A person travelling through a geodesic.

[Kevin_spencer2]

A person traveling through a geodesic. Does experiment some kind of acceleration?, since the geodesic equation analogue to Newton one is:

$$\Delta _{u} u =0$$ and in an Euclidean space there's no acceleration for a particle line $$X(u)=au+b$$

 

[pervect]

Someone following a geodesic will be in "free fall". They won't feel any acceleration - if they have an accelerometer, it will also read zero. If you set up a global coordinate system, however, the second time derivatives of the position coordinates will in general be nonzero.

Think, for example, of an object orbiting a central mass in a circular orbit. Such an object is locally in free fall, and could set up a local coordinate system that is nearly inertial over small distances.

In a global coordinate system anchored to the central mass, the second time derivative of the spatial postion coordinates will be nonzero, however.