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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 it a minimum of assumptions and seeks to find a new dynamical 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 the first three in a series of papers on the theory of the discrete electron. 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 On the Quantum Kinematics of the Electron and Chemical Periodicity Abstract: The application of quantum mechanics to chemistry has not led naturally to an explanation of the well known periodicity of reactivity among the natural elements. Here an analysis of the oscillation of the Dirac electron, in a discrete framework, coupled with the Aristotelian distinction between potential and actual leads to a description of electron kinematics that is quantum mechanical and dependent upon the rules of special relativity with respect to mass, the speed of light and the mass–energy transformation relation; Lorentz symmetry is also preserved. Upon extension of the analysis to the component particles of the atom, it is found that the single-atom electron collectivities of the noble gases are uniquely complete and chemically inert; they lack the potential to donate, share or engage the electrons of other atoms. Electron collectivities mirror orbital configurations for the noble gases helium to krypton. Key words: Oscillation of the Dirac electron, Actualization of Potential, Chemical Periodicity, Quantum Mechanics and Special Relativity, Noble Gases Full Text is here
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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 it a minimum of assumptions and seeks to find a new dynamical 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 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: The application of quantum mechanics to chemistry has not led naturally to an explanation of the well known periodicity of reactivity among the natural elements. Here an analysis of the oscillation of the Dirac electron, in a discrete framework, coupled with the Aristotelian distinction between potential and actual leads to a description of electron kinematics that is quantum mechanical and dependent upon the rules of special relativity with respect to mass, the speed of light and the mass–energy transformation relation; Lorentz symmetry is also preserved. Upon extension of the analysis to the component particles of the atom, it is found that the single-atom electron collectivities of the noble gases are uniquely complete and chemically inert; they lack the potential to donate, share or engage the electrons of other atoms. Electron collectivities mirror orbital configurations for the noble gases helium to krypton.

Key words: Oscillation of the Dirac electron, Actualization of Potential, Chemical Periodicity, Quantum Mechanics and Special Relativity, Noble Gases