Top Document: Invariant Galilean Transformations On All Laws Previous Document: 12. But Isn't (x'x.c')=(xx.c) a Tautology? Next Document: 15. But The Transform Won't Work On Wave Equations? See reader questions & answers on this topic!  Help others by sharing your knowledge Now, how on earth can we relate a tautology to a basic definition in math? From the top, bottom, middle, and other books in the stack we get this definition:  A linear transformation, A, on the space is a method of corr esponding to each vector of the space another vector of the space such that for any vectors U and V, and any scalars a and b, A(aU+bV) = aAU + bAV.  Let points on the sphere satisfy the vector X={x,y,z,1}, and the circle center satisfy C={x.c,y.c,z.c,1}. Let a=1, and b=1. Let A= ( 1 0 0 ut ) ( 0 1 0 vt ) ( 0 0 1 wt ) ( 0 0 0 1 ) A(aX+bC) = aAX + bAC. aX+bC = (xx.c, yy.c, zz.c, 0 ). The left hand side: A( x  x.c , y  y.c, z  z.c, 0 ) = ( xx.c , yy.c, zz.c, 0 ). The right hand side: aAX= ( xut, yvt, zwt, 1 ). bAC= (x.c+ut, y.c+vt, z.c+wt, 1 ). and aAX+bAC = ( xx.c, yy.c, zz.c, 0 ). Need it be said? Sure: QED. On the galilean transform the definition of a linear transform, A(aU+bV)=aAU + bAV, is completely satisfied. The generalized form transforms exactly and nonredundantly  with ONE TRANSFORM, not a transform and reverse transform  and non tautologically, just as the very definition of a linear transform says it should. And does so with absolute invariance, with this galilean transformation.  Subject: 14. But The Transform Won't Work On Time Dependent Equations? The main crackpot that has asserted such a thing was referring to equations such as in Subject 4, above. The Light Sphere equation; for which we have shown repeatedly elsewhere that the numerical calculations are identical for any primed values as for the unprimed values. The presence  before transformation  of a velocity term seems to confuse the crackpots. It turns out there is ex treme historical reason for this, as you will see in the subject on Maxwell's equations. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Invariant Galilean Transformations On All Laws Previous Document: 12. But Isn't (x'x.c')=(xx.c) a Tautology? Next Document: 15. But The Transform Won't Work On Wave Equations? Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: Thnktank@concentric.net (Eleaticus)
Last Update March 27 2014 @ 02:12 PM
