Re: A Geometrical Proof of the Non-invariance of the Spacetime In terval

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

Michael gave about as good a response as I could and correctly interpreted
(corrected actually!) what I meant to say regarding "occuring at the same
location".

Joel R.

> -----Original Message-----
> From: David Rutherford [mailto:drutherford@SOFTCOM.NET]
> Sent: Thursday, January 16, 2003 1:09 PM
> To: PHYS-L@lists.nau.edu
> Subject: Re: A Geometrical Proof of the Non-invariance of the
> Spacetime
> Interval
>
>
> "RAUBER, JOEL" wrote:
> > Continuing the dialog:
> >
> > (In all my comments I assume that we are discussing events
> as measured by
> > inertial reference frames.)
> >
> > > > > Suppose you have breakfast in Los Angeles then you
> drive to San Diego
> > > > > and have lunch there. Do you claim to have had
> breakfast and lunch in
> > > > > the same place?
> > > >
> > > > Perhaps if we stick to this example we can get somewhere.
> > > >
> > > > I claim that breakfast and lunch occur at different
> locations (not the same
> > > > location).
> > >
> > > Special relativity claims that you claim that breakfast
> and lunch occur
> > > at the same location.
> >
> > It does?  I am aware of no such requirement.  I thought we
> just stipulated
> > that breakfast was in LA and lunch was in San Diego?
>
> According to relativity, from my viewpoint (in the earth
> frame) you had
> breakfast in Los Angeles and lunch in San Diego. But from
> your viewpoint
> (in you) you had breakfast in you and lunch in you (the same place). I
> was just trying to point out that the way we actually view
> things is not
> the way that relativity says we view things.
>
> The way we actually view things is the way we _should_ view
> things (and
> apparently, you agree). The time at which each of us actually
> determines
> the space and time interval between breakfast and lunch is at the time
> of your lunch, since we have to wait until then to know what the
> location and time of your lunch is. According to relativity,
> at the time
> of your lunch, if I am asked what is the location of your breakfast, I
> say it's Los Angeles, but you say it's the location of you,
> which is now
> San Diego. Relativity puts the location of your breakfast in two
> different places. That means that the location of your breakfast,
> according to relativity, is not at the same place in spacetime.
>
> > Two events may or may not occur at the same location (same
> location defined
> > as the same spatial coordinates at the two different times
> as measured by a
> > *single* frame of reference. Note: this definition is frame
> independent).
> > > > I also claim that the special relativistic space-time
> interval between the
> > > > events of lunch and breakfast are the same as measured
> in all inertial
> > > > reference frames.
> > >
> > > Special relativity doesn't apply if you claim that
> breakfast and lunch
> > > occur at different locations.
> >
> > I disagree with the above statement.  The theory of special
> relativity is
> > fully capable of handling the situation of two events
> occuring at different
> > locations.  (location defined as above).
>
> I wasn't saying that special relativity doesn't give the same
> spacetime
> interval in all reference frames. That's not my argument. I'm saying
> that, in special relativity, the lines between breakfast and lunch in
> the two frames are the same length, but 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
>
> 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