I asked this question on Quora: If photon is massless, how is mass defined in physics? Most answers that I got were cookie cutter answers from quantum mechanics perspective that do not see the following inconsistencies:
(1) The concept of particle comes from matter. A material particle is discrete because it can be treated mathematically as a point particle as it has a center of mass. The concept of particle ends when there is no center of mass.
(2) Electrons have mass, but no center of mass. In the absence of center of mass a particle cannot be distinguished from another particle. There is still mass but no discreteness. Electrons are, therefore, a fluid-like continuum rather than discrete particle-like collection. This logic is ignored by quantum mechanics.
(3) Energy interactions are always discrete because it takes a precise amount of energy for a unique interaction to take place. But a discrete energy interaction does not imply that the interacting elements are discrete in space also. Einstein’s “energy particle” is a discrete energy interaction. It was an error to assume that a discrete “energy particle” is also a discrete “mass particle” in space.
Electrons and light are fluid-like continuum per the above logic, but they can have discrete energy interactions. That is perfectly okay. Electrons and light are fluid like continuum is confirmed by the mathematics of Quantum Electrodynamic, as shown by Richard Feynman in his lecture on quantum behavior. Please see Feynman on Quantum Behavior.
What is missed by quantum mechanics is that mass can be fluid-like continuum that is infinitely divisible. This is what Newton implied in his Corpuscular theory of Light. From Corpuscular theory of light – Wikipedia:
“Corpuscular theories… are similar to the theories of atomism, except that in atomism the atoms were supposed to be indivisible, whereas corpuscles could in principle be divided. Corpuscles are single, infinitesimally small, particles which have shape, size, color, and other physical properties which alter their functions and effects in phenomena in the mechanical and biological sciences.”
Corpuscles, thus, provide a dimension of fluid-like continuum of “mass concentrations” that can be reduced indefinitely. These concentrations are represented by the frequency of EMR. Frequencies formed the basis of the original concept of quantum.
The idea of “rest mass” may be understood as follows: If we are traveling at the speed of light along side a beam of light, that beam shall appear as a fluid continuum that has the mass concentration of E/c^2. Mass is more basic than energy. Kinetic energy is the energy of moving mass.
Light’s speed is intrinsic and finite because of its mass concentration. Please see The Logic of Motion.
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Addition Nov 9, 2022:
Originally, a particle was understood to be a small part of matter that obviously had a fied boundary and a center of mass. Example of this would be a dust particle, or a particle of sand. In Chemistry, a particle was related to parts of substance that took part in a chemical reaction. Ultimately, a particle of matter was reduced to the idea of an atom or a molecule. Its boundaries were considered to be well defined and fixed, and it had a center of mass.
This idea of particle shifted as one looked at the sub-atomic region beyond the nucleus. Here the substance is no longer rigidly structured as in the case of matter, or even an atom. This sub-atomic substance is rather thin in consistency and spread out. It appears as a continuum with no definite boundaries and no center of mass. Only definite amount of this subtance seem to take part in sub-atomic reactions. Therefore, we fall back on concept of particle similar to that in Chemistry. It is a definite amount of “energy substance” that takes part in a reaction. At sub-atomic level, this is referred to as a “quantum.”
Therefore, in its most basic sense, a particle is defined in terms of its associations. And that, by definition, is a perceptual element.
