FlyingLemons wrote:
Crazy Eddie wrote:
Minkowsky space assumes the flatness of space even when it demonstrably isn't. You could still account for that curvature even if the metric doesn't explicitly reflect its presence.

No, you just use a metric more suited to the property of that space.

Which is what a modified Minkowsky space would be: a metric suited for transformations on objects large enough to curve space around them. The reason I don't think the other methods would suffice (for what I'm talking about) is that they are not, AFAIK, scalable.
That's why it's special relativity  a special case for locally flat spacetimes.

Am I incorrect in my belief that physicists have spent an impressive amount of time trying to arrive at a unified field theory that would render special relativity superfluous, or am I misunderstanding something here?
Crazy Eddie wrote:
And yet you say it gives correct answers when calculating transformations on GPS satellites in Earth orbit...

That's because it's not applying the Minkowski metric but instead an approximation of the Schwarzchild metric, the one you use for a spherically symmetric body such as the Earth.

The page you linked to did not. But I think we've already covered that topic.
Moreover, I am under the distinct impression that the FRW Metric is used primarily in bigbang cosmology to describe the expansion of the universe from a point singularity and describe the movements of all galaxies
as a whole and is inherently inapplicable on the small scale. Am I wrong about this, and if so, set me straight.
I am also under the impression that the Schwarzchild metric accounts for gravitational time dilation between higher and lower gravitational potentials but not inherently the angular velocity or relative of any two objects in different orbits of a gravitating mass. IOW, time dilation due to relative velocity is not included in the Schwarzchild metric. Am I wrong about this, and if so, set me straight.
It's been ages since I did any real work in relativistic physics and I could just need a refresher course.