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One of the most remarkable achievements of the project to develop quantum theory in the first three decades of the twentieth century was Dirac's relativistic equations for the electron. Like so many of the foundations of quantum mechanics, those equations were full of surprises at the time and remain, eighty years later, a mine whose ore is yet to be fully worked out. One of the ore bodies still to be extracted is an interpretation of the negative energy electron that moves at the speed of light and whose description gives an equal role to time and space. Each is a physical consequences of the Dirac equation for the electron.

The negative energy solutions remain a challenge to the physical relevance of the equations. Dirac realised that the mathematics and physical reality were inconsistent, which, on the face of it, could be interpreted to mean that either was a satisfactory representation of the electron and the other was not. It also remains possible that neither were satisfactory representations of reality.

\| HOME \| QUANTUM INTERPRETATION \| DQG \| DISCRETE ELECTRON \| NUCLEAR MODEL \| Peter Fimmel's \| SPACE CONCEPT \| DISCRETENESS \| BACKGROUND IDEAS \| PROCESS \| ORDER \| Web Site The Discrete Electron Discrete Electrodynamics One of the most remarkable achievements of the project to develop quantum theory in the first three decades of the twentieth century was Dirac's relativistic equations for the electron. Like so many of the foundations of quantum mechanics, those equations were full of surprises at the time and remain, eighty years later, a mine whose ore is yet to be fully worked out. One of the ore bodies still to be extracted is an interpretation of the negative energy electron that moves at the speed of light and whose description gives an equal role to time and space. Each is a physical consequences of the Dirac equation for the electron. The negative energy solutions remain a challenge to the physical relevance of the equations. Dirac realised that the mathematics and physical reality were inconsistent, which, on the face of it, could be interpreted to mean that either was a satisfactory representation of the electron and the other was not. It also remains possible that neither were satisfactory representations of reality. Dirac’s response was to leave the prevailing picture of reality in place and to remove the inconsistency by extending the mathematics. He proved that, by a unitary symmetry transformation, negative energy solutions could be transformed into positive energy solutions with opposite charge and the same mass. In taking the decision to extend the mathematics, Dirac made a choice between the alternatives of mathematics and reality and he chose in favour of the latter. The other alternative, which is studied here, assumes that the original mathematics were an adequate representation of the quantum electron and that the problem arises from the inadequacy of the prevailing understanding of physical reality. The present approach to understanding the electron together with the three 'unphysical' consequences of the Dirac equation begins with a minimum of assumptions and seeks to find a new kinematical framework in which the electron behaves both quantum mechanically and relativistically while remaining consistent with observed phenomena. The starting point of the investigation is the issue of the reality of mathematical models. Mathematics is very often assumed to represent reality with little in the way of closely reasoned argument. Here it is assumed that what is a monumental mathematical achievement in the history of twentieth-century physics needs no tinkering to make it congruent with reality. Rather, it is the equation that is trying to tell us something about how reality actually works. The following are four in a series of papers on the theory of the discrete electron. Title On the Electrodynamics of Stationary Events Abstract: The present paper traces the consequences of a natural reinterpretation of the allowed energy states of the Dirac electron. It is argued that a physical model should not rely upon quantity and number. That constraint is met by the substitution of the mathematical opposites of positive and negative with the physical opposites of actual and potential, which leads naturally to a picture of elementary particle behaviour which conforms with special relativity, and exhibits many well-known counterintuitive features of quantum mechanics. Individual elementary particles oscillate between actual and potential states. The oscillation requires that geometrical relations and other observables are discrete. In addition, stationarity is generalized to all system variables. The oscillation is serial oneparticle creation and annihilation, in which particle position changes not by continuous motion but by stochastic re-localization in time and space. Spacetime for the electron is serially absent and continuous. The energy of an elementary particle can only be known for the duration of a complete cycle of the oscillation and not at an instant. Energy is bounded from below and is always non-negative. The model physically restricts particle interactions to two-particle antisymmetrical ensembles, which therefore comply naturally with Pauli exclusion. Key words: Discrete electron • Physical model • Quantum mechanics • Special relativity • Mathematics and reality. Full Text is here Title A Discrete Model of the Dirac Electron Abstract The relativistic equation for the electron, when first developed by Dirac, had several problematic physical consequences. Among them were the physical reality of the allowed negative energy states of the electron. Dirac assumed that the problem was due to a mathematical shortcoming rather than the adequacy of the usual picture of physical reality and so he extended the mathematics in order to bring it into better agreement with reality. We return to the problem of the reality of mathematical models and entertain the proposition that Dirac's original mathematics is a satisfactory representation of Nature and turn our attention to the kind of physical reality of which the mathematics could be indicative. By subjecting the analysis to a broader than usual special relativistic constraint we are led to a picture of the electron whose chief feature is a continual actualisation of potential, of the Aristotelian type. The model is novel and contrary to the doctrine of continuity; it is parsimonious and conforms with the well-known counterintuitive quantum behaviour of elementary particles. Key words: Discrete Dirac electron • Physical model • Quantum theory • Special relativity • Mathematics and reality Full Text is here Title On the Electrodynamics of Motionless Events Abstract: The problem of electrodynamics among charged particles is analyzed by a physical interpretation of the consequences of the Dirac relativistic equation for the electron. By replacing the mathematical opposites of positive and negative energies with the physical opposites of actual and potential energies and serially coupling them in an oscillation the electron becomes fully discrete in both space and time. When the oscillations of individual charged particles and photons are suitably geometrically related their classical aspects reduce to motionless events whose genesis and interactions form a seamless union of quantum mechanics and special relativity. The model is simply particulate, fields and waves play no role. The logical development of the extension of the model among electrons and protons leads naturally to the electromagnetic interaction of the components of the helium atom. Full Text is here Title Chemical Inertness of the Group 18 Elements Evolves Naturally with the Extension of the Discrete Kinematics of the Dirac Electron Abstract: We describe a fully deductive explanation of the chemical inertness of the group 18 (VIIIA) elements of the periodic system. A qualitative analysis of the oscillation of the Dirac electron, coupled with the Aristotelian doctrine of the actualization of immaterial potential, is sufficient for a description of discrete, charged-particle kinematics that is quantum mechanical and dependent upon the rules of special relativity. In that framework, an extension of the kinematics of the one-electron system is shown to evolve naturally into the single-atom, electromagnetic interactions of each member of the group 18 elements. The virtual photon- and electron–pair coboson–mediated electromagnetic interactions of the charged-particle ensembles for a single, neutral atom of each member of the group 18 elements forms a complete interaction. That completeness leaves no tendency to react with additional electrons, and is unique to the group 18 elements. The electron collectivities of the interactions of the group 18 elements from helium to krypton are seen to mirror the electron occupancies of the quantum orbitals of those elements. The interactions of the two higher–mass elements of the group show no such relationship. Key words: group 18 elements, actualization of potential, composite bosons, quantum mechanics and special relativity PACS numbers: 82.40.Bj, 71.45.-d, 31.15.X-, 31.15.aq Full Text is here
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© Peter Fimmel 2002-2014 Last page update 15/03/14
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Dirac’s response was to leave the prevailing picture of reality in place and to remove the inconsistency by extending the mathematics. He proved that, by a unitary symmetry transformation, negative energy solutions could be transformed into positive energy solutions with opposite charge and the same mass. In taking the decision to extend the mathematics, Dirac made a choice between the alternatives of mathematics and reality and he chose in favour of the latter.

The other alternative, which is studied here, assumes that the original mathematics were an adequate representation of the quantum electron and that the problem arises from the inadequacy of the prevailing understanding of physical reality. The present approach to understanding the electron together with the three 'unphysical' consequences of the Dirac equation begins with a minimum of assumptions and seeks to find a new kinematical framework in which the electron behaves both quantum mechanically and relativistically while remaining consistent with observed phenomena.

The starting point of the investigation is the issue of the reality of mathematical models. Mathematics is very often assumed to represent reality with little in the way of closely reasoned argument. Here it is assumed that what is a monumental mathematical achievement in the history of twentieth-century physics needs no tinkering to make it congruent with reality. Rather, it is the equation that is trying to tell us something about how reality actually works.

Abstract: The present paper traces the consequences of a natural reinterpretation of the allowed energy states of the Dirac electron. It is argued that a physical model should not rely upon quantity and number. That constraint is met by the substitution of the mathematical opposites of positive and negative with the physical opposites of actual and potential, which leads naturally to a picture of elementary particle behaviour which conforms with special relativity, and exhibits many well-known counterintuitive features of quantum mechanics. Individual elementary particles oscillate between actual and potential states. The oscillation requires that geometrical relations and other observables are discrete. In addition, stationarity is generalized to all system variables. The oscillation is serial oneparticle creation and annihilation, in which particle position changes not by continuous motion but by stochastic re-localization in time and space. Spacetime for the electron is serially absent and continuous. The energy of an elementary particle can only be known for the duration of a complete cycle of the oscillation and not at an instant. Energy is bounded from below and is always non-negative. The model physically restricts particle interactions to two-particle antisymmetrical ensembles, which therefore comply naturally with Pauli exclusion.

Abstract The relativistic equation for the electron, when first developed by Dirac, had several problematic physical consequences. Among them were the physical reality of the allowed negative energy states of the electron. Dirac assumed that the problem was due to a mathematical shortcoming rather than the adequacy of the usual picture of physical reality and so he extended the mathematics in order to bring it into better agreement with reality. We return to the problem of the reality of mathematical models and entertain the proposition that Dirac's original mathematics is a satisfactory representation of Nature and turn our attention to the kind of physical reality of which the mathematics could be indicative. By subjecting the analysis to a broader than usual special relativistic constraint we are led to a picture of the electron whose chief feature is a continual actualisation of potential, of the Aristotelian type. The model is novel and contrary to the doctrine of continuity; it is parsimonious and conforms with the well-known counterintuitive quantum behaviour of elementary particles.

Abstract: The problem of electrodynamics among charged particles is analyzed by a physical interpretation of the consequences of the Dirac relativistic equation for the electron. By replacing the mathematical opposites of positive and negative energies with the physical opposites of actual and potential energies and serially coupling them in an oscillation the electron becomes fully discrete in both space and time. When the oscillations of individual charged particles and photons are suitably geometrically related their classical aspects reduce to motionless events whose genesis and interactions form a seamless union of quantum mechanics and special relativity. The model is simply particulate, fields and waves play no role. The logical development of the extension of the model among electrons and protons leads naturally to the electromagnetic interaction of the components of the helium atom.

Abstract: We describe a fully deductive explanation of the chemical inertness of the group 18 (VIIIA) elements of the periodic system. A qualitative analysis of the oscillation of the Dirac electron, coupled with the Aristotelian doctrine of the actualization of immaterial potential, is sufficient for a description of discrete, charged-particle kinematics that is quantum mechanical and dependent upon the rules of special relativity. In that framework, an extension of the kinematics of the one-electron system is shown to evolve naturally into the single-atom, electromagnetic interactions of each member of the group 18 elements. The virtual photon- and electron–pair coboson–mediated electromagnetic interactions of the charged-particle ensembles for a single, neutral atom of each member of the group 18 elements forms a complete interaction. That completeness leaves no tendency to react with additional electrons, and is unique to the group 18 elements. The electron collectivities of the interactions of the group 18 elements from helium to krypton are seen to mirror the electron occupancies of the quantum orbitals of those elements. The interactions of the two higher–mass elements of the group show no such relationship.

Key words: group 18 elements, actualization of potential, composite bosons, quantum mechanics and special relativity