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From: glird on 8 Apr 2010 15:28 On Apr 7, 11:14 am, "Dirk Van de moortel" <dirkvandemoor...(a)nospAm.hotmail.com> wrote: > glird <gl...(a)aol.com> wrote in message > >  5e3772b4-ea8d-4599-a60b-f818df55b...(a)11g2000yqr.googlegroups.com > > > On Apr 6, 9:27 pm, glird <gl...(a)aol.com> wrote: > > [snip TL;DR] > > >  See you later. > >   glird > > Dirk Vdm Thanks for waiting. Here is today's message from me: "A little general equation for these relativistic deformations is: (t'/t * j'/j * k'/k)/(i'/i) = 1, in which each expression is the algebraic symbol for the ratio of size of âone unitâ of the viewed system compared to âone unitâ of the viewing system. "Since ø = j'/j = k'/k and ï³ = i'/i; this reduces to t'/t * ø2/ï³ = 1. Since ï³ always equals qø, this too can be reduced, becoming: t'/t * ø/q = 1; or, therefore, ï³Ã¸ = q. "Since this reduction eliminates an essential ingredient in these deformations, however, such a step is a mathematical trap for the unwary. Other than during calculations, needed symbols should never be rendered invisible; even and especially if they happen to sometimes equal 1. (Whereas both Lorentz and Einstein tried to prove that l = ø(v) = 1, Lorentz later abandoned l = 1 as a general value.) Even though in all these cases ï³ = qø and ø(t'/t) = q, the numerical values of these deformation-ratios cannot be mathematically derived until that of at least one of the others is stipulated." From A Flower, and some of my prior books. Other than that the symbols in the general equation are boldfaced (to indicate that they are vector quantities), I will now convert the above math into a form that can be understood via these verstunckena newsgroup versions. A little general equation for these relativistic deformations is: (t'/t * j'/j * k'/k)/(i'/i) = 1, in which each expression is the algebraic symbol for the ratio of size of âone unitâ of the viewed system compared to âone unitâ of the viewing system. Since phi(v) = j'/j = k'/k = dy'/dy = @z'/@z, and ï³ = i'/i = dx'/dx, this reduces to t'/t * ø2/ï³ = (dtau/dt)phi^2/(dxi/dx) = 1. Since ï³ always equals qø = sqrt(1 - v^2^/c^2)phi(v); ï³Ã¸ = phi(v)(dxi/dx) = q. The penultimate step: In P1 E was doing deformations, with K (x,t) moving at v. In P2 he tried to let x,t be stationary with xi,tau moving at âv; as in Poincare's Sur la Dynamique. The final step to eq 7: Returning to the format of Voigt and Lorentz, he let BOTH systems move at v! Given THAT plus my little equation, i will let you fill in the details. If nobody can, I will do it for you in another day or so. Meanwhile, here is another morsel for you to contemplate: "As the special theory of relativity so catastrophically demonstrated, mathematics permits operations that the physical problem at hand does not. The result is that the resulting equations then quite accurately say things that neither the mathematicians nor physicists understand. The catastrophe isn't that we don't understand the resulting equations, but that we think we do!" From "The Universe". Ciao, glird |