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## Main Question or Discussion Point

Although I can follow many of the equations, given the Schwarzschild metric, I am stuck on what seems like a contradiction between two things.

1) Objects follow geodesics, which exhibit the principle of extremal aging, meaning most (or least) time along the path between given start/endpoints.

2) Decreasing distance from a center of gravitational mass corresponds to slower clocks (and increasing distances), as compared to far-away observers.

My understanding of these two ideas would imply that things move away from gravity, not toward it. What do I have backwards?

In trying to understand curvature at its most basic, I picture a particle released from a position at rest above the earth; then I imagine three nearby events in space time: 1) the particle is motionless during the time-interval, 2) the "next event" in the direction of gravitational mass (down), and 3) the "next event" in the opposite direction (up). Someone show me why event 2) is the natural one because the spacetime interval to it exhibits extremal aging.

(Bonus: in what cases does "extremal aging" turn into minimal rather than maximal?)

1) Objects follow geodesics, which exhibit the principle of extremal aging, meaning most (or least) time along the path between given start/endpoints.

2) Decreasing distance from a center of gravitational mass corresponds to slower clocks (and increasing distances), as compared to far-away observers.

My understanding of these two ideas would imply that things move away from gravity, not toward it. What do I have backwards?

In trying to understand curvature at its most basic, I picture a particle released from a position at rest above the earth; then I imagine three nearby events in space time: 1) the particle is motionless during the time-interval, 2) the "next event" in the direction of gravitational mass (down), and 3) the "next event" in the opposite direction (up). Someone show me why event 2) is the natural one because the spacetime interval to it exhibits extremal aging.

(Bonus: in what cases does "extremal aging" turn into minimal rather than maximal?)