dorsal/arxiv
View SchemaThe language of Einstein spoken by optical instruments
| Authors | Sibel Baskal, Y. S. Kim |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407222 |
| URL | https://arxiv.org/abs/quant-ph/0407222 |
| DOI | 10.1134/1.2055941 |
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 Poincar\'e 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.
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"abstract": "Einstein had to learn the mathematics of Lorentz transformations in order to\ncomplete his covariant formulation of Maxwell\u0027s equations. The mathematics of\nLorentz transformations, called the Lorentz group, continues playing its\nimportant role in optical sciences. It is the basic mathematical language for\ncoherent and squeezed states. It is noted that the six-parameter Lorentz group\ncan be represented by two-by-two matrices. Since the beam transfer matrices in\nray optics is largely based on two-by-two matrices or $ABCD$ matrices, the\nLorentz group is bound to be the basic language for ray optics, including\npolarization optics, interferometers, lens optics, multilayer optics, and the\nPoincar\\\u0027e sphere. Because the group of Lorentz transformations and ray optics\nare based on the same two-by-two matrix formalism, ray optics can perform\nmathematical operations which correspond to transformations in special\nrelativity. It is shown, in particular, that one-lens optics provides a\nmathematical basis for unifying the internal space-time symmetries of massive\nand massless particles in the Lorentz-covariant world.",
"arxiv_id": "quant-ph/0407222",
"authors": [
"Sibel Baskal",
"Y. S. Kim"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1134/1.2055941",
"title": "The language of Einstein spoken by optical instruments",
"url": "https://arxiv.org/abs/quant-ph/0407222"
},
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