Re: Teaching logic is urgent (the only reasonable transformations)

[Ken Caviness <caviness@SOUTHERN.EDU>]

Bob Sciamanda wrote:

> Ken's analysis is fine except for his statement that Pentcho's
> | "equations /3/ and /5/ above likewise only hold true for points on the
> | worldline of the primed observer, i.e., for points where x'=0."
>
> Pentcho's (3) is a statement involving only constants and is true in general.
>
> Statement (5) is true only for events occuring at x=0 (the unprimed observer's
> position).

Thanks, I see that now.  I stand corrected.

I wasn't paying sufficiently close attention there.  /3/ is derived from
/1/ and /2/, and so, like /2/ it holds true for points on the worldline
of the primed observer, but since it contains only constants, it must
also hold true in general.  Also /5/ is derived from /1/, /3/ and /4/,
and since /1/ & /3/ apply for all points in spacetime, and the
individual parts of /4/ are true only for points on the worldline of the
unprimed observer, it follows that /5/ (t' = a t) is valid for events
occuring at the unprimed observer's position.

Incidentally, since a = gamma in the Lorentz tranformation, we've got t'
= gamma t for events such that x = 0 (and indeed delta-t' = gamma
delta-t whenever x is constant), and a symmetric argument shows that t =
gamma t' for events such that x' = 0 (and delta-t = gamma delta-t'
whenever x' is constant).  This is a nice demonstration that time
dilation does not simply mean that processes in one frame run faster
than in another, but instead that processes which occur at a fixed
position in one frame (any one) are observed as running slower by
observers in other frames moving relative to the first.

Ken