Does Gravity Cause Acceleration?

Re: Gravity and General Relativity On Television I've heard it said that gravity is not a force; it is a curvature in space time. If space is curved by a massive object like the earth, I can understand how this would affect the direction of motion of a falling object (i.e. along the curved space caused by the massive earth). However, if gravity is not a force, what makes the falling object accelerate?
- Frank Kirby (age 68)
Dedham, MA, USA

Let's take one step backward. Does the falling object "accelerate"? In its free-fall reference frame, it feels no forces. It sees some changing motion with respect to other objects, but can attribute that to the acceleration of the other objects. Thus there isn't an obvious absolute sense in which you can say that the object accelerates. So we'd better be careful about coming up with some explanation that says that it must accelerate.

What does general relativity say instead? Given the spacetime curvature and how it depends on the distribution of momentum and mass, you can calculate the geodesics (free-fall paths through spacetime) for different objects, using any one of a large number of coordinate choices.  The paths for the little object and the Earth are at different spatial points in one time slice, but the paths reach the same spatial point in another time slice. All sorts of forces happen when they bump into each other, so then they stop following geodesics.

Is there any reason to prefer coordinate systems that say that the little object accelerated a lot compared to the Earth? Yes, for those most of spacetime looks quite simple, almost like the Euclid-Newton picture. That's a great convenience for most problems. So there is a reason to choose a description in which you say the little object does most of the accelerating, but you can make other valid choices.

Mike W.

(published on 06/09/2013)