Abstract
The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics; the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.
Highlights
For the electron, Dirac’s unspecified “internal motion”, that is implied by relativity and quantum physics, is only fleetingly mentioned in his Principles [1]
The first is the “internal motion” in the wave function of the electron that is expressed through dispersion dynamics; the second is the physical origin for mathematical quantization
The model of the packet opposes one kind of quantum theory that is axiomatic and mathematical, against physical quantum mechanics that is empirical
Summary
Dirac’s unspecified “internal motion”, that is implied by relativity and quantum physics, is only fleetingly mentioned in his Principles [1]. Each method has its merit at different phases of development in various fields in physics This merit is partly psychological: mathematical tautologies carry undeniable certainties: as a simple example, the summation 2 + 2 = 4 is certain because of number definition. Some examples of these features are described in what follows. Some examples of these features are described in what follows1 Whereas mathematicians believe their axioms when they are consistent within restrictive incompleteness [12] [13]; in physics by contrast, only falsifiable propositions are admissable: they begin logically “true”, and become unphysical upon. Approximate solutions at low relativistic energies can be accounted more than occurs in a wide literature e.g. [14] [15]
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