Quantizing dynamics. Issue 1 (1st March 2022) - Kanda, A; Prunescu, M; Wong, R
Abstract: In theoretical physics, quantization means reducing a continuum structure to discrete structure. This process was widely used in the development of quantum mechanics since Planck's convention of the discretization of the energy of electromagnetic (EM) waves e = nhf as a solution to the crisis of the blackbody radiation. When combined with Einstein's relativistic particle energy equation e = mc 2 it became a most fundamental process of the 20th century theoretical physics. Planck was reluctant to consider his energy quanta e = nhf as a physical particle. His concern was forgotten in the process of development of quantum mechanics, which was Einstein's relativity theory dynamics combined with Planck's wave-particle duality. This framework was later extended by Dirac into the quantization of the entire EM field theory of Maxwell in which the EM fields, which are mathematically a continuous structure, themselves were quantized in terms of Einstein's special theory of relativity dynamics using Fourier expansions. As it appears that the mathematical error of using wave numbers, which form a real continuum, as indexes of the Fourier expansion for the discretization of waves went unnoticed, this quantization of electrodynamics, called quantum electrodynamics (QED), became a model for further quantizing continuum based physical theories. This error was thus passed down to all of the successors of QED. The theory of quantum gravity is yet another attempt to quantize a major force field theory of gravitational forces. Here as well the issue of the difference between the continuum and the discrete was overlooked.