The concept of photons, bundles of energy located in a small volume of space, was proposed by Einstein in 1905 following Planck’s successful blackbody spectrum expression. Einstein assumed that the bundle of energy remains localised as it moves away from the source with the velocity of light c. He assumed that the energy  content of the bundle, or photon, is related to its frequency ɣ by the equation E=hɣ, where h is Plank’s constant, and that the photon was either totally absorbed or emitted by one electron.

Having specialised in industrial optics for many years, I am very familiar with the practical aspects of the Dual Nature of Electromagnetic Radiation. We need a photon as a localised particle interpretation of the processes dealing with the interaction between radiation and matter, but at the same time we also need a wave theory of radiation to understand interference and diffraction phenomena. The idea that radiation is neither purely a wave nor merely a stream of particles must therefore be taken seriously. Electromagnetic radiation behaves wave-like under some circumstances and particle-like under other circumstances.

However, when reading about the Compton Effect as part of my research resulting in the theory of Physics in 5 Dimensions, I was still very surprised to find the description of an experiment which clearly demonstrated that you can effectively play billiards with electrons & photons. In this case the photon is not absorbed into the electron, but on meeting, both the photon and electron are deflected in the same way as billiard balls on contact deflect to new paths with changed velocities.

In 1923 Compton confirmed the particle like nature of photons¹⁷ from experiments which demonstrated that photons can be received from definite directions and scattered in definite directions. In his paper on the quantum theory of the scattering of X-rays (photons) by light elements, Compton also addressed the issue of the Dual Nature of Electromagnetic Radiation. He noted the remarkable agreement between his formulas and the experiments which left no doubt that the scattering of X-rays is a quantum effect.

He continued: The present theory depends essentially upon the assumption that each electron which is effective in the scattering, scatters a complete quantum (photon). It involves also the hypothesis that the photons of radiation are received from definite directions and are scattered in definite directions. The experimental support of the theory indicates very convincingly that a photon carries with it momentum as well as energy. 

Later Maurice de Broglie, a French experimental physicist, supported Compton's view of the particle nature of radiation and in 1929 de Broglie established the hypothesis that the dual wave-particle behaviour of radiation applies equally well to matter¹⁸. Just as a photon has a light wave associated with it that governs its motion, so a material particle (e.g. an electron) has an associated matter wave that governs its motion. Since the universe is composed entirely of matter and radiation, de Broglie’s suggestion is essentially a statement about a grand symmetry of nature (unified theory of physics).  

According to de Broglie, for matter and for radiation alike, the total energy E of an entity is related to the frequency ɣ of the wave associated with its motion by the equation E=h ɣ and the momentum p of the entity related to the wavelength λ of the associated wave by the equation p=h/λ. Here the particle concepts, energy E and the momentum p, are connected through Planck’s constant h to the wave concepts of frequency ɣ and wavelength λ. The equation λ = h/p is called the de Broglie relation and predicts the de Broglie wavelength λ of a matter wave associated with the motion of a material particle having a momentum p.

At the end of his Nobel Lecture de Broglie writes: Thus to describe the properties of matter as well as those of light, waves and corpuscles have to be referred to at one and the same time. The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave and this wave is no myth; its wavelength can be measured and its interferences predicted. It has thus been possible to predict a whole group of phenomena without their actually having been discovered. And it is on this concept of the duality of waves and corpuscles in Nature, expressed in a more or less abstract form, that the whole recent development of theoretical physics has been founded and that all future development of this science will apparently have to be founded.

In Physics in 5 Dimensions¹⁹  electromagnetic radiation matter waves produce wave groups with the properties of matter, where the wave amplitude A and frequency ɣ are parameters associated with the matter waves, while length (ref.  Einstein’s measuring rods), time t, wavelength λ, mass m and the velocity of light c are the resulting parameters of a particle (wave group) and its energy.

References:

(17) The Physical Review, Second Series May 1923 Vol. 21 No. 5 page 486 – A Quantum Theory of the Scattering of X-rays by Light Elements – by Arthur H. Compton

(18) de Broglie’s “ The wave nature of the electron” – Nobel Lecture December 12, 1929 https://www.nobelprize.org/uploads/2018/06/broglie-lecture.pdf

(19) Pages 120 to 123 - Physics in 5 Dimensions, Alan Clark, 2017, Winterwork, Borsdorf, ISBN: 978-3-96014-233-1

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