爱因斯坦、巴塞罗那、对称性与宇宙学：宇宙方程的诞生
Einstein, Barcelona, Symmetry & Cosmology: The Birth of an Equation for the Universe
AI总结：
本文回顾爱因斯坦百年前唯一一次西班牙之行，阐述其经历如何促成爱因斯坦-弗里德曼之争，推动现代宇宙学成为物理理论，并探讨相对论原理与对称性破缺的深层联系。
摘要：
阿尔伯特·爱因斯坦一生中仅访问过西班牙一次，那恰好是一百年前。本文将解释这次访问的背景，其情形颇为特殊。特别是，爱因斯坦在那段时期经历了一些重要事件，这些事件最终对于将现代宇宙学转变为真正的物理理论起到了关键作用。其中包括著名的爱因斯坦-弗里德曼之争，首先涉及弗里德曼方程的数学有效性，随后是关于它们作为描述现实世界的可靠工具的可能用途。在讨论之前，将先概述爱因斯坦在其访问之前已经完成的相对论理论贡献背后的最深刻思想，并辅以对三种主要相对论理论（即伽利略的相对论，以及爱因斯坦的狭义和广义相对论）的非常简明的描述。这些理论为通往迄今尚未实现的终极总相对论理论铺平了道路。文中将指出，最一般的相对性原理，忠实反映了恩斯特·马赫的深远思想，可能与对称性破缺范式有很大关系，而对称性破缺是量子场论和高能物理中最为关键的工具。
英文摘要：
Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern cosmology into a genuine physical theory. Among them is the famous Einstein-Friedmann controversy, first, on the mathematical validity of Friedmann's equations and, later, their possible usefulness as a reliable tool to describe the real world. A summary of the deepest ideas underlying Einstein's contributions to the theory of relativity, which he had already completed before his visit, will precede the discussion, also supplemented with a description, in very simple terms, of the three main relativistic theories, namely Galileo's one, and Einstein's special and general theory. They pave the way towards a definitive theory of total relativity, so far unattainable. It will be recalled that the most general relativity principle, faithfully reflecting Ernst Mach's far-reaching ideas, might have much to do with the symmetry-breaking paradigm, a most crucial tool in quantum field theory and high energy physics.
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。
