What Gives a Motionless Meteorite Shard Momentum in the Curvature of the Sun?

[feynmann]

ah … but the ball doesn't feel the bumps, it looks at them …

so it's using eyesight to calculate gravity! ​

How long does the ball take to calculate gravity?

 

[feynmann]

Hi Chaste,

This is best understood in geometrical terms. Do you understand (in SR) how the worldline of an inertially moving object is a straight line? If two inertially moving objects are at rest wrt each other then their worldlines are two parallel lines. In a flat space the distance between two parallel lines is constant and they never intersect.

Now, consider geometry on a sphere. On a sphere a "straight" line is a great circle. Longitude lines are examples of great circles. If you consider two nearby longitude lines at the equator they are parallel, and yet at the poles they intersect and the distance between the two lines is not constant.

So, on a sphere two lines can be parallel at one point and intersect at another point despite the fact that both lines are straight at all points. Translating back to physics, in a curved spacetime two observers can be at rest wrt each other at one point and their paths can intersect despite the fact that neither accelerates at any point (they are each inertial at all points).

Isn't that called geodesic deviation and shows that the tidal forces of a gravitational field (which cause trajectories of neighboring particles to converge/diverge) can be represented by curvature of a spacetime in which particles follow geodesics

 

[Dale]

Yes, but I would add the qualifier "inertial" so that it is "trajectories of neighboring inertial particles to converge/diverge" and "a spacetime in which inertial particles follow geodesics".