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>]

RAUBER, JOEL wrote:

> > So we agree that |t2'-t1'| ~= |t2-t1|, for very, very small v.
>
> Yes, approximately, but not exactly. The absolute deviation 
> from equality
> gets greater as one looks at longer and longer time intervals.

Agreed.

> > Does |x2'-x1'| ~= |x2-x1|, for very, very small v?
>
> No.
>
> With the above stipulation that LA to San Diego distance is *not*
> approximately zero.

Good.

So, at very small v, the difference in distance results in
a very tiny difference in elapsed time such that the
magnitude of the four vector remains invariant.

This means that the difference in time (as measured in
each frame) is independent of v, i.e., an insignificant
difference relative to a long time (if v<<c) or a
significant difference relative to a short time (for large
v).

I think this was the key that confused me some while back (not
to mention the multiple uses of "he" as one observer or the
other).

Thank you.

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