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

[David Rutherford <drutherford@SOFTCOM.NET>]

Michael Burns-Kaurin wrote:
> Relativity does not put the location of your breakfast in two different
> places.  Breakfast occurred where it occurred, at a particular time.  Both
> sets of observers agree that breakfast occurred at Los Angeles, at you.  At
> lunchtime, you are now in San Diego, but that does not put the location of
> breakfast in San Diego.

It does for "you". The measurement of the _spatial_ separation
(distance) between breakfast and lunch in each frame is necessarily
instantaneous in each frame. The measurement is made at the time of
lunch since, before then, the distance between lunch and dinner is
unknown. That means that the locations attributed to the event
"breakfast" are Los Angeles for the earthbound  frame (F), and San
Diego for the travellers frame (F'), since for F', breakfast and lunch
occur at the same place.

Say that F' stops at the time of lunch in San Diego. Since he claims
that breakfast and lunch were in the same place, he then proclaims aloud
"this is where breakfast occurred" (San Diego). At the _same_time_ a guy
in F, standing in Los Angeles, shouts "no, this is where breakfast
occurred" (he's slightly precognitive). But since F' has stopped, he can
claim to be in F, which means that breakfast is claimed to have
occurred at two separate places in F. If breakfast is at two separate
places in the same frame at the same time, then it is at two separate
locations 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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