Re: Causation in Physics: F=ma

[Stephen Speicher <stephen@SPEICHER.COM>]

On Fri, 14 Nov 2003, Brian Whatcott wrote:
> This gets us to the nub of an argument - which may not be
> the one which we should be considering - on the relativity.
>   This is to say that what precedes in one frame, may be
> simultaneous in another, and may follow in a third.
>
> It is this idea which above all, argues with causality.
> If you show a preceding and 'causal' event in one frame,
>   I can show it succeeding in another, I suppose I can say.

Saying it does not make it so. In special relativity _all_
inertial observers will agree on the temporal ordering of events
A and B _if_ those two events are causally related in _any_
inertial frame. This can be proved with mathematical rigor using
a partial order relation and the Collinear Set theorem. See
"Independent axioms for Minkowski space-time," John W. Schutz,
Pitman Research Notes in Mathematics Series, _Longman_, 1997.

In general relativity the causal structure of spacetime is
locally the same as special relativity, but that does not exclude
global differences. Hawking has shown that the conditions of
chronology and causality are the same for all "physically
realistic solutions." See "The large scale structure of
space-time," S.W. Hawking and G.F.R. Ellis, _Cambridge University
Press_, 1973/1999. Or, for a short discussion on the strong
causality condition and why non-stable causality is "generally
believed" to be physically unrealistic in general relativity, see
"General Relativity," Robert M. Wald, _The University of Chicago
Press_, 1984.

--
Stephen
stephen@speicher.com

Ignorance is just a placeholder for knowledge.

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