had not these steps been taken. Today one has an empirical