Physical foundations for relativistic spacetimes are revisited in order to check at what extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the foundations of special relativity and classical mechanics) are shown to correspond with a double linear approximation in the measurement of space and time. While general relativity appears by dropping the first linearization, Finsler spacetimes appear by dropping the second one. The classical Ehlers–Pirani–Schild approach is carefully discussed and shown to be compatible with the Lorentz–Finsler case. The precise mathematical definition of Finsler spacetime is discussed by using the space of observers. Special care is taken in some issues such as the fact that a Lorentz–Finsler metric would be physically measurable only on the causal directions for a cone structure, the implications for models of spacetimes of some apparently innocuous hypotheses on differentiability, or the possibilities of measurement of a varying speed of light.

中文翻译：

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观察者观点的芬斯勒时空的基础

相对论时空的物理基础被重新研究，以检查芬斯勒时空在其框架中处于何种程度。基于惯性观测器的论点（如狭义相对论和经典力学的基础）在空间和时间的测量中与双线性近似相对应。广义相对论通过删除第一个线性化而出现，而Finsler时空则通过删除第二个线性化而出现。仔细讨论了经典的Ehlers–Pirani–Schild方法，并证明它与Lorentz–Finsler案例兼容。使用观察者的空间讨论了芬斯勒时空的精确数学定义。