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2/2 [sorry that this will be out of order] For a (physical) relativist, the speed of light is really simple. c = 1, everywhere and everywhen. <https://en.wikipedia.org/wiki/Geometrized_unit_system> This is because we have excellent evidence for the utility of <https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#App...>, and the further astrophysically-driven demands of global hyperbolicity or at least reasonably strong causality conditions, no isometric embeddings, geodesic incompleteness, asymptotic flatness around sources, junctions in sufficiently flat space, and energy conditions. Those further demands are the basis for continuing to rely on Special Relativity in laboratory settings. For a theoretical relativist, well, the best metric signature is probably +,+,+,...,+ (89,0). (cf. Egan's (4,0) "Riemannian General Relativity", <https://www.gregegan.net/ORTHOGONAL/06/GRExtra.html>) - -- [1] quoting your wikipedia link, "... inertial frames and coordinates are defined from the outset so that space and time coordinates as well as slow clock-transport are described isotropically". Well, yes. Establish points first then assign coordinate labels is the relativist's procedure, surely? On this point, Earth laboratories are in general not in inertial frames, thanks to gravitation. No laboratory is in general in an inertial frame, thanks to the metric expansion of space. We can in principle extract a preferred foliation (e.g. the scale factor a, or some function on lunisolar tides) and use that as the basis for time coordinates instead. In effect this is what we do for high-redshift objects and many lunar laser ranging experiments <https://ssd.jpl.nasa.gov/ftp/eph/planets/ioms/>[a] <https://arxiv.org/abs/1606.08376> §3,§4. <https://link.springer.com/article/10.1007/s10569-010-9303-5> discusses aspects of how to choose a preferred foliation (in the context of gauge freedom) in the solar system, and in the context of grinding out a results-prediction for some future LLR experiment. The goal is to be able to show that the locations of the three instruments were accurately predicted, and Lorentz-invariance is thoroughly baked in (the calculations are so exceptionally sensitive to the introduction of tiny breaking parameters in the style of SME <https://arxiv.org/abs/0801.0287> that it has led to the discovery and/or better understanding of several of the features listed as parameters at [[a] LLR_Model_2020_DR.pdf §4]). [2] <https://archive.org/details/principleofrelat00eins/page/n189...>. Einstein 1916 is adapted into the arguably handier <https://en.wikisource.org/wiki/The_Foundation_of_the_General...> §9. c.f. there pages marked in square brackets [776-777] [3] Baez: <https://math.ucr.edu/home/baez/einstein/node2.html> 2nd and 3rd paragraph "Preliminaries". |