Aeschylus

We say a cylinder has extrinsic curvature, but no intrinsic curvature.

The 2-D surfaces are just visual aids they do no represnt spacetime which is four dimensional (infact due to the signature of it's metric even two dimensional spacetime can never be proeperly represented in 3 dimensional approximately Euclidean space). The curvature of spacetime is something hat is very difficult to grasp, but people are already famir with the idea of two dimensional curved spaces, so it makes a good starting place.

lenght contarction refers to solid objects, so no we wouldn't call this lenght contraction. Of course the distance between the two points does vary from frame to frame like the length of a rod.

lenght contarction refers to solid objects, so no we wouldn't call this lenght contraction. Of course the distance between the two points does vary from frame to frame like the length of a rod.

It's when they make you draw the multplictaion table for the trivial group that you should rise up and overthrow your maths teachers.

What do you mean by a "mean zero difference"? if your talking in terms of total time expreinced then your dead wrong. The noninertial twin always exprinces less time this is as in Minkowski spacetime the worldline of inertial observers are geodesics and therefore (because of the signtaure ofw the Minkowski metric) an observer whose worldine is a geodesic between two events will experince the maximal amount of time between those two events.

No offence, but did you just make all of that up! 1) spacetime in both the special and general theory of relativty has four dimensions 2) Friedmann's main contribution was his equations, howvere he died when relativty was still very young consquently he did not have a major influence on how relativty is viewed today. 3)The theory of the electroweak force orginated in the 1970's, Einstein died in 1955. I think you may be slightly confused with Kaluza-Klein theory which was an early failed attempt at uniting general relativty and electromagnetism by introducing a fifth spatial dimensions, later some of the ideas from this theory were used in braneworld and stringy theories.

Try Cherenokov radiation: http://scienceworld.wolfram.com/physics/CherenkovRadiation.html

That site's a load of crap. Spacetime has four dimensions (as Sverian indicated these days the convention is take time as the 'zeroth dimension', but it is only just a convetion and it doesn't really matter, infact rather than assigning numbers we could assign the names 'John', 'Paul', 'George' and 'Ringo' if we wanted), for any given obsrever 3 of them will be the three dimenisions of spaceas experinced by him (i.e. 'space' for some observer is a hypersurface of spacetime) and one will be his time dimensions. I personally like to think of thing in terms of vector spaces, so a dimension to me is just the cardinality of the largest set of linearly indpendent vectors.

You must make this clear: relative to what (you cannot talk about the relative speed of an object without syaing what the speed is relative to otherwise it tells us nothing). The problem is that enrgy really isn't conserved in spacetime that is not asymptotically flat. Knowldge of Newtonian physics and the basic principles of general relativty is enoguh to see thta this must be the case as enrgy is not conserevd in non-inertial refernce frames in Newtonian physics, yet in general relativty inertial and non-inertial refrence frames are given an equality of sorts. ou msut also be clear what you mean by maximum aviadable space and maximum avidable time as thta to me has no obvious meaning.

the gravitaional field of a spherically symmetric object is spherically itself, the reasn for the phenumna you describe is not grvaity itslef, but the fact that the objects in question possess angular momentum.

It's interesting, but you did mess up as graviational collapse is not dependet on relative velocity (also you shouldn't really talk about mas schanging with relative velcotiy as in all but the most out-dated or most basic text mass is defined as rest mass which is a Lorentz scalar, infact generally we don't even talk about 'relativstic mass even as it merely represents the energy of the object). Consider this: in relativty there invaraibly exists a frame of refrence where you are travelling at such a speed that according to your reasoning you would collapse into a black hole. However you are not a black hole so clearly any line of reasoning that says you are must be incorrect.