4 ms·
Because we define the speed of light in terms of spatially homogeneous and isotropic inertial coordinates. We do that because we want "the statements of the na
by cygx 7y ago
Because we define the speed of light in terms of spatially homogeneous and isotropic inertial coordinates.
We do that because we want "the statements of the natural laws [to be] as simple as possible" (Poincaré), but it's not the only way to do it...
- 6gvONxR4sf7o 7y agoSure the speed is a function of the metric you use, but physics also tells us what metric is useful.
- cygx 7y agoIt's less about the metric but the choice of space/time decomposition.
- 6gvONxR4sf7o 7y agoI'm not talking about a metric over space, but rather a metric over spacetime, if that's what you mean. I would consider that to encode the space/time decomposition. My differential geometry sucks, but I thought you could write general relativity in a coordinate free manner that specifically doesn't rely on strong coordinate choices like you're talking about.
- cygx 7y agoI thought you could write general relativity in a coordinate free manner that specifically doesn't rely on strong coordinate choices Indeed. But even before you start messing with the formalism, the metric alone cannot be used to define a speed as 4-velocities are normalized. You need to decompose your tangent space into timelike and spacelike subspaces so you can have a dx and a dt.
- burnte 7y agoYou can over-complicate anything, that doesn't mean you should, or that it's useful.
- cygx 7y agoInvestigating which axioms of your theory can be weakened whithout affecting its predictions seems worthwhile to me even if it's useless from a practical perspective.