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



Hugh Haskell wrote:

At 17:21 -0800 1/20/03, David Rutherford wrote:

(4) If you had breakfast in Los Angeles and lunch in San Diego, would
you really tell _anybody_ that you had breakfast and lunch in the
same place?

That depends entirely upon whether you are in the same reference
frame as Los Angeles and San Diego (which I assume are in the same
reference frame--at least most of Los Angeles is on the same tectonic
plate as San Diego is).

If my frame of reference is a uniformly moving train that passes Los
Angeles at breakfast time and San Diego at lunch time, then I can
easily say that I had breakfast and lunch in the same place--the
dining car.

I'm not denying that you _can_ say that you had breakfast and lunch in
the same place. I'm arguing that it's not valid, geometrically to do so.
When you (the moving observer) determine the spatial distance between
breakfast and lunch at lunchtime, you put the breakfast end of the tape
measure at San Diego, not Los Angeles, and the lunch end of the tape
measure at San Diego. The Los Angeles observers put the breakfast end of
the tape measure at Los Angeles and the lunch end of the tape measure at
San Diego. The locations, in space, of breakfast at the time of lunch,
are what both frames consider to have been the locations of breakfast,
at the time of breakfast, since both frames say that the locations have
not changed, in their frame, since the time of breakfast. These
locations don't coincide in space, thus, they don't coincide in
spacetime.

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

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