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

[David Rutherford <drutherford@SOFTCOM.NET>]

Bob LaMontagne wrote:
> David Rutherford wrote:
>
> > Maybe I can show the way I think it should be by using Galilean
> > relativity as an analogy. I know that the Galilean transformations
> > aren't used to find the spacetime interval between events, but I think
> > they can be used to make my point.
> >
> > Say the situation is the same as before, so that event E1 occurs at the
> > coincidence of the origins of F and F'. Then at time t = t, event E2
> > occurs at x = vt. The Galilean transformations give the coordinates of
> > E2 in F', in this situation, as
> >
> > x' = x - vt = vt - vt = 0
> > y' = y = 0
> > z' = z = 0
> > t' = t
> >
> > Now suppose that observers in F' are asked to give the distance between
> > E1 and E2. Should they say that x' = 0 (which is what the analogous
> > Lorentz transformations say), or should they say x' = x = vt = vt'? I
> > say they should say the latter.
>
> 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.

--
Dave Rutherford
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