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Re: A Geometrical Proof of the Non-invariance of the Spacetime In terval



-----Original Message-----
From: David Rutherford [mailto:drutherford@SOFTCOM.NET]
Sent: Tuesday, January 21, 2003 1:48 PM
To: PHYS-L@lists.nau.edu
Subject: Re: A Geometrical Proof of the Non-invariance of the
Spacetime
Interval


"RAUBER, JOEL" wrote:

This may be obvious to others, but I'll keep at it.

It appears to me that the problem is that you think person
F' can not
determine the city in which they are located at any
particular time. Which
as your intuition is telling you is patently absurd. And
*is not* the
implication of SR.

Sure his stomach's coordinates are always zero, but the
spatial coordinates
of breakfast as measured by F' is a different question than
what city
breakfast occured in and F' is fully capable of answering
either question.

F' can easily determine in what city he ate breakfast. His
stomach is the
origin of F' and he eats breakfast at t' = 0. So the
coordinate location of
breakfast is F's origin, as is lunch. But the city in
which breakfast
occured is simply determined by F' noticing that LA's
coordinates are also
at the origin at breakfast (hence breakfast is in LA). But
San Diego's
coordinates are at the origin when he eats lunch, therefore
he concludes
that he at lunch in the city of San Diego.

Then he _should_ say that the distance between breakfast (in Los
Angeles) and lunch (in San Diego) is the distance between Los Angeles
and San Diego, in his frame, which is _not_ zero. But in SR,
the Lorentz
transformations say that he _must_ get a distance of zero between
breakfast and lunch.


No, you said in prior posts that you understand that distance as measured in
two different frames of reference may disagree in SR, but you proceed to
claim its a problem when you discover that they do indeed differ in this
example. Which is it?

Joel Rauber