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



Once again, an event occurs at a particular place and time. In your final
paragraph, both observers are right relative to their own reference frames.
The fact that I am in San Diego at a later time does not mean my breakfast
occurred in San Diego. It occurred at me. In my frame, San Diego happens
to be where I am at a later time. An observer who lives in San Diego,
however, would place my breakfast in Los Angeles. I put the distance
between breakfast and lunch as being zero, the California-bound observers
say the distance is some other number. I would agree with the California
observers that, at the time of my breakfast, Los Angeles coincided with my
location. The California observers would agree that, at a later time, my
location coincides with San Diego. That does not put my breakfast as
coinciding with San Diego--my location did not coincide with San Diego at
the time of the breakfast event.

The whole point of relativity is that observers do not agree on "here" and
"now". Sure, it seems counterintuitive, especially the "now" part, but
that's how the universe is. Centuries of experiments back up Galilean
relativity, decades of experiments back up special relativity.

If I actually stop in San Diego, then I have changed reference frames. My
original frame goes moving off to Mexico. The origin of that frame (set at
my location, of course) also goes off towards Mexico. I am now in a new
frame, whose origin is somewhere else.

You are trying to tie the location of an event (which is a particular place
and time) to an object (which has location that may change with time). An
event is not tied to a particular reference frame. An event simply has
coodinates in space and time. The transformation equations allow you to
calculate the coordinates of an event in one frame, knowing them in another
frame.

Michael Burns-Kaurin
Spelman College





David Rutherford
<drutherford@SOFT To: PHYS-L@lists.nau.edu
COM.NET> cc:
Sent by: Forum Subject: Re: A Geometrical Proof of the Non-invariance of
for Physics the Spacetime Interval
Educators
<PHYS-L@lists.nau
.edu>


01/17/2003 01:39
AM
Please respond to
Forum for Physics
Educators






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

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