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

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

David Rutherford wrote:

> In response to a question asking if it's a fair statement that I expect
> a line drawn from E1 to E2 to "coincide" in different frames, I replied:
>
>         No, I don't expect the line to coincide in different reference
>         frames. In the case I gave, the lines don't coincide in F and
>         F', but the point I'm trying to make is that they don't coincide
>         in spacetime, either. When I say they don't coincide in
>         spacetime, I mean, they don't coincide independently and apart
>         from either reference frame.

If E1 is a an event in spacetime, and E2 is a separate event in spacetime,
how is there more than one unique "line" connecting them? F and F' may have
different descriptions for that line, but there's nothing to "coincide
independently" since there's only one line being referred to.

You certainly wouldn't ask if E1 "coincides independently" in F and F'
because it's only one event. Likewise for E2. Why then ask that question of
the line from E1 to E2?

Bob at PC