3 ms·
Newton's first law tells us that in the absence of external forces, a body will keep going in the same direction, uniformly, ie its wordline will be straight.
by cygx 6y ago
Newton's first law tells us that in the absence of external forces, a body will keep going in the same direction, uniformly, ie its wordline will be straight.
However, that concept is not available in arbitrary manifolds, you need additional structure: The covariant connection, which allows you to parallel transport velocity vectors, enabling you to define the concept of straight lines (autoparallels, which will be geodesics if the connection is 'metric').
According to general relativity, gravity hooks into that. So from that perspective, the gravitational force on a test particle will be a consequence of (the generalization of) the first law instead of the second one, making it into a pseudo-force like the Coriolis force.
- immmmmm 6y agocorrect! but if you introduce a derivative which is covariant under diffeomorphisms and u(1) transformations D = d + \omega + A you see that gravitation (connection \omega) enters on a somewhat same footing as the electromagnetic potential (A). there are nuances ofc, but the view (force/curvature) depends from where you're looking. also in real life particles don't real exist... they're excitations in a field