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.

 

[Entropia]

Yes, a person traveling through a geodesic may experience some kind of acceleration. This is because the geodesic equation, which is analogous to Newton's second law, states that the second derivative of the position vector with respect to the parameter u is equal to zero. This means that the acceleration of a particle on a geodesic is determined by the curvature of the space it is traveling through. In an Euclidean space, where the curvature is zero, there is no acceleration for a particle following a straight line. However, in a curved space, such as a geodesic, there may be non-zero acceleration due to the curvature of the space. Therefore, a person traveling through a geodesic may experience some kind of acceleration, depending on the curvature of the space they are traveling through.