用光学仪器说的爱因斯坦的语言
The language of Einstein spoken by optical instruments
摘要：
爱因斯坦必须学习洛伦兹变换的数学才能完成麦克斯韦方程的协变公式。洛伦兹变换的数学，称为洛仑兹群，继续在光学科学中发挥重要作用。它是相干态和压缩态的基本数学语言。值得注意的是，六参数洛伦兹群可以用二乘二矩阵表示。由于射线光学中的光束传输矩阵主要基于2 × 2矩阵或$ABCD$矩阵，洛伦兹群必然是射线光学的基本语言，包括偏振光学，干涉仪，透镜光学，多层光学和庞加莱球。由于洛伦兹变换和射线光学都是基于相同的二乘二矩阵形式，因此射线光学可以进行与狭义相对论中的变换相对应的数学运算。它示出，特别是，单透镜光学提供了一个数学基础，统一的内部时空对称性的大质量和无质量的粒子在洛伦兹协变的世界。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
