From: scerir (scerir@libero.it)
Date: Tue Nov 19 2002 - 03:10:35 MST
> If event A causes event B then event A certainly does occur before event
> B in time, unless and until someone proves that faster than light
> communications are possible.
- gts
'Post hoc, propter hoc' said the latins and also Reichenbach who,
in 1956, suggested that the directionality of causality was
linked to the temporal asymmetry (Reichenbach also developed the
'common cause' principle, which introduces another kind of
directionality, and which is very relevant in the quantum
context).
Causal explanations satisfy two expectations: temporal (asymmetrical)
and/or statistical (not always asymmetrical). Within the statistical
expectations (probabilistic causality) it is possible to attribute
directionality also to the choice of language, to special assumptions
(Occam's razor, i.e.), etc. [see also Judea Pearl, Causality,
Cambridge UP, 2001].
In the quantum domain the situation is completely messy, because
there is also a time-symmetrical-two-state quantum mechanics,
because Schroedinger's eq. is time-symmetrical, because the
'common cause' principle seems to be invalid, because there is
the so called Wheeler's 'delayed choice' effect, and because
in general it is not sure there is a 'real time' ordering.
"Is there a real time ordering behind the nonlocal correlations?"
http://arxiv.org/abs/quant-ph/0110124
It is argued that recent experiments with moving beam-splitters
demonstrate that there is no real time ordering behind the nonlocal
correlations: In Bell's world there is no "before" and "after".
In Minkowski spacetime, ordering can be defined as
(x, y, z, t) <= (x', y', z', t') if and only if
(x - x')^2 + (y - y')^2 + (z - z')^2 <= c^2 (t - t')^2
*and* t <= t'
Thus, i.e., knowing that A and B are both in the past lightcone of C
is insufficient to say anything about the time order of A and B (they
could be either timelike, lightlike, or spacelike related to each other).
Actually lightcones of an event only provide a partial time ordering.
As any relativity book says the 'temporal' ordering resulting from choice
of a particular Cartesian coordinate chart, on the Minkowski spacetime,
is not a 'causal' ordering, because causality relationships in SR are
Lorentz invariant, whereas temporal relationships in Minkowski
spacetime are not.
See also, L. Sklar, Space, Time, and Spacetime, U. California Press, 1977,
chapter 4, 'causal order and temporal order'.
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