Quantum Puzzle, The: Critique Of Quantum Theory And Electrodynamics

Critique of Quantum Theory and Electrodynamics

Barry R Clarke

• Publisher: WSPC
• Year: 2017
• ISBN:
  9789814696999
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

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In 1861, James Clerk–Maxwell published Part II of his four-part series "On physical lines of force". In it, he attempted to construct a vortex model of the magnetic field but after much effort neither he, nor other late nineteenth century physicists who followed him, managed to produce a workable theory. What survived from these attempts were Maxwell's four equations of electrodynamics together with the Lorentz force law, formulae that made no attempt to describe an underlying reality but stood only as a mathematical description of the observed phenomena. When the quantum of action was introduced by Planck in 1900 the difficulties that had faced Maxwell's generation were still unresolved. Since then theories of increasing mathematical complexity have been constructed to attempt to bring the totality of phenomena into order with little success. This work examines the problems that had been abandoned long before quantum mechanics was formulated in 1925 and argues that these issues need to be revisited before real progress in the quantum theory of the electromagnetic field can be made.

--> Contents:

• Introduction
• The Faraday–Maxwell Fields
• The Electron
• Blackbody Radiation
• Atomic Structure
• Light and Action
• Mass Vortex Rings
• The Magnetic Vortex Field
• The Electric Vortex Field

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Readership: Advanced undergraduate and graduate students interested in quantum physics.
-->Quantum Physics;Quantum Mechanics;History of Science;Hydrogen Atom;Electromagnetism;Barry Clarke Key Features:

• Written by Daily Telegraph (UK) puzzlist
• All derivations are complete and so easy to follow
• Invites the reader to think about the still unsolved conceptual difficulties

1 Introduction

I still believe in the possibility of a model of reality–that is, to say, of a theory which represents things themselves and not merely probabilities of their occurrence.

— (Albert Einstein)¹

1.1The method of theoretical physics

After the Bohr-Heisenberg philosophy had demanded the abandonment of all attempts to produce a visualizable theory of atomic structure and fields, and focus instead on the mere description of sense data, physics began to hit an impasse. As a result, theory has descended into two unproductive epistemologies, rationalism and empiricism, the exclusivity of which Popper has argued against in his Logik der Forschung (1935).²

For those physicists who have taken a rationalist position, visual clarity has been sacrificed at the altar of mathematical economy. As Baggott aptly puts it

Some modern theoretical physicists have sought to compensate for this loss of understanding [... and have] been led – unwittingly or otherwise – to myth creation and fairy tales [...] wrestling with problems for which there are as yet no observational or experimental clues to help guide them towards solutions. They have chosen to abandon the scientific method [...] for a ‘post-empirical science’. Or if you prefer, they have given up [... and] these theorists have been guided instead by their mathematics and their aesthetic sensibilities.³

Paul Dirac, who focused exclusively on mathematical form and for whom the creation of a visual model was not a desirable goal, might well have been the inspiration for this movement:

the main object of science is not the provision of pictures, but it is the formulation of laws governing phenomena and the application of these laws to the discovery of new phenomena [...] In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word ‘picture’ by means of which is meant a model functioning essentially on classical lines.⁴

Mathematics is a language that should be used to convey the geometrical structure of Nature, not presented as a representation of Nature itself. Such a structure is to be discovered by an iterative process of postulate and test against the results of experiments. If an idea falls short against experiment it is to be adjusted. It is a metaphysical mistake to disconnect from empirical data altogether, and believe that the criterion of formal economy in mathematical structure is the sole guide to what the fundamental concepts might be. It would be like asserting that, given two men in dialogue, the one who speaks more articulately expresses the greater degree of reality. Mathematics must not be the content of the theory but a means of expressing the content, and the content must be a visualisable geometrical model honed from its repeated improvement as new experimental data is accommodated. Even four hundred years ago, Francis Bacon had the wisdom to suggest that “mathematics, [...] ought only to give definiteness to natural philosophy, not to generate or give it birth.”⁵

Those physicists who have elected to follow an empiricist approach have completely abandoned the program of geometrically elucidating the unobservable world that must lie behind our perceptions.⁶ In confining themselves to the description of phenomena, the concepts that any such scheme attempts to represent, being only one level removed from our unprocessed sense data, cannot possibly be fundamental enough to embrace a unifying scheme. In his Treatise, Maxwell had the integrity to recognise the need for a realistic geometrical model:

A knowledge of these things [whether or not a current is material] would amount to at least the beginnings of a complete dynamical theory of electricity, not, as in this treatise, as a phenomenon due to an unknown cause, subject only to the general laws of dynamics, but as a result of known motions of known portions of matter, in which not only the total effects and final results, but the whole intermediate mechanism and details of the motion, are taken as objects of study.⁷

It will be argued in this work that his progress was impeded by attempting to construct light rays from a matter ether rather than the proposal presented here, matter from a light-ray ether. Unfortunately, in his commentary on the electromagnetic field, Lorentz did not share Maxwell’s philosophy

we need by no means go far in attempting to form an image of it and [...] we can develop the theory to a large extent and elucidate a great number of phenomena, without entering upon speculations of this kind. Indeed, on account of the difficulties into which they lead us, there has of late years been a tendency to avoid them altogether and to establish the theory on a few assumptions of a more general nature.⁸

At least Maxwell found a supporter in Larmor

The time has fully arrived when, if theoretical physics is not to remain content with being merely a systematic record of phenomena, some definite idea of the connexion between aether and matter is essential to progress.⁹

There are problems that still remain unresolved from this era. Reporting on the work of his father Carl Anton Bjerknes, Vilhelm Bjerjnes has declared

We have theories relating to these [E-M] fields, but we have no idea whatever of what they are intrinsically, nor even the slightest idea of the path to follow in order to discover their true nature.¹⁰

In more recent times, David Deutsch has called for a return to the contemplation of the world beyond the senses:

Being able to predict things or to describe them, however accurately, is not at all the same thing as understanding them [...] Facts cannot be understood just by being summarized in a formula [...] Scientific theories explain the objects and phenomena of our experience in terms of an underlying reality which we do not experience directly [...] To [some scientists ...] the basic purpose of a scientific theory is not to explain anything, but to predict the outcomes of experiments [...] This view is called instrumentalism (because it says that a theory is no more than an instrument for making predictions).¹¹

In the last century, the focus has been mainly on the ‘particle’ and ‘wave’ concepts. The photographs of tracks in a Wilson cloud chamber undoubtedly point to directed emissions.¹² However, Wilson as well as those who followed him assumed that each of these directed emissions was a ‘particle’, that is, a solid undefined substance contained in a arbitrarily small but finite bounded spherical volume. On the other hand, the work of Davisson and Germer in which an electron beam passing through a crystal of nickel showed that the beam intensity depended on the scattering angle, clearly pointed to a wave-like interference effect. This diffraction phenomenon required that the emission was not confined to a small localized spherical volume but that it needed a lateral spatial extent in order for parts of it to interfere with other parts.¹³ Davisson and Germer assumed, as did those that followed them, that they were witnessing a wave front of matter. However, neither the ‘particle’, ‘wave’, nor ‘wave-particle’ theories has led to the desired clarification of mass, charge, and field.

Taking all this into account, it is the abandonment of the program of finding a geometrical-mechanical theory of the electric and magnetic fields at the turn of the twentieth century that needs to be addressed. It should now be accepted that no combination of a ‘particle’ and a ‘wave’ theory can lead to a deeper understanding of Nature. However, there is a third way which has recently been receiving attention in the laboratory, and that is the notion of optical¹⁴ and electron vortices.¹⁵ These vortex tubes are directed emissions with a limited cross-section in common with particles, but they also have lateral extent in common with waves, in the form of a vortex field. In Chapters 7, 8, and 9, a new theory of the toroidal mass ring is developed based on the curved helical trajectories of circular polarized rays. These are vortex rings with two component rotations, one around the axis of the ring tube, and the other around the ring circumference, and it is suggested that it is the curvature of the Poynting vector that generates the accompanying vortex momentum field of which there is a magnetic (tube-concentric) and electric (ring-concentric) component.

Einstein has made the point that many others have made since, that

neither Maxwell nor his followers succeeded in elaborating a mechanical model for the ether which might furnish a satisfactory mechanical interpretation of Maxwell’s laws of the electro-magnetic field. The laws were clear and simple, the mechanical interpretations clumsy and contradictory.¹⁶

However, a structural model of mass and charge is absolutely necessary before reliable progress can be made in a unified theory.¹⁷

This present work returns to the problems of the late nineteeth century and shows how Coulomb’s law, the Lorentz force law, the attraction and repulsion of parallel conductors, electromagnetic induction, and the hydrogen atom ground state can all be obtained from a theory of the mass vortex ring. The concepts of mass, charge, and electric potential energy which have previously had no visualizable basis, arise naturally from this theory. An experimental test is proposed for non-conservation of charge in which the flight of cathode rays in a magnetic field is reversed in order to observe whether or not their deflection also reverses. A further test is proposed for the speed of cathode rays through crossed electric and magnetic fields which it is suggested has been overestimated.

However, a theory need not offer new predictions to be instructive. In 1543, when Copernicus published the De revolutionibus orbium coelestium,¹⁸ there was an important feature of his heliocentric theory that immediately raised it above the Apollonius–Ptolemy geocentric model of deferents, epicycles, and equants.¹⁹ The seven double-rotation geocentric models that had been proposed to account for the motions in the then-known solar system²⁰ could be replaced by a unified model that employed single-rotation circular orbits. Although the Copernican system could provide no better agreement with data than the geocentric theory, it dramatically reduced the number of independent hypotheses required for the model to function. In fact, a better agreement had to wait for Kepler’s introduction of elliptic orbits,²¹ a development that finally secured the heliocentric system’s advantage over its predecessor. An example such as this suggests that even if a new theory offers no new results, the principle of theoretical economy is an important measure of the ‘truth’ content of any theory that has been proposed to imitate the machinery of Nature.

My wish for the mass ring theory outlined in these pages, is that those with a greater mathematical facility might identify any imperfections, recognise its utility, and press its application further. As Popper very wisely said:

We must be clear in our own minds that we need other people to discover and correct our mistakes (as they need us); especially those people who have grown up with different ideas in a different environment.²²

Although the theory of the vortex mass ring presented here leaves many unanswered questions, my aim has been merely to focus attention to a point where I believe others might better direct their efforts. In the words of Francis Bacon, “I have only taken upon me to ring a bell to call other wits together”.²³

1.2Overview of the work

Chapter 2 deals with the theory of the Maxwell–Faraday fields. A detailed background to this work is given, covering the early experiments on static electricity, the one- and two-fluid theories of electricity, the...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Acknowledgments
• Prologue
• Contents
• Chapter 1: Introduction
• Chapter 2: The Faraday–Maxwell Fields
• Chapter 3: The Electron
• Chapter 4: Blackbody Radiation
• Chapter 5: Atomic Structure
• Chapter 6: Light and Action
• Chapter 7: Mass Vortex Rings
• Chapter 8: The Magnetic Vortex Field
• Chapter 9: The Electric Vortex Field
• Appendix A
• Appendix B
• Appendix C
• Epilogue
• Bibliography
• About the Author
• Index