牛顿相对论、引力与宇宙学
Newtownian Relativity, Gravity, and Cosmology
摘要：
牛顿引力可以被理解为时空中的测地线运动，其中时间是绝对的，空间是欧几里得的。赫克曼所表述的牛顿宇宙学与嘉当将牛顿力学表述为时空中的测地线运动的表述是一致的，但并没有揭示其背后的几何图景。本文介绍了Cartan和Heckmann发展的牛顿力学和引力的变换理论，并通过坐标变换证明了Heckmann的牛顿宇宙学模型有一个中心，因此宇宙学原理不能全局成立。相对性原理与相对主义的立场是可能混淆的。马赫原理与后者关系很大，与前者无关。广义相对论和非线性动力学都告诉我们，大多数坐标系是由全局不可积的微分方程局部定义的：局部坐标的全局扩展通常不存在。我解释如何定义惯性系局部的自由降落短路马赫的哲学objectios牛顿动力学。
英文摘要：
Well-known to specialists but little-known to the wider audience is that Newtonian gravity can be understood as geodesic motion in space-time, where time is absolute and space is Euclidean. Newtonian cosmology formulated by Heckmann agrees implicitly with Cartan's formulation of Newtonian mechanics as geodesic motion in space-time, but does not unfold the underlying geometric picture. I present the transformation theory of Newtonian mechanics and gravity developed by Cartan and Heckmann, and show via coordinate transformations that Heckmann's Newtonian cosmological model has a center, so that the cosmological principle cannot hold globally. It is possible to confuse the relativity principle with a position of relativism. Mach's principle has much to do with the latter and nothing to do with the former. Both general relativity and nonlinear dynamics inform us that most coordinate systems ae defined locally by differential equations that are globally nonintegrable: global extensions of local coordinates usually do not exist. I explain how defining inertial frames locally by free fall short-circuits Mach's philosophic objectios to Newtonian dynamics.
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