From my understanding, objects like to take straight-line paths through spacetime when there is a zero net force acting on them.

If you make a spacetime diagram with three space axes and one time axis, then an object with zero net force will travel at zero acceleration, which will trace a straight line through spacetime.

But when objects with mass exist, they bend spacetime, and the straight paths are ones which fall toward a massive object.

So how, exactly, do we define a straight line through spacetime? Someone in another thread mentioned that it maximizes the proper time between the points. Proper time is defined as the time elapsed between two events from a frame where the events occured at the same time.

Let's go to special relativity for a second. We know that for any two events, the expresion

(dx)^2 - (dt)^2

does not depend on the frame of reference, where dx is the distance between the events, and dt is the time between them. That means that as dx increases, we must increase dt as well, and vice versa. So for an object travelling with zero acceleration, the proper time between any two points along its path is minimized, not maximized.

Can someone help?