Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity

TL;DR

This paper explores how quantum optics, through two-photon states and harmonic oscillators, can underpin the derivation of Lorentz symmetry and relativity from quantum mechanical principles.

Contribution

It demonstrates that the Lorentz-covariant space-time symmetry can be derived from quantum optical constructs and Heisenberg's uncertainty relations.

Findings

Two-photon states produce symmetry for Dirac's two-oscillator system.

The O(3,2) symmetry can be contracted to the Lorentz group.

Lorentz symmetry is derivable from quantum uncertainty relations.

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 $E = mc^2$, is derivable from Heisenberg's uncertainty relations.