Re: Ken Tucker, meet Robert Brown ...


Jim Black wrote:
> R. Brown wrote:
>
> [about the discussion at http://www.math2.org/mmb/thread/35125]
>
> > Mr. Michaeld did seem to prove that the Rbtx-galilean transform
> > won't compute on some levels, so it may never be the foundation of a
> > new space-time theory..TRUE! Yet further study indicates that it's
> > 'inverse transform' works from the related 'reciprocal of the Que
> > factor', which means that it maintains a marvelously 'reciprocal
> > symmetry' that is lovely to behold!
> >
> > Que = [gamma]^p .........forward transform
> > Que = 1/[gamma]^p .......inverse transform
> >
> > This finding suggests that the Rbtx-Galilean transform IS
> > superior in quality to all transforms EXCEPT Lorentz!
> >
> > NOTE: The 'condensed version' posted on MMB is NOT consistent!
> > always use the 'long-definition' of Time, from the original paper.
>
> ... Robert Brown, meet Ken Tucker. I think you will get along just
> fine. Who knows? You might even teach each other something.
>
> Followups set to sci.physics.relativity.

Thanks Jim (I think)...read over the provided refs.
AE's SR is straightfoward, speed of light c=constant
in all CS's, so a sphere of light is a sphere of light w.r.t
all uniformly moving CS's.
(See Dovers Principle of Relativity pg.46).

That's expressed in CS K as

(ct)^2 = x^2 + y^2 +z^2

and CS K' as

(ct')^2 = x'^2 + y'^2 +z'^2

in the ref. That is the basis of the Lorentz Transform.

Later Minkowski "invented" SpaceTime by finding,

(ct)^2 - x^2 + y^2 +z^2 = (ct')^2 x'^2 + y'^2 +z'^2

is invariant. That was generalized in GR to be

ds^2 = g_uv dx^u dx^v,

s^= g_uv x^u x^v (is ok in SR),

and ds=0 for light-ray measurements for all CS's.

IMO, anyone can set any values for the g_uv
provided it gets back to the light sphere, relativity
demands, and can include "nonorthogonal" metrics
like g_12 =/=0, that can get into specific trigonometries
like "elliptical CS's", where serious paper work is
required.

What Robert Brown is possibly attempting to do is
using some *new* math to cross from orthogonal to
nonorthogonal CS's, which may be reasonable, but
there is already the conventionally accepted tensor
analysis that makes all that clear.

I guess the thing to determine is if Brown's "new"
math is logically consistent, and if it's new, so I'll
bump that back to math, for your decision.

Regards
Ken S. Tucker

.