Dirac’s Refined Unification of Quantum Mechanics and Special Relativity: An Intertheoretic Context

Rinat M Nugayev

doi:10.46938/tv.2022.518

Abstract

One of the key episodes of history of modern physics – Paul Dirac’s startling contrivance of the relativistic theory of the electron – is elicited in the context of lucid epistemological model of mature theory change. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s sophisticated methodology of the General Relativity contrivance. The subtle structure of Dirac’s scientific research program and first and foremost the odd principles that put up its powerful heuristics is scrutinized with special emphasis on the highly controversial tenet of “mathematical beauty.” It is contended that despite the relentless Dirac’s remarks denigrating the controversial role of philosophy one can trace its indirect influence through Arthur Eddington’s and Hermann Weyl’s whimsical mathematical models. Accordingly, the milestones of Dirac’s research programme realization in the distinctive context of the applied epistemological doctrine are indicated.

Highlights

Paul Dirac’s refined unification of the special theory of relativity (STR) and nonrelativistic quantum mechanics (QM) occupies a peculiar place in the history & philosophy of science due to the following circumstances.First, Dirac’s skeptical attitude to epistemology is too well-known to dwell on
The subtle structure of Dirac’s scientific research program and first and foremost the odd principles that put up its powerful heuristics is scrutinized with special emphasis on the highly controversial tenet of “mathematical beauty.”
Dirac’s views apparently were at odds with the Weltanschauung of another smart youngster and one of his strongest competitors – Werner Heisenberg, the future author of Physik und Philosophie,1 who often quoted Kant, or, say, Niels Bohr himself, who even mentioned Sören Kierkegaard

Summary

Introduction

Paul Dirac’s refined unification of the special theory of relativity (STR) and nonrelativistic quantum mechanics (QM) occupies a peculiar place in the history & philosophy of science due to the following circumstances. It is necessary to reveal the “dual” (according to Eddington) or “hybrid” (in our terminology) nature of the theoretical object and display that it simultaneously possesses certain “geometric” properties, transforming itself as a tensor gμν and, on the other hand, has “physical” properties since it is transformed as an irreducible representation of the Poincaré group, the Lorentz group, etc. This elucidation of the so-called “physical,” operational sense of mathematical terms should allow comparing the obtained quantitative relationships with experimental data. Dirac’s theory featured the geometric properties of bispinors, but was able to predict the magnetic moment of an electron, as well as the fine structure of lines in the spectrum of atoms, and, most importantly, the existence of antiparticles (or positrons)

The Milestones of Dirac’s Electron Theory Contrivance

Main Conclusions and Prospects of the Research