The Particle Menace Part 2 The Wave Model of the Atom

Schrodinger's wave model of the atom is described and how he chose to interpret it by looking for analogies in light and fluid mechanics. His realism was rejected and one of the main criticisms was that the wave model could not provide the permanence and stability required of the atom. This criticism is dealt with in the fifth podcast in this second series, on 'The Space Theory of Matter and the Vortex Atom'. On the website there is a more detailed essay, a note on Dirac and the QFT, a booklist and  papers by C.G. Darwin 'The Electron as a Vector Wave' and Maxwell's 'Analogies in Nature'. 

Transcript

The Particle Menace Part 2: The Wave Model of the Atom

Hello. The previous podcast highlighted the shortcomings of the solar system model of the atom. This podcast looks at Schroödinger's alternative wave model. Schrödinger believed that atomic activity could best be expressed by a wave model of the atom. For example, he argued that it was more intuitive to view the movement or changes in the energy of electrons as the changes in frequency of a standing wave. That is why he maintained that his famous wave equation described real physical activity. The mathematics and the solution to his wave equation forced him to use the imaginary number i, and so the resulting wave function was complex. It had a real part and an imaginary part. There is, however, nothing imaginary about i. It is a mathematical method of avoiding tedious trigonometry and has been around for centuries. The key is that use of the complex function is avoidable, but involves a lot of trigonometry, explained more fully in the additional material section for the podcast on the Quantum Cat meets the Quantum Computer. 

   Einstein had told Schrödinger, ‘of course every theory is true, provided you suitably associate its symbols with observed quantities.’ As Max Jammer points out in his book The Philosophy of Quantum Mechanics, the formalism of wave mechanics had preceded its interpretation, but an interpretation could be arrived at, ‘by showing that the formalism F of Schrödinger's wave mechanics could be regarded as being part of, or at least isomorphic with, the formalism F of another theory, T, which was fully interpreted’. Schrödinger looked for parallels in the well-developed classical physics of electromechanics and hydrodynamics. In this he was following the traditions of the physicist -philosophers of the 19th century, particularly Maxwell. Maxwell was not content with using terms such as attraction, repulsion, lines of force and charge without understanding the mechanism under which they operated. And in arriving at his dynamical theory, he drew upon analogous phenomena such as light, fluid, and heat. He defended his appeal to those other areas of scientific inquiry in his paper Analogies of Nature:

‘Whenever scientists see a relation between two things they know well and think they see there must be a similar relation between things less known, they reason from one to the other. This supposes that although pairs of things may differ widely from each other, the relation in the one pair may be the same as that in the other. Now, as in a scientific point of view, the relation is the most important thing to know. A knowledge of the one thing leads us a long way towards a knowledge of the other.’ 

   In following past masters, a certain amount of opprobium was cast on Schrödinger as being behind the times and clinging to the outdated classical idea that physics describes reality. It was argued this no longer held true, and Schrödinger had to be left behind in the new age of indeterminacy and counterintuitive phenomena such as entanglement and superposition of particles and so on. Notwithstanding the success of the Copenhagen interpretation at predicting results, I believe it was a blunder which has led physics down a rabbit hole. The classic wave function describes the displacement of the wave at a point in time, and Schrödinger's function should do much the same thing, but because of the determination to construe the structure of the atom in terms of particles, virtual or real, the equation was hijacked and basically the maximum displacement of the wave, that is the amplitude, was identified not as stimulating the appearance of a particle, but as the probability of locating a particle. 

   I believe Schrödinger accepted that a wave packet could be mathematically construed as a particle without relinquishing his belief in the ontological priority of waves. Schrödinger tried to clarify his position in his acceptance speech for the Nobel Prize in Physics in 1933, entitled The Fundamental Idea of Wave Mechanics. He describes how the old model of the structure of the atom, although fine for macroscopic interactions, is inadequate at these minute scales, and how the wave mechanical description is more natural and appropriate. 

‘This is the reason why in these minute systems the old view was bound to fail, which though remaining intact as a close approximation for gross mechanical processes, is no longer adequate for the delicate interplay in areas of the order of magnitude of one or a few wavelengths. It was astounding to observe the manner in which all those strange additional requirements developed spontaneously from the new undulatory view, whereas they had to be forced upon the old view to adapt them to the inner life of the atom and to provide some explanation of the observed facts.’

   A fuller account of Schrödinger's argument is in the essay accompanying this podcast. The most telling criticism against the wave model of the atom was that its structure could not endure. Lorentz, who preferred the wave model, nevertheless pointed out that a wave packet, which, when moving with the group velocity, should represent a particle, can never stay together and remain confined to a small volume in the long run. 

‘The slightest dispersion of the medium will pull it apart in the direction of propagation, and even without that dispersion, it will always spread more and more in the transverse direction. Because of this unavoidable blurring, a wave packet does not seem to me to be very suitable for representing things to which we want to ascribe a rather permanent individual existence.’ 

   This flaw in the wave model is addressed in the fifth podcast on the space theory of matter and the vortex atom. For those who eschewed models of any type and believed mathematical formalism was the correct approach, following Dirac was considered the best course, despite all the logical anomalies his relativistic wave equation encountered. There is a critique of Dirac and quantum field theory and a note on renormalization in the additional material sections of the website for this podcast and a later one on fields. 

   Sticking obstinately to the particle model reverses progress and the return to a solar system of orbits and forces. Forces, along with charges, are as occult as the Greek god Zeus, but in modern imagination stripped of a personality. Reformulating these as motion and direction of waves, I believe, would go some way in providing a clearer ontological picture and bring together classical and quantum physics. By this I mean a scalable ontology. 

   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 Farewell to Primitive Concepts and looks at how to replace some primitive concepts associated with particle physics that may be blocking progress. I hope you can join me again in tracking down the true identity of the quantum.

© K. Strang