Essay Abstract
While it is obvious that no experiment can tell discrete from continuous due to limited resolution, even within reasonably well defined quantum theories telling discrete from continuous or particles from waves can be less than trivial. For example, due to natural line width, it is not so obvious that atom spectra are discrete, and while it is believed that a measurement of a spin projection of a spin 1/2 particle can only yield values +1/2 or -1/2, the situation is not quite clear-cut due to the well-known measurement problem in quantum mechanics. Point-like particles could be another manifestation of discrete, but using some versions of electrodynamics, one can show that matter particles of quantum theory can be emulated by continuous fields. For example, matter field can be naturally excluded from the equations of scalar electrodynamics (the Klein-Gordon-Maxwell electrodynamics), and the resulting equations describe independent evolution of the electromagnetic field. These equations can also be naturally embedded into a quantum field theory. Some surprising new results for spinor electrodynamics (the Dirac-Maxwell electrodynamics) suggest that similar conclusions may be true for that theory, which is more realistic.
Author Bio
Andrey Akhmeteli obtained his PhD in theoretical and mathematical physics from Moscow University and has worked there, in other research and education institutions, and in industry.