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Old Game, New Rules: Rethinking the Form of Physics

5244 Birrhard, Switzerland
Academic Editor: Young Suh Kim
Symmetry 2016, 8(5), 30; https://doi.org/10.3390/sym8050030
Received: 26 February 2016 / Revised: 8 April 2016 / Accepted: 28 April 2016 / Published: 6 May 2016
(This article belongs to the Special Issue Harmonic Oscillators In Modern Physics)
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wavefunction in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras. View Full-Text
Keywords: Hamiltonian mechanics; coupled oscillators; Lorentz transformation; Dirac equation; 45.20.Jj; 47.10.Df; 41.75; 41.85; 03.65.Pm; 05.45.Xt; 03.30.+p; 03.65.-w; 29.27.-a Hamiltonian mechanics; coupled oscillators; Lorentz transformation; Dirac equation; 45.20.Jj; 47.10.Df; 41.75; 41.85; 03.65.Pm; 05.45.Xt; 03.30.+p; 03.65.-w; 29.27.-a
MDPI and ACS Style

Baumgarten, C. Old Game, New Rules: Rethinking the Form of Physics. Symmetry 2016, 8, 30.

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