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

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

Okay.  So, |x2'-x1'| != |x2-x1|, even for very, very small v.

Does |t2'-t1'| ~= |t2-t1|, for very, very small v?

What is the magnitude of the four-vector?  Is it (x2'-x1')^2 -
c^2(t2'-t1')^2 for F' and (x2-x1)^2 - c^2(t2-t1)^2 for F?

Is the magnitude invariant?

I know these questions are pretty naive and, perhaps, a tangent
to the thread, but I've been reading this thread for a while
and I'd like to be able to follow it.

____________________________________________
Robert Cohen; rcohen@po-box.esu.edu; 570-422-3428; http://www.esu.edu/~bbq
Physics, East Stroudsburg Univ., E. Stroudsburg, PA 18301

> -----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'
>
> > 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|