3 ms·
It's a bit more involved than that. That simple equation you quoted has been derived from the geodesic equations. Geodesics are the equivalent of straight line
by mr_mitm 2y ago
It's a bit more involved than that.
That simple equation you quoted has been derived from the geodesic equations. Geodesics are the equivalent of straight lines on curved manifolds, which is a mathematical object. The shape and geometry of the manifold in question, which in turn influences the shape of the geodesics, is given by the matter distribution, or more specifically the energy stress tensor. The relationship between the manifold and the energy stress tensor is described by the Einstein field equations.
We gave that manifold the name "spacetime".
- raattgift 2y agoCouple minor additions: geodesics are physical in that (i) they are the paths taken by objects in free-fall and (ii) light (massless waves, etc etc) in free space is always in free-fall: all allowable null curves are null geodesics. Massive objects and light may be accelerated (the direction part of the velocity vector changes with scattering even if the magnitude part does not) and during acceleration will not be bound to a geodesic because they aren't in free-fall. Even though I agree with the way you put it, I'll say it's probably a bit too strong to write that stress-energy is the (sole) source of curvature given the extremely curved spacetime of our expanding universe. However, Einstein was OK with Schrödinger taking that view <https://arxiv.org/abs/1211.6338 https://arxiv.org/abs/1211.6338> (a super-interesting bit of science history), and we don't know enough about the cosmological constant vs dark energy, nor cosmic inflation.