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41 pages, 1229 KB

Open AccessArticle

The Classical Origin of Spin: Vectors Versus Bivectors

by Bryan Sanctuary

Axioms 2025, 14(9), 668; https://doi.org/10.3390/axioms14090668 - 29 Aug 2025

Cited by 1 | Viewed by 2033

There are two ways of linearizing the Klein–Gordon equation: Dirac’s choice, which introduces a matter–antimatter pair, and a second approach using a bivector, which Dirac did not consider. In this paper, we show that a bivector provides the classical origin of quantum spin. At high precessional frequencies, a symmetry transformation occurs in which classical reflection becomes quantum parity. We identify a classical spin-1 boson and demonstrate how bosons deliver energy, matter, and torque to a surface. The correspondence between classical and quantum domains allows spin to be identified as a quantum bivector,

i σ

. Using geometric algebra, we show that a classical boson has two blades, corresponding to magnetic quantum number states

m = \pm 1

. We conclude that fermions are the blades of bosons, thereby unifying both into a single particle theory. We compare and contrast the Standard Model, which uses chiral vectors as fundamental, with the Bivector Standard Model, which uses bivectors, with two hands, as fundamental. Full article

(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization)

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17 pages, 849 KB

Open AccessArticle

EPR Correlations Using Quaternion Spin

by Bryan Sanctuary

Quantum Rep. 2024, 6(3), 409-425; https://doi.org/10.3390/quantum6030026 - 13 Aug 2024

Cited by 3 | Viewed by 3291

Abstract

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic [...] Read more.

\frac{1}{2}

—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of

\frac{1}{2}

, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q₈, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox. Full article

(This article belongs to the Special Issue 100 Years of Quantum Mechanics)

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14 pages, 398 KB

Open AccessArticle

Algebrodynamics: Shear-Free Null Congruences and New Types of Electromagnetic Fields

by Vladimir V. Kassandrov, Joseph A. Rizcallah and Ivan A. Matveev

Axioms 2023, 12(11), 1061; https://doi.org/10.3390/axioms12111061 - 20 Nov 2023

Viewed by 1556

Abstract

We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (

B

) in particular. We demonstrate that any

B

-differentiable function gives rise to a null shear-free congruence (NSFC) on the

B

-vector space

C M

and [...] Read more.

We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (

B

) in particular. We demonstrate that any

B

-differentiable function gives rise to a null shear-free congruence (NSFC) on the

B

-vector space

C M

and on its Minkowski subspace

M

. Making use of the Kerr–Penrose correspondence between NSFC and twistor functions, we obtain the general solution to the equations of

B

-differentiability and demonstrate that the source of an NSFC is, generically, a world sheet of a string in

C M

. Any singular point, caustic of an NSFC, is located on the complex null cone of a point on the generating string. Further we describe symmetries and associated gauge and spinor fields, with two electromagnetic types among them. A number of familiar and novel examples of NSFC and their singular loci are described. Finally, we describe a conservative algebraic dynamics of a set of identical particles on the “Unique Worldline” and discuss the connections of the theory with the Feynman–Wheeler concept of “One-Electron Universe”. Full article

(This article belongs to the Special Issue Computational Mathematics and Mathematical Physics)

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12 pages, 3859 KB

Open AccessArticle

Homogeneous Finite-Time Pose Tracking of Leader–Following Spacecraft Formation Using a Twistor-Based Model

by Yunhe Guo, Jing Chen, Bo Zhang and Hanqiao Huang

Electronics 2023, 12(21), 4451; https://doi.org/10.3390/electronics12214451 - 29 Oct 2023

Cited by 2 | Viewed by 1690

Abstract

For integrated pose control of six-degree-of-freedom (6-DOF) leader–following spacecraft formations, the coupled relative pose between two spacecraft is described by a unified model in the framework of twistors, based on which a finite-time control law is devised for the 6-DOF dynamic system. Firstly, some necessary coordinate frames are defined, and then, relative 6-DOF dynamics of the follower spacecraft with respect to the desired frame are modeled by using twistors. Secondly, an integrated pose controller is designed for the 6-DOF formation that takes full advantage of homogeneous theory to guarantee finite-time stability. Finally, numerical simulations are carried out to validate the effectiveness of the proposed controller. Developing integrated 6-DOF formation control law based on twistors is more straightforward than conventional methods, and the finite-time algorithm achieves stronger robustness than asymptotic ones. Full article

(This article belongs to the Special Issue Autonomous Unmanned Systems Technology: Selected Papers from ICAUS 2022 and 2023)

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18 pages, 353 KB

Open AccessArticle

Philosophical Aspects of Astrobiology Revisited

by Rainer E. Zimmermann

Philosophies 2021, 6(3), 55; https://doi.org/10.3390/philosophies6030055 - 2 Jul 2021

Viewed by 3890

Abstract

Given the idea that Life as we know it is nothing but a special form of a generically underlying dynamical structure within the physical Universe, we try to introduce a concept of Life that is not only derived from first principles of fundamental physics, but also metaphysically based on philosophical assumptions about the foundations of the world. After clarifying the terminology somewhat, especially with a view to differentiating reality from modality, we give an example for a mathematical representation of what the substance of reality (in the traditional sense of metaphysics) could actually mean today, discussing twistor theory as an example. We then concentrate on the points of structural emergence by discussing the emergence of dynamical systems and of Life as we know it, respectively. Some further consequences as they relate to meaning are discussed in the end. Full article

(This article belongs to the Special Issue The Meaning of Life in the Universe)

20 pages, 391 KB

Open AccessArticle

Quaternion Electromagnetism and the Relation with Two-Spinor Formalism

by In Ki Hong and Choong Sun Kim

Universe 2019, 5(6), 135; https://doi.org/10.3390/universe5060135 - 3 Jun 2019

Cited by 10 | Viewed by 5090

Abstract

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary “i” should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotation. Full article

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35 pages, 395 KB

Open AccessReview

On Exact Solutions and Perturbative Schemes in Higher Spin Theory

by Carlo Iazeolla, Ergin Sezgin and Per Sundell

Universe 2018, 4(1), 5; https://doi.org/10.3390/universe4010005 - 1 Jan 2018

Cited by 20 | Viewed by 3434

Abstract

We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev’s equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is also described. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green’s functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev’s equation involving an infinite dimensional generalization of anti de Sitter space are revisited and improved. Full article

(This article belongs to the Special Issue Higher Spin Gauge Theories)

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