A geodesic is the path an object follows to extremise (maximise) its proper time. I am still confused why the final position of the apple should be near the earth.
My argument: an apple falls so that it can maximise its proper time. It stays far from the ground for a higher period of time because the clock is faster there, then is slowly accelerates because the clock is slower near the ground, and it tries to spend less time there. If that argument is correct, the apple should not fall at all, it should stay far from the ground, or even fly away from it so that it can age even faster.
What's wrong with my argument? Why should an apple fall towards the ground to extremise its proper time?
