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Re: A Geometrical Proof of the Non-invariance of the Spacetime Interval



"RAUBER, JOEL" wrote:

-----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,

Right, they do for this example.

but you proceed to claim its a problem when you discover that they
do indeed differ in this example.

I never claimed that they don't differ. My problem is not with the fact
that the distances between the two events differ, it's with the fact
that the assigned locations of breakfast, in the two frames, at times
later than the occurrence of breakfast, don't coincide in spacetime.

Which is it?

Which is what?

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf