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. Key Features • There are no competing titles • This is an entirely original examination of unsolved problems in theoretical physics. It reinterprets experiments in photoionics to revisit the wave-particle dilemma, gives an alternative view of Bose–Einstein statistical counting, and uses the latest experiments on the orbital angular momentum (OAM) of light to suggest a new model of the hydrogen atom

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