TL;DR
This paper constructs 4D Minkowski space-time from quantum harmonic oscillators, linking quantum physics to space-time geometry and exploring Lorentz invariance and potential applications in quantum optics and condensed matter.
Contribution
It introduces a novel method to derive Minkowski space-time from quantum harmonic oscillators and discusses extensions related to quantum optics and condensed matter physics.
Findings
Minkowski space-time can be constructed from quantum harmonic oscillators.
Lorentz invariance is recovered in the constructed space-time.
Connections to quantum optics and condensed matter physics are discussed.
Abstract
A construction of the real 4D Minkowski space-time starting from quantum harmonic oscillators is proposed. First, a 2D spinor space and its dual are derived from the standard commutation relations obeyed by the ladder operators of two independent 1D harmonic oscillators. The complex 4D Minkowvski vector space V is then constructed from these spinor space. The flat, real 4D Minkowski manifold is finally built as an approximate description of a manifold of unitary operators constructed from V. Lorentz invariance is recovered and several possible extensions are discussed, which connections to quantum optics and condensed matter physics.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Quantum Mechanics and Applications · Relativity and Gravitational Theory