We all know, a geodesic is the path an object follows to maximize it’s proper time. Geodesic equations of an object near a gravitational field shows that it should fall towards the ground, which is the expected behaviour. However, this is counterintuitive. Clocks tick slower near the ground, so an apple will age slower if it falls than if it floats or even soars upwards.

I know that the geodesic an apple chooses maximizes it’s proper time between the tree and the ground. But it could have chosen other directions, which would maximize it’s proper time even more. What causes it to take this particular geodesic? Please notice that, if I am standing on earth I have countless geodesics to choose from at every direction.

Now you can say that the equations dictate that, the free fall geodesics say that if you have no initial spatial velocity, only a temporal velocity, you must fall towards the ground. My question is, why? Why not some other direction where you can age even more?

We all know, a geodesic is the path an object follows to maximize its proper time. Geodesic equations of an object near a gravitational field show that it should fall towards the ground, which is the expected behaviour. However, this is counterintuitive. Clocks tick slower near the ground, so an apple will age slower if it falls than if it floats or even soars upwards.

I know that the geodesic an apple chooses maximizes its proper time between the tree and the ground. But it could have chosen other directions, which would maximize its proper time even more. What causes it to take this particular geodesic? Please notice that, if I am standing on earth I have countless geodesics to choose from at every direction.

Now you can say that the equations dictate that, the free fall geodesics say that if you have no initial spatial velocity, only a temporal velocity, you must fall towards the ground. My question is, why? Why not some other direction where you can age even more?