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Interference of electromagnetic waves from the point of view of photon wave function in coordinate representation

DOI 10.18127/j15604128-201808-04

Keywords:

A.P. Davydov – Ph.D.(Phys.-Math.), Associate Professor, Department of Applied and Theoretical Physics, Institute of Natural Science and Standardization of Nosov Magnitogorsk State Technical University
E-mail: ap-dav@yandex.ru
T.P. Zlydneva – Ph.D.(Pedagogic), Associate Professor, Department of Applied Mathematics and Informatics, Institute of Natural Science and Standardization of Nosov Magnitogorsk State Technical University
E-mail: pmi@magtu.ru, tapazl@yandex.ru


Recently, the concept of wave-particle duality of light and microparticles has been actively discussed again in connection with the emergence of new experiments. They affect both the essence of quantum theory itself and the its attendant metaphysics, as well as purely pragmatic questions concerning quantum computing, teleportation, and cryptography. In various kinds of interpretations of quantum mechanics, used in the discussion of these experiments, the wave function of the quantum system plays an important role. However, as applied to the photon, the wave function in the coordinate representation has not yet received wide recognition and application. The purpose of the article is to illustrate the possibilities of the mathematical apparatus of photon quantum mechanics, built in previous works, simulating the photon wave function in the coordinate representation in the form of a wave packet with Gaussian momentum distribution and applying it to explain the interference of light in Young’s experiment.
The article also argues that the correct presentation of the physical essence of the methods of obtaining coherent non-laser sources, used to observe the light interference, inevitably requires the use of the concept of the photon wave function in the coordinate representation at the present stage of knowledge. The essence of the arguments lies in the fact that the statements of classical electrodynamics about the division of a train of electromagnetic waves, supposedly emitted by a separate atom, are incorrect, because in fact the photon energy in such cases is not divided. Therefore, it should be assumed that when receiving coherent sources of non-laser radiation, the photon's wave function is divided, which then interferes with itself, thereby distributing the probability of a photon hitting different points of space. In fact, this «mechanism of division» of the wave function also applies to particles with mass.
The stated results of a single-photon approach to the description of electromagnetic phenomena, in particular, the interference pattern of Young’s experience, demonstrate that these phenomena can be described not only by classical and quantum electrodynamics, but also in the language of quantum mechanics without involving of secondary quantization of the electromagnetic field.
This significantly expands the field of application of the «usual» quantum mechanics and significantly reduces the problem of wave-particle duality at the modern level of knowledge. Although, according to the authors, the photon is a quasi-particle, and the light is the result of the propagation of a «spin-flip» wave in a physical vacuum, the structure and nature of which must be considered at Planck distances. Perhaps this circumstance will make it possible to look from a new point of view at such problems as quantum entanglement and nonlocality of interactions.
It is emphasized that the wave function of physical objects, from the author's point of view, is not itself a physical object. Therefore, to solve the «radiation» problem of a wave function, which really does not exist as a physical object, and of its «propagation» in space over time and its «collapse» in measurements, the new experiments are needed, especially in identifying the role of the physical vacuum. It is in the physical vacuum that some more unclear processes of transfer of interactions and information should take place.

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