The Particle menace part 3: Farewell to Primitive Concepts
Hello. It is clear that the rather occult concepts such as energy, mass, space, force, and charge are useful up to a point, especially if the objective is of a purely practical or instrumental nature. In delving into ontology, these concepts are inadequate and result in confusion. This podcast investigates ways of replacing them.
Starting with energy, Faraday's great insight over a century ago that all phenomena were composed of the same fundamental substance but in different concentrations has been largely ignored. Schrödinger was one of the exceptions. In a letter to Max Planck in May 1926, Schrödinger writes:
‘The concept of energy is something that we have derived from macroscopic experience and really only from macroscopic experience. I do not believe that it can be taken over into micromechanics just like that, so that one may speak of the energy of a single particle oscillation. The energetic properties of the individual particle oscillation is its frequency.’
This is clear from the equation energy equals h times f where h is the Planck constant and f the frequency. Basically, the frequency is divided up to manufacture individual particles, which in turn produce a balanced accounting record of the photoelectric effect. By dispensing with the concept of energy, it follows that the principle of the conservation of energy which forms the basis of the stationary states and quantum jumps view of the structure of the atom is irrelevant. Schrödinger, in a paper titled Might Perhaps Energy Be Merely a Statistical Concept, states:
‘I am sure that if an advocate of the orthodox view cares to argue the case with me, the first thing he's going to tell me is, would I please have a look at a line spectrum and see that the levels are not blurred but very sharply distinguished and privileged. But this argument is based on the idea that an observed spectral frequency is emitted by single atoms jumping from a certain higher level to a certain lower level, each atom producing in this process a photon with the energy equal to the difference of the two levels. This, of course, presupposes the detailed validity of the conservation law, which is just the point under discussion that I do not take for granted.’
So energy could be replaced by frequency, and this could lead to a return to Faraday's idea of the distinction between mass and space being one of concentration and densities.
Turning to mass and space, Sir Arthur Eddington took a stab at reformulating mass as density, as Max Jammer has pointed out in his book The Concept of Mass. The procedure would be,
‘ . . . to assign a density directly to the wave function with a distribution over the nominally infinite wavefront. Integrating this density over all three-dimensional space would then yield the mass value of the particle represented by the wave or wave packet. Such a definition of mass in quantum mechanics was in fact employed by Eddington in his reformulation of the exclusion principle by assigning a saturation value for the density of an elementary wave function.’
Eddington clearly states in his paper titled A New Derivation of the Quadratic Equation for the Masses of the Proton and Electron that the equivalence between the saturated density of a system and defining this as a particle is a circumlocution. Quoting from Eddington's paper,
‘ . . . accordingly, in extending relativity theory to microscopic physics, our starting point must be the representation of density in wave mechanics rather than the representation of mass or energy. By the general principles of wave analysis, the whole density of the system is considered to be the sum of contributions from a set of elementary wave functions. By a survival of classical terminology, we often describe the density associated with a particular wave function as due to a particle occupying the state which the wave function describes. This circumlocution is difficult to avoid, though it often involves using the term particle in a sense remote from ordinary conceptions. Our point of entry into wave mechanics is therefore the density of a fully occupied wave function in contrast to elementary quantum theory, which begins with the mass or energy of a particle.’
Following Faraday, it's clear that this analysis, which unifies mass and space via wave mechanics, avoids the many pitfalls of pursuing a false dichotomy inherent in the particle view of mass plus space or plus a void. You will find a note on gravitational and inertial mass in the additional materials section of my website. It covers the different interpretations of Newton’s spinning bucket of water and some surprising qualities of spinning gyroscopes.
Moving on to force and charge, retaining a particle view of the phenomena leads to the necessity of introducing forces, and what follows is the unpalatable and unavoidable action at a distance. To get round this problem, Heisenberg introduced something he called exchange forces. Max Jammer in his book The Concept of Force states,
‘ . . .this was done in analogy to the quantum mechanical theory of covalent bonds, such as exist between two hydrogen atoms in the hydrogen molecule. The chemical force is attractive if the wave function is symmetric under exchange of the coordinates of the electrons, and is repulsive if the wave function is anti-symmetric in this respect.’
Unfortunately, the exchange of forces were envisaged as an exchange of force carrying particles, and so the particle view mushroomed. Logically, retaining a particle view is untenable because discrete entities have to be differentiated from their surroundings, and the intervening space between any two particles cannot be bridged by the introduction of many more particles. It just moves the problem into a smaller dimension. As Leibniz pointed out,
‘ . . . no kind of arrangement will ever be found which can make a genuine substance out of a number of entities by aggregation.’
The idea of replacing charge and force with complementary shapes of a configuration of waves which can be superimposed on each other to represent attraction, and asymmetric waves out of synchronization representing repulsion is a more robust and satisfying description. In analysing force and special relativity, Max Jammer states on grounds of rejection of an absolute simultaneity of two distant events, special relativity comes to the conclusion that action at a distance has to be excluded as a legitimate physical notion. Forces, in other words, can only be contact forces. This rules out a large part of a particle description because they have charges and there is no contact between two repelling particles or attractive particles. It is like energy imported from classical physics with the billiard ball analogy. Only quantum phenomena that can be built up through superposition, namely waves, can the word contact acquire an ontological and logical meaning. One can view the concept of charge as a shorthand, as is much of the nomenclature in electrodynamics.
A constructive exercise is to read the correspondence between Faraday and William Wywell on the appropriate terminology of the new physics of electricity. Faraday wrote,
‘The usual notions attached to positive and negative and to the term current I suspect are altogether wrong, but I have not yet a clear view of what ought to be put in their place.’
Faraday also thought of aligning the two charges with a line of latitude of the Earth's magnetic field and naming them East Node and West Node. This would capture the directional motion of two waves either coming together as in attraction of proton and electron in a superposition or moving apart as in the repulsion of two protons in a form of reflection as each proton bounces off the boundary of the other. The protons in a nucleus could be considered to combine in a synchronistic way where they pulse in unison and something similar for electrons. Einstein had removed the concept of force acting at a distance in his theories of relativity, and centuries before Newton had made it clear that force was a mathematical term.
‘The words attraction, impulse, or any propensity to a centre, however, I employ indifferently and interchangeably, considering these forces not physically but merely mathematically. The reader should hence be aware lest he think that by words of this sort I anywhere define a species or mode of action or a physical cause or reason.’
That was from Principia in 1687. It is difficult not to view these early concepts as linked to Ovid's metamorphosis, describing transformations from chaos into order and the gods like energy, immortal or conserved, but changing form at will. The underlying concept is a fluidity in nature which I believe is best described by waves. The proponents of the particle view of phenomena struggle at every turn with logical and ontological problems. The resistance to wave mechanics over the decades is baffling.
If you want to find out more, please visit my website at quantumid.science, where you will find more in-depth downloadable essays, book lists, additional material, and original papers by some 19th and 20th century physicists. The next podcast is titled Fields and covers gravitational, electro, magnetic, and quantum fields. I hope you can join me again in tracking down the true identity of the quantum.
© K. Strang 2025
