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



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. 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.

Bob at PC