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Symmetry
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Symmetry in the Foundations of Physics
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Symmetry in the Foundations of Physics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (30 September 2021) | Viewed by 10844

Special Issue Editor

Prof. Dr. Peter Rowlands

E-Mail Website
Guest Editor
Department of Physics, University of Liverpool, Oliver Lodge Laboratory, Oxford Street, Liverpool L69 7ZE, UK
Interests: fundamental physics; quantum mechanics; quantum physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

That symmetry has been a major key to developing theories of physics is not surprising. The ability to recognize patterns has been a significant factor in the evolution of the human and other species precisely because symmetrical patterns are at the root of all natural processes. In physics the patterns have frequently assumed mathematical form as mathematics provides a compactified high-level ordering for physical symmetries. However, Nature is an accidental mathematician rather than a designer one. If we are to understand the origins of the mathematical structures at the heart of the Standard Model, for example, such as the SU(3) ×  SU(2) × U(1) theory of the fundamental forces, the 4-vector connection of space and time, the dual nature of matter and antimatter, and the triple generational arrangement of quarks and leptons, we need to step outside of these symmetries as they are now presented, and find even deeper symmetries from which they originate. We will not attain to a more fundamental understanding if we see the familiar symmetries in their present form as the foundational basis for physics. They are in themselves too complicated to be the most primitive level concepts. Many of them, for example, describe broken symmetries, an arrangement which is not likely to be primitive. Consequently, the attempt to combine the Standard Model of particle physics with, say, General Relativity in a combined theory which is inevitably more complicated is likely to lead away from the kind of foundational symmetries that are their origin. Rather than synthesis we need analysis. It is inconceivable that symmetry is not significant at the foundational level, but to reach this level we need new approaches to symmetry which explain the complex symmetries we have so far discovered in terms of ones which are simpler and more general.

Prof. Dr. Peter Rowlands
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Foundational basis of physics
  • Primitive level concepts
  • Broken symmetries
  • Standard Model
  • Mathematical representation

Published Papers (5 papers)

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Research

17 pages, 873 KiB  
Article
How Does Spacetime “Tell an Electron How to Move”?
by Garnet Ord
Symmetry 2021, 13(12), 2283; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122283 - 01 Dec 2021
Cited by 1 | Viewed by 1300
Abstract
Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way [...] Read more.
Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way that ’quantum’ propagation occurs on appropriate scales. This is done by starting in a discrete space and explicitly taking a continuum limit. The argument is direct and illuminates the special tension between ’rest’ and ’uniform motion’ found in Minkowski space, showing how the formal analytic continuations involved in Minkowski space and quantum propagation arise from the same source. Full article
(This article belongs to the Special Issue Symmetry in the Foundations of Physics)
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31 pages, 399 KiB  
Article
Iterants, Majorana Fermions and the Majorana-Dirac Equation
by Louis H. Kauffman
Symmetry 2021, 13(8), 1373; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13081373 - 28 Jul 2021
Viewed by 1509
Abstract
This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise [...] Read more.
This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands. Full article
(This article belongs to the Special Issue Symmetry in the Foundations of Physics)
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20 pages, 336 KiB  
Article
Relativistic Inversion, Invariance and Inter-Action
by Martin B. van der Mark and John G. Williamson
Symmetry 2021, 13(7), 1117; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13071117 - 23 Jun 2021
Viewed by 1496
Abstract
A general formula for inversion in a relativistic Clifford–Dirac algebra has been derived. Identifying the base elements of the algebra as those of space and time, the first order differential equations over all quantities proves to encompass the Maxwell equations, leads to a [...] Read more.
A general formula for inversion in a relativistic Clifford–Dirac algebra has been derived. Identifying the base elements of the algebra as those of space and time, the first order differential equations over all quantities proves to encompass the Maxwell equations, leads to a natural extension incorporating rest mass and spin, and allows an integration with relativistic quantum mechanics. Although the algebra is not a division algebra, it parallels reality well: where division is undefined turns out to correspond to physical limits, such as that of the light cone. The divisor corresponds to invariants of dynamical significance, such as the invariant interval, the general invariant quantities in electromagnetism, and the basis set of quantities in the Dirac equation. It is speculated that the apparent 3-dimensionality of nature arises from a beautiful symmetry between the three-vector algebra and each of four sets of three derived spaces in the full 4-dimensional algebra. It is conjectured that elements of inversion may play a role in the interaction of fields and matter. Full article
(This article belongs to the Special Issue Symmetry in the Foundations of Physics)
45 pages, 1037 KiB  
Article
The Geometrical Meaning of Spinors Lights the Way to Make Sense of Quantum Mechanics
by Gerrit Coddens
Symmetry 2021, 13(4), 659; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040659 - 12 Apr 2021
Viewed by 2884
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry in the Foundations of Physics)
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27 pages, 431 KiB  
Article
The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down
by Gerrit Coddens
Symmetry 2021, 13(1), 134; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010134 - 14 Jan 2021
Cited by 3 | Viewed by 2749
Abstract
The Stern–Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. However, that theory is based on mathematical errors [...] Read more.
The Stern–Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. However, that theory is based on mathematical errors in the way it (mis)treats spinors and group theory. We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry. Contrary to what Pauli has been reading into the Stern–Gerlach experiment, the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured. Surprisingly, this leads to only two energy states, which should be qualified as precession-up and precession-down rather than spin-up and spin-down. Indeed, despite the presence of the many different possible angles θ between the spin axis s and the magnetic field B, the fermions can only have two possible energies m0c2±μB. The values ±μB thus do not correspond to the continuum of values −μ·B Einstein and Ehrenfest had conjectured. The energy term V=−μ·B is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies ±μB, and as such not valid for individual fermions. The two fermion states with energy ±μB are not potential-energy states. We also explain the mathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clear and understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle. Full article
(This article belongs to the Special Issue Symmetry in the Foundations of Physics)
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