Breakfast in LA - lunch in San Diego ( was Re: A Geometrical Pro of of the Non-invariance of the Spacetime Interval)

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

Both Hugh an I failed to follow the excellent admonition of "First Define
your terms".  I think we meant different things with the same symbols????

Perhaps what I said will be more helpful with a more careful definition of
terms.  I first define the terms and then repeat the quote.

(x1,t1) are the space-time coordinates of event A (breakfast) as measured by
frame F (the v=0 person).  (x1',t1') are the space-time coordinates of the
same event A (breakfast) as measured by frame F' (v != 0 person) .

Similarly (x2,t2) and (x2',t2') are the coordinates assigned to event B
(lunch) by frames F and F' respectively.

Consequently using ordinary notions of distance (not space-time interval!)

F claims the spatial distance between breakfast and lunch is |x2-x1| and F'
claims it is |x2'-x1'|.  Both special relativity and galilean relativity
will claim that in general the two distances will differ for non-zero v.

Original post:

> One person is going at v=0.  The other is going at v<<c.

Let's call the v=0 person frame F and the v<<c person F'

> Each measures event A (breakfast) occurring at a particular point in
> space-time (x1,t1) and event B (lunch) occurring at a particular point
> in space-time (x2,t2).

Each measures event A (breakfast) occurring at a particular point in
space-time labeled (x1,t1) by F and (x1',t1') by F' and event B (lunch) at a
different point in space-time labeled (x2,t2) by F and (x2',t2') by F'

I think DH is bothered by the fact that F' says |x2'-x1'| = 0 while F says
|x2-x1| = LA--->San Diego distance.

As I understand the misconception, it has little to do with SR, as the same
statements can be made with a Galilean Relativistic model (i.e. v<<c). I.e.
both the Lorentz transformation or the Galilean transformation equations say

|x2'-x1'| != |x2-x1|