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Article

The Geometrical Meaning of Spinors Lights the Way to Make Sense of Quantum Mechanics

Laboratoire des Solides Irradiés, Institut Polytechnique de Paris, UMR 7642, CNRS-UMR-Ecole Polytechnique, Route de Saclay, F-91128 Palaiseau CEDEX, France
Academic Editor: Manuel Asorey
Symmetry 2021, 13(4), 659; https://doi.org/10.3390/sym13040659
Received: 22 March 2021 / Revised: 3 April 2021 / Accepted: 9 April 2021 / Published: 12 April 2021
(This article belongs to the Special Issue Symmetry in the Foundations of Physics)
This paper aims at explaining that a key to understanding quantum mechanics (QM) is a perfect geometrical understanding of the spinor algebra that is used in its formulation. Spinors occur naturally in the representation theory of certain symmetry groups. The spinors that are relevant for QM are those of the homogeneous Lorentz group SO(3,1) in Minkowski space-time R4 and its subgroup SO(3) of the rotations of three-dimensional Euclidean space R3. In the three-dimensional rotation group, the spinors occur within its representation SU(2). We will provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra. We will then use the understanding that is acquired to derive the free-space Dirac equation from scratch, proving that it is a description of a statistical ensemble of spinning electrons in uniform motion, completely in the spirit of Ballentine’s statistical interpretation of QM. This is a mathematically rigorous proof. Developing this further, we allow for the presence of an electromagnetic field. We can consider the result as a reconstruction of QM based on the geometrical understanding of the spinor algebra. By discussing a number of problems in the interpretation of the conventional approach, we illustrate how this new approach leads to a better understanding of QM. View Full-Text
Keywords: quantum mechanics; group theory; spinors quantum mechanics; group theory; spinors
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MDPI and ACS Style

Coddens, G. The Geometrical Meaning of Spinors Lights the Way to Make Sense of Quantum Mechanics. Symmetry 2021, 13, 659. https://doi.org/10.3390/sym13040659

AMA Style

Coddens G. The Geometrical Meaning of Spinors Lights the Way to Make Sense of Quantum Mechanics. Symmetry. 2021; 13(4):659. https://doi.org/10.3390/sym13040659

Chicago/Turabian Style

Coddens, Gerrit. 2021. "The Geometrical Meaning of Spinors Lights the Way to Make Sense of Quantum Mechanics" Symmetry 13, no. 4: 659. https://doi.org/10.3390/sym13040659

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