The language of Einstein spoken by optical instruments

Abstract

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincaré sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.

LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceedings

References in corpus (6)

• Stokes Parameters as a Minkowskian Four-vector
• Wigner Rotations and Iwasawa Decompositions in Polarization Optics
• Iwasawa Effects in Multi-layer Optics
• Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics
• Lens optics as an optical computer for group contractions
• Binary Representations of ABCD Matrices

Cited by in corpus (1)

• Quantum Trajectory Thermodynamics with Discrete Feedback Control