SynthDude wrote:

In both cases, the classical physics model was REPLACED by a new
theory (special relativity/general relativity) that covers ALL
scenarios. But in both cases, we can still use classical physics to
make calculations for "non-extreme" scenarios (e.g. car going 55 mph,
earth orbiting the sun).

Yes, but SR and GR don't "cover ALL scenarios", as the laws of physics
break down with the singularity at the center of a black hole. Matter
becomes infinitely dense and gravity is infinitely strong there.

Alfred Einstead wrote:
wrote:
Not quite as right -- the earth moves through curved spacetime, not
just curved space.

Things don't move through spacetime. They ARE in spacetime;
particularly: they are worldlines.

Motion is 3-dimensional language. There is no motion in 4
dimensions.

A timelike geodesic in spacetime is a parametrized curve, with
proper time as a nice parameter. At one value of proper time,
it describes one location in spacetime; at a later value, it describes
another location. Whether you want to call this ``motion in
four dimensions'' or not is a matter of semantics that does not
affect the physics, and is, frankly, boring.

Steve Carlip