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-----Original Message-----
From: RAUBER, JOEL [mailto:JOEL_RAUBER@SDSTATE.EDU]
Sent: Wednesday, January 22, 2003 9:43 AM
To: PHYS-L@lists.nau.edu
Subject: Breakfast in LA - lunch in San Diego ( was Re: A Geometrical
Pro of of the Non-invariance of the Spacetime Interval)
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'
particular point
Each measures event A (breakfast) occurring at a particular point in
space-time (x1,t1) and event B (lunch) occurring at a
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|