Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity

Abstract

Two-photon states produce enough symmetry needed for Dirac's construction of the two-oscillator system which produces the Lie algebra for the O(3,2) space-time symmetry. This O(3,2) group can be contracted to the inhomogeneous Lorentz group which, according to Dirac, serves as the basic space-time symmetry for quantum mechanics in the Lorentz-covariant world. Since the harmonic oscillator serves as the language of Heisenberg's uncertainty relations, it is right to say that the symmetry of the Lorentz-covariant world, with Einstein's $E=m{c}^2$, is derivable from Heisenberg's uncertainty relations.

arXiv commentLatex 16 pages with 6 figuresbased on an invited talk presented at the 26th International Conference on Quantum Optics and Quantum Information (Minsk, Belarus, May 2019)