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. 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? 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 big-bang 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.
Not to speak for FlyingLemons or the iguana, but after a certain point aren't you basically asking for a private tutoring session here? People get paid to teach these subjects; why should they do it for you for free? Crazy Eddie, you remind me of every eager grad student I've met, thinking they can tackle every major problem in their field, until reality sets in. Most research is incremental not revolutionary. Trying to redefine major components of relativity strikes me as a bit much for any one person to tackle.
Especially if you're still learning about it. Dethroning scientific theories is like jazz. Before you go against the establishment, you need to become a part of it. Before coming up with SR, Einstein did not go around claiming “Newtonian mechanics are wrong”, on the contrary, he knew all about them, used them, knew they worked, and why and where they worked. But then again I guess you don't brag too much when you're about to invite the hate by replacing the simple math everyone uses with that barely comprehensible dinosaur I had always been afraid to touch personally.
Not to any poster in particular, but: School teachers here in India teach us a lot about how half-baked knowledge can be silly at best and dangerous at worst.
Some people are playing all the right notes but not necessarily in the right order. [yt]http://www.youtube.com/watch?v=R7GeKLE0x3s[/yt]
It breaks down as soon as you bring strong gravity into the picture. Far from it. Most of the work I do these days involves the use of special relativity to study the physics of QGPs produced in heavy ion collisions. Trying to replace special relativity would be futile because it's an important part of modern quantum field theory. Any kind of unified field theory, if it even exists, would include special relativity as it would need to be able to retrieve the results of quantum field theory on non-gravitational backgrounds. FRW describes cosmological dynamics on the largest scales and equations for both cosmological expansion and the movement of cosmological dust and fluids can also be derived. Schwarzchild describes the dynamics of bodies on the astrophysical scale in and around spherically symmetric objects (that is, black holes, stars, planets) and is the source of the gravitational time dilation equation. In the instance of the GPS, there's dilation due to both the effects of special and general relativity, as confirmed by the Hafele-Keating experiment among others. You'd probably find it quite interesting to go and read about these yourself, as a) the forum does not support LaTeX and b) I don't have the time to fully explain all of this, most of which can be found elsewhere.
Not much time to dither this week, but I'll leave with this: I've read about a number of experiments using clock times from satellites to test for relativistic effects of time dilation. Reflections on those experiments is a big part of what got me going on this line of thought, since the conclusion -- or so it very strong appeared to me -- did not follow from the results. Looking a the numbers myself, and looking at the general logic and mathematics behind Special Relativity itself, I concluded that the Lorentz transformation itself is sufficient to account for the invariance of the speed of light, where dilation appears to occur in space mainly because of the shortening of moving objects. That is, when a fast-moving object is contracted longitudinally due to its high velocity, the relative distance between that object and the observer likewise appears dilated consistent with the frequency doppler shift. The net result is almost the same -- in GPS satellites, a very small increase in pseudorange -- but the time between clocks is otherwise unchanged. The main reason I believe this is because relativistic equations for time dilation have some odd and contradictory implications if you treat time as a variable between observers; from both points of view it is equally valid to speak of the other's clock as running behind, since in both reference frames each observes the OTHER clock as the one in motion. This contradiction disappears when you treat DISTANCE as the variable, wherein each one measures the same distance to the moving object but has no way of knowing that the moving object -- and his perception of distance -- is distorted. I am less sure about the implications for General Relativity but it seems to be the case that the same effect occurs: the physical distortion of objects in lower gravitational potentials necessarily distorts the physical distances between two objects, which IMO would be more consistent with things like the Oberth Effect (space is literally smaller in lower gravitational potentials and therefore the same impulse results in a larger displacement). The reason I figured Minkowski space would work in the presence of strong gravity is that you could still treat Minkowski space as being effectively flat and account for the curvature of space by mapping the distortions onto the various objects within that space time. Put that another way: space ALWAYS appears flat in your own reference frame, and the only reason you know it's curved is because other objects farther from the origin are behaving strangely. A Minkowski spacetime applied to strong gravity would add an additional factor that would inherently distort all objects in given coordinate system as if they were being stretched longitudinally in a particular direction. Without running the numbers I am not sure what this would change about the nature of gravity on a cosmic scale applying to galaxies or clusters of galaxies, except to say that the physical contraction of space around a gravitating object could mean that our measurements of the SIZES of those galaxies is in error. Is it that obvious?
And there's your problem. If you're not going to run the numbers, what's the point of the discussion? You seem to just want your impressions and preconceptions validated.
Einstein was extremely good at coming up with thought experiments (Gedankenexperimente) that he used to explore the consequences of the principles of Special and General Relativity. Unfortunately, that clarity of thought is not apparent here.