6 ms·
"Fun fact: The speed of light is only constant by convention." Well, the speed of light through a non-vacuum isn't the same as any medium will slow it to some
by burnte 7y ago
"Fun fact: The speed of light is only constant by convention."
Well, the speed of light through a non-vacuum isn't the same as any medium will slow it to some extent, but the speed of light in a vacuum is the definition of "c" and as such, that IS a constant and invariant.
- cygx 7y agoBecause 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.