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

[David Rutherford <drutherford@SOFTCOM.NET>]

David Rutherford wrote:
> David Rutherford wrote:
> > Robert Cohen wrote:
> > > I hesitate to get into this fray because I know very little about
> > > relativity but here goes.
> > >
> > > David Rutherford wrote:
> > >
> > > > I'm just saying that they lead to a paradox when you compare the
> > > > assigned locations of breakfast, in the two frames, at the time of
> > > > lunch, which is when you "draw the lines" between breakfast and lunch,
> > > > in the two frames.
> > >
> > > [snip]
> > >
> > > > Therefore, both lines (from breakfast) start at time zero, but at
> > > > different spatial locations. That means that they start at different
> > > > points in spacetime, thus, they don't coincide in spacetime and
> > > > cannot describe a geometically invariant quantity (the spacetime
> > > > four-vector between the events).
> >
> > It's interesting that you snipped the (one) line out of the whole
> > paragraph:
> >
> > "Each frame draws his line starting from the assigned location _in space_
>
> Sorry, this should be "...the assigned spatial location in each frame...".

Sorry, again, I didn't read the whole line. The entire line should read:

"Each frame draws his line starting from the assigned spatial location,
in his frame, of breakfast, at the time of lunch, but he assigns it
_time_ zero, since he says that the location of breakfast at the time
of lunch is the same as it was at the time of breakfast."

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

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