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

[David Rutherford <drutherford@SOFTCOM.NET>]

"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"
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