I have some issues with some of the things you say about relativity here.
David Thomson wrote: > Hi Stephen, > >>> On the other hand, the Aether Physics Model solidly backs General >>> Relativity. > >> Say what?? SR is a subset of GR -- it is exactly equal to general >> relativity in the absence of mass (flat "background" space). > > Say what?? GR was derived completely independent of SR. The "link" > to SR was added later. The original SR paper aimed to show the > equivalence of mass and energy. Einstein published more than one paper in 1905. The one which is generally considered to be the "seminal" paper on SR was "On The Electrodynamics of Moving Bodies" and it covers a great deal more than the mass/energy equivalence -- in fact, it's a complete derivation of special relativity, couched in terms of Euclidean space with the Lorentz transforms written algebraically. As far as I can see, there is one mistake in the paper, in the derivation of the transverse mass equations at the end of the paper; the rest of it appears to be solid (I mean, mathematically, of course!). None of it uses Riemannian geometry because Einstein hadn't yet mastered that, and no imaginary numbers were used because Minkowski hadn't added that little filip as yet. Minkowski's interpretation in the "World" space, with an imaginary time coordinate, came some time later, and was a side track, IMHO. It can be safely ignored, as it seems to have fallen out of most modern texts (though I believe Stephen Hawking may still favor that approach). Einstein spent many of the years between 1905 and 1916 learning enough math to build general relativity. (This is presumably part of what inspired his quote about having a great difficulties with mathematics...) In particular he learned Riemannian geometry and figured out how to use it to model gravity, _and_ he invented a chunk of what we now call tensor calculus. The "big theorems" are all named after other people but the notation used, even today, is Einstein's. This culminated in Einstein's 1916 paper on general relativity, "The Foundation of the General Theory of Relativity". That's the basis for the theory; it's the "big paper" of general relativity. It starts with a brief discussion of special relativity and the need for a generalization, and takes it from there; in fact Einstein builds GR on top of SR. In section 4, formula (4) (page 120 in the Dover edition) is the SR metric: | -1 0 0 0 | | 0 -1 0 0 | | 0 0 -1 0 | | 0 0 0 1 | That's what GR reduces to when the curvature is nil, and it's just plain old special relativity. Einstein observes that it's not generally possible to reduce the metric to that over a finite region; it is, however, possible to reduce it to that at any single point, and it's possible to choose coordinates which reduce it to that at a point _and_ which reduce its first derivatives with respect to all coordinates to zero at that point. That's commonly referred to as the "local flatness theorem" FWIW, and the coordinates one obtains in that case are those of a body in free-fall. So, I don't understand what you mean when you say the theories were completely independently derived. In regions far from large masses, in which the stress tensor is nearly zero for a large distance in all directions, space is nearly flat and one can choose coordinates in which the metric is almost exactly as given above over a large region. In this region SR is (almost) precisely correct. In the limiting case of small masses, GR and SR become the same theory. Why don't you believe that? The result is dressed up in Riemann's clothes, and may not, at first glance, look quite like the theory presented in "Electrodynamics of Moving Bodies" but the use of tensors in SR just packages it all up nicely in an easy to manipulate form. It doesn't change the semantics. In fact the theory can be, and occasionally is, presented that way from the get-to; see, for instance, Rindler's "Introduction to Special Relativity". > GR shows that space-time influences and is influenced by matter. > You can't have matter without mass, so a massless interpretation of > GR is complete nonsense. It's not nonsense, though I could have phrased it better. It's also not an "interpretation" of GR: rather, it's a limited subset of GR. The issue is the limit: when mass densities are all small the curvature can be so small it is ignorable. In that case the metric reduces to diag(-1,-1,-1,1) and you end up with special relativity. Similarly, the low-speed limit of SR is Newtonian mechanics. >> I can't imagine how you believe you can have GR without SR. > > I don't see how you believe they have anything in common. SR is GR with curvature set to zero. That's all. If you disagree please explain why. >>> It derives the GR simplified field equation in terms of charges >>> from first principles. > >> Do you mean the linearized theory? Didn't follow this. > > The simplified GR field equation is: > > G = 8pi T > > where G is the space-time curvature tensor and T is the mass/energy > tensor. Almost. That's the way the Einstein field equation is typically written, all right (without the cosmological constant), _but_ G is not the thing generally called "the curvature tensor" (and T is more often referred to as the "stress-energy tensor", as it includes stress terms, not just mass and energy -- the stress terms are (more or less) what lead to black holes, in fact). G in that equation is the "Einstein tensor", which is defined as G^ab = R^ab - (1/2)g^ab R where "R^ab" is the Ricci tensor, "R" is the Ricci scalar, and "g^ab" is the metric. The Ricci tensor is the first contraction of the Riemann tensor and the Ricci scalar is the contraction of the Ricci tensor. It's the Riemann tensor which is normally called "the curvature tensor". The Riemann tensor is computed from the second partial derivatives of the metric, and it says how two geodesics which are initially parallel will diverge. In concrete terms, a nonzero Riemann tensor manifests itself as tidal effects. Special relativity, again, is simply the geometry of general relativity, in the special case where the Riemann tensor is zero. The Ricci tensor, which is the contraction of the Riemann tensor, might be called a measure of local gravity. If the Ricci tensor is nonzero, then a sphere of initially comoving particles will shrink in volume as time goes by (they will be drawn in on themselves). > > The Aether Physics Model equivalent is: > > e^2 = 8pi (a * e.emax^2) > > where e^2 is spherical electrostatic charge (from the Aether) and > e.emax^2 is toroidal electromagnetic charge (from matter). I haven't really looked at this yet. I got side tracked by your assertion that SR and GR are unrelated. More tomorrow, maybe... > >> Einstein's version of GR presents in terms of mass, and is a >> tortured process. But tortured or not, the concept that space- >> time interacts with matter is valid in both physics models. > > Dave >
