Geodesic Paths in Spacetime

If gravity is fully explained by objects moving in straight lines through curved space, why would an object's trajectory change due a different speed?
- Ed Goldberg (age 43)
Los Gatos, CA, USA

That's a great question. If It were simply a matter of spatial geometry, separate from time, the velocity-dependent trajectories in free-fall would make no sense. However, the overall geometry has four intertwined dimensions, the fourth one being time. Time appear somewhat differently than the three space dimensions in the math, but it still isn't separable. Even in special relativity, it's only a combination (d²-c²t²) of space (d) and time (t) intervals that's invariant, i.e.  doesn't depend on which coordinate frame you choose. Thus two objects that happen to be going along the same spatial path (in some coordinate frame) at different rates are already on different trajectories in 4D spacetime. In fact, even saying whether their spatial paths are the same or not depends (within limits) on what coordinate frame you choose.

Mike W.

(published on 05/25/2012)