Posted 13 June 2012 - 11:28 PM
How does this fit in with General Relativity (GR), where the inertia of an object arises from its resistance to have its motion change from that of a geodesic in a Riemann space whose metric (tensor) is given by the gravitational field (tensor)?
(1) The motion of an object can be represented by a changing set of 4 points or 4-vector V which, if the object is acted on only by gravity, forms a geodesic curve G (again, in a Riemann Space whose metric is equal to the gravitational field the object is acted on).
(2) From the "strong" Principle of Equivalence, the object's weight/inertia arises because gravity acts on the object in such a way as to MAINTAIN the object on this geodesic G.
In other words, an object on a geodesic will "want" to remain on the geodesic unless acted on by an external non-gravitational interaction.
This is the GR version of Newton's 2nd Law.
For example, when you lift a bowling ball, the ball will "resist" you, since it "wants" to travel on its geodesic: free fall straight down onto the wooden floor.
And when you throw the balling ball and feel it resisting a forward acceleration, the ball will "resist" you, since the ball's geodesic does NOT involve it having any change in horizontal speed.
If you free fall with the bowling ball and (1) try to have the bowling ball have the same vertical speed as the bowling alley floor, it will resist you, since relative to you, its geodesic is to have zero acceleration in all directions. and (2) if you try to push it parallel to the bowling alley floor, same thing.
So mass and weight are the same thing: and both are caused because an object on a geodesic world line will stay on the geodesic world line ... unless acted upon by one of the other quantum fields (electroweak, strong, etc).
Loosely speaking, gravity "forces" an object to have a geodesic trajectory in the Riemann 4-Space (or Riemann space-time) whose metric is described by the gravitation field contained in GR's field equations.