steve waterman wrote:Round and round. x is defined as distance...you all insist upon comparing points
Damn straight, because that's what the Galilean transform is talking about. Whatever are the brilliant ideas are created by your singular genius that will revolutionise maths forever, they are not related to the Galilean transform because they're talking about something different than
the Galilean transform, as we have informed you on numerous occasions.
PolakoVoador wrote:C'mon Steve! It's been pointed out to you before. The equation x'=x-vt is a shorthand for S'(x,y,z)=S(x-vt,y,z) because who the hell has time to type all this stuff? Can you understand this? Are you OK with this?
Just to avoid confusion, this should read x'=x-vt is a shorthand for S'(x',y',z')=S'(x-vt,y,z)=S(x,y,z)
steve waterman wrote:when vt = 3, I wonder if we now finally all agree that
S(2,0,0) and S'(-1,0,0) share the same location in spaaace in the manifold.
Correct: they map to the same point.
steve waterman wrote:the distance x from S(0,0,0) to S(2,0,0) does not equal the distance x' from S'(0,0,0) to S'(-1,0,0).
Correct: the origins are also separated in this case.
steve waterman wrote:the distance x from S(0,0,0) to S(2,0,0) equals the distance x' from S'(0,0,0) to S'(2,0,0).
you have three-dimensional Cartesian co-ordinate systems in the four-dimensional space (and not four-dimensional co-ordinate systems which we were using to help avoid this confusion) and the co-ordinate systems have the same unit size.
steve waterman wrote:x is defined as the distance x from S(0,0,0) to S(x,0,0).
One could define x=d(S(0,0,0), S(x,0,0)
); note this does not necessarily hold for non-Cartesian systems
steve waterman wrote:x' is defined as the distance x' from S(0,0,0) to S'(x',0,0).
False. By our previous definition it would be the distance between S'(0,0,0) to S'(x',0,0) parallel to the x' axis.