Disguised electromagnetic connections in classical electron theory

In the first quarter of the 20th century, physicists were not aware of the existence of classical electromagnetic zero-point radiation nor of the importance of special relativity. Inclusion of these aspects allows classical electron theory to be extended beyond its 19th century successes. Here we review spherical electromagnetic radiation modes in a conducting-walled spherical cavity and connect these modes to classical electromagnetic zero-point radiation and to electromagnetic scale invariance. Then we turn to the scattering of radiation in classical electron theory within a simple approximation. We emphasize that, in steady-state, the interaction between matter and radiation is disguised so that the mechanical motion appears to occur without the emission of radiation, even though the particle motion is actually driven by classical electromagnetic radiation. It is pointed out that, for nonrelativistic particles, only the harmonic oscillator potential taken in the low-velocity limit allows a consistent equilibrium with classical electromagnetic zero-point radiation. For relativistic particles, only the Coulomb potential is consistent with electrodynamics. The classical analysis places restrictions on the value of e^2/(hbar c).

2. Productive ambiguity

‘Productive ambiguity’ begins with Bohr’s move to Cambridge in 1911 to work with J. J. Thompson on the electron theory and to publish an English translation of his thesis. He did not flourish in Cambridge, however, and moved to Manchester in early 1912 to study under Ernest Rutherford. He soon took an interest in the work of another researcher in the laboratory, Charles Galton Darwin, who was wrestling with the problem of how electrons in a nuclear atom interact with passing alpha particles. Consideration of Darwin’s problem prompted Bohr to discover the radical mechanical instability of the nuclear atom, a result for which his thesis and his philosophy had prepared him. He exploited the instability to develop his quantum atom. His several attempts to ground his invention in existing physics give a precious insight into his mind at work, into his way of entertaining several contradictory formulations of his thought at the same time.