Simultaneity, Convention and Gauge: Foundational and Historical Dimensions

爱因斯坦在1905年发表狭义相对论时，提出了两个关于非线性的不同命题，一个是非线性的相对性，另一个是非线性的约定性。时间的相对性说，两个类空间的分离事件，这是事件，只能通过比光更快的影响因果连接，没有客观的时间顺序相对于过去，现在和未来。在这种情况下，时间排序是相对于给定的参考系（也称为惯性系）的，并且该顺序可以从一个系到另一个系而变化。这是在课堂和教科书中通常讨论的理论的一个众所周知的结果。另一个论题，即非一致性的约定性，认为即使相对于一个给定的参照系，关于两个类空间的分离事件之一是否早于、晚于或同时于另一个事件，也没有客观事实。如果人们可以确定光在任何给定方向上的速度，那么这件事就有了一个客观的（但取决于框架的）事实。爱因斯坦解释说，没有办法做出这样的决定，并建议通过规定（即，光在所有方向上以相同的速度传播。传统性的论点已经争论了很长时间，仍然没有解决，不像相对性的一致性。这个项目建议通过考虑对爱因斯坦发现广义相对论至关重要的洞察力来大大推进我们对约定性命题的理解。它在文献中被称为洞论证，它是爱因斯坦在1915年发表通论的前一年提出的。与这一论点相关的是物理等价的概念和相关的约定性概念，两者都与关于非一致性命题的约定性的争论有关。洞论证与约定性命题的相关性迄今为止一直被忽视，显然连爱因斯坦本人也忽视了。PI希望研究的技术成果在几个实质性的，文章长度的期刊出版物中传播。更广泛的影响。由于关于这一主题的文献如此之多，PI将与马克斯·普朗克科学史研究所（柏林）关于量子物理学史的类似项目协调，建立一个可公开访问的关键书目数据库，以及一个版权不受限制的来源的数字档案，预计将托管镜像网站。数据库和数字档案旨在满足学生，教师和研究人员的需求。还将开发适用于cogito.org的教学材料--这是约翰霍普金斯大学为对数学和科学特别感兴趣的有才华的大学前青年维护的一个网络资源。PI还预计最终将编写一个技术性较低的专题专著，供学生和对科学感兴趣的公众以及广大科学家使用。请求支持。为了实现这些目标，PI要求在2008年春季学期（前一个秋季的休假学期之后）为休假时间提供4.5个月的工资支持，并在2008年夏季提供2.0个月的工资支持。

There are two distinct theses concerning simultaneity that are put forth by Einstein in his 1905 presentation of the special theory of relativity, one is the relativity of simultaneity and the other is the conventionality of simultaneity. The relativity of simultaneity says that two space-like separated events, which are events that can only be causally connected by a faster than light influence, have no objective temporal ordering with respect to past, present, and future. In such cases, the temporal ordering is relative to a given reference frame (also referred to as an inertial frame), and that order can vary from one frame to another. This is a well-known consequence of the theory that is typically discussed in the classroom and in textbooks. The other thesis, the conventionality of simultaneity, says that even with respect to a given reference frame there is no objective fact to the matter as to whether one of two space-like separated events is earlier than, later than, or simultaneous with the other. If one could determine the speed of light in any given direction, then there would be an objective (but frame dependent) fact to the matter. Einstein conjectured that there is no way to make that determination, and proposed that one introduce by stipulation (i.e., as a convention) that light travels at the same speed in all directions. The conventionality thesis has been long debated and remains unresolved, unlike the relativity of simultaneity.Intellectual Merit. This project proposes to significantly advance our understanding of the status of the conventionality thesis by considering an insight that was pivotal to Einstein's discovery of the general theory of relativity. It is known in the literature as the hole-argument, and it was introduced by Einstein one year prior to his 1915 presentation of the general theory. Associated with that argument is a notion of physical equivalence and a related notion of conventionality, and both are relevant to the debate over the conventionality of simultaneity thesis. The relevance of the hole argument for the conventionality thesis has hitherto been overlooked, apparently even by Einstein himself. The PI expects the technical results of the research to be disseminated in several substantive, article-length journal publications. Broader Impacts. Since the literature on the subject is so voluminous, the PI will construct a publicly accessible critical bibliographic data base, together with a digital archive of the copyright unrestricted sources, in coordination with a similar project on the history of quantum physics at the Max Planck Institute for History of Science (Berlin) with the anticipation of hosting mirroring web sites. The data base and digital archive are intended to serve the needs of students, teachers, and researchers alike. Also to be developed are instructional materials suitable for cogito.org - a web resource maintained by Johns Hopkins for talented, pre-college youth who are especially interested in mathematics and science. The PI also anticipates eventually writing a less technical, monograph-length treatment of the subject accessible to students and the scientifically interested public, as well as scientists at large. Support Requested. In order to achieve these goals, the PI requests 4.5 months salary support for leave time during the spring semester of 2008 (subsequent to a sabbatical semester the previous fall) and 2.0 months of salary support for the summer of 2008.