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

[David Rutherford <drutherford@SOFTCOM.NET>]

Bob LaMontagne wrote:
> David Rutherford wrote:
>
> > Bob LaMontagne wrote:
> > >
> >
> > > Place observer F' in the trailer of a moving truck - no windows. F' dills a hole
> > > in the floor of the trailer and drops a stone throgh the hole. A minute later F'
> > > drops anopther stone. Since F' is unaware of his motion, he would say the
> > > "distance" between the stones was 0.
> >
> > Assuming that the observer in F' drops the stones from a flying trailer,
> > high above the ground so that the stones drop straight down without
> > hitting the ground, and neglecting air resistance, yes you are right.
> > He would say the "distance" between the stones in the x-direction is
> > zero.
> >
> > > But F, of course, gets an entirely different
> > > answer. They could only agee on a common value for the distance if they somehow
> > > communicate with each other and become aware of their relative motion. Whether
> > > it's Galilean or Relativistic transformations is irrelevant.
> >
> > No, observers in F would also say the "distance" between the stones in
> > the x-direction is zero.
>
> Oops - obviously should have checked my spelling before hitting <send> :-)
>
> Anyway, I really don't understand your last statement.

Both stones fall along a vertical line extending down from the hole in
the trailer. At a given time, the stones are aligned vertically along
this line in F _and_ F', meaning that their separation along the x and
x'-axes is zero, at all times, in both frames.

> Let me make the example more
> specific. The F' people in the trailer drop a stone. When it hits the floor it shakes
> dirt loose from the bottom of the trailer and it falls on the ground (F frame). Later,
> F' drops another stone on top of the first and again dirt is loosened and falls to the
> ground. F' measures a distance of 0 between the stones (they lie on top of each
> other).

F also measures a distance of 0 (in the x-direction) between the stones,
since they're on top of each other in F, as well.

> F measures about a mile between the patches of dirt.

F' can't see the patches of dirt, anymore, since his hole has passed
them by. So he has no idea how far apart they are. If he could see them,
he would say that they are (nearly) a mile apart.

> How does this fit with your last comment? (Again, your example was Galilean - but same idea in Relativity.)

This doesn't fit with my last comment, since the dirt hits the ground in
F, unlike the stones in the first example. Remember, I said above that
"the stones drop straight down without hitting the ground".

Bye the way, thanks for mentioning that my clock/date were off. The
battery was dead.

--
Dave Rutherford
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