# Cause of Coordinate Acceleration in Free Fall [duplicate]

So I understand that objects in free fall are in an inertial frame, at rest in terms of relativity. However, from a person on the surface of earth, a falling apple is accelerating constantly until it hits the ground.

This is coordinate acceleration, but I still don't understand why it's there: what about the gravitational field makes the movement along the geodesic appear as acceleration to the observer?

Why isn't it, say, a constant velocity or something?

• The observer on Earth is in a non-inertial frame due to Earth's gravity. This creates a fictitious force, like a centrifugal force, that bends the spacetime around the observer. The apple follows a geodesic in the curved spacetime, but to the observer, it appears to accelerate because their reference frame doesn't match the curvature. Think of it like rolling a ball on a warped surface - it appears to deviate from a straight line, even though it's following the most natural path on that surface. Commented Jul 15 at 2:44

It looks like an apple is accelerating at a uniform rate when you drop it because you aren't following a geodesic, because a force is being impressed upon you: when you stand on the ground, the Earth exerts a force on you to keep you from falling into it, which doesn't happen frequently$$^\text{citation needed}$$. You, held in place by this reaction force, then observe the apple, which is following a geodesic, to accelerate towards the Earth.
The reason that things can start at rest - like an apple - and then begin to accelerate is because geodesics are four-dimensional. If you are "at rest" in a given frame, then your velocity isn't zero, it's just all in the "time direction". In fact, your velocity is actually always equal to exactly $$c$$. When you accelerate in any spatial direction, your four-velocity doesn't change in magnitude, it just rotates away from the time direction, sort of. Same reason why things start at rest and then fall: geodesics in curved spacetime temporarily curve away from the time-direction and towards the spatial directions, resulting in an apparent acceleration.