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



Hugh Haskell wrote:

At 23:04 -0800 1/20/03, David Rutherford wrote:

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.

No.

All I know for certain is what goes on in *my* reference frame. If a
location in my reference frame happens to coincide with one point in
another reference frame at one time and a different point in that
reference frame at another time, so be it. The person in the Los
Angeles/San Diego reference frame can measure the distance between
those two points with a tape measure. I cannot. All I can do is
calculate the distance by multiplying the relative speed between the
two frames by the time *I* measure on the clock I carry with me.

If you do it that way, you will _not_ get zero for the distance between
breakfast and lunch in F'. SR definitely says that you _will_ get zero
for that distance. Therefore, by your own admission, SR gives the wrong
results for this situation.

The times and the distances measured by observers in the two reference
frames will not be the same.

I never said they would be (except for the Galilean case).

But since the Lorentz transformation
allows us to find the relationships between those times and
distances, it is also true that both observers will find the
magnitude of the spacetime interval between the two to be the same.

Not if they make the measurements using the method you described.

--
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