With clear illustrations throughout and without recourse to quantum
mechanics, the reader is invited to revisit unsolved problems lying
at the foundations of theoretical physics. Maxwell and his
contemporaries abandoned their search for a geometrical
representation of the electric and magnetic fields. The
wave-particle dilemma and Bose-Einstein statistical counting have
resulted in unsatisfactory non-realistic interpretations.
Furthermore, a simple structure of the hydrogen atom that includes
hyperfine levels is still wanting. Working with the latest
experimental data in photoionics a proposed solution to the
wave-particle dilemma is suggested based on an array of
circular-polarized rays. The Bose-Einstein counting procedure is
recast in terms of distinguishable elements. Finally, a vortex
model of a 'particle' is developed based on a trapped photon. This
consists of a single ray revolving around a toroidal surface, and
allows a geometrical definition of mass, electric potential, and
magnetic momentum. With the adjustment of two parameters, values to
4 dp for the hyperfine frequencies (MHz) of hydrogen can be
obtained for which a computer program is available.
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