Folks,
As responding to Michel's question:
> when A and B are events of void intersection, the equality
> P (A U B) = P(A) + P(B)
> could be violated ? Or what else ?
Andrei answered:
>Yes.
My entry is yes and no. A key is in how to prepare an ensemble of events
through the act of identification or measurement, whatever it may be. In one
scheme, one can make the two events A and B mutually exclusive (e.g., the
head or tail of tossing a coin), with void intersection. In another scheme,
on the other hand, one can make the two of them mutually interfering (e.g.,
the heads or tails of tossing two identical coins at the same time). The act
of measurement is crucial in preparing the ensemble of events with void
intersection, and the notion of probability remains innocent in this regard.
Nonetheless, Born's interpretation of the wavefunction as a probability
amplitude happened to open a can of worms despite its supreme usefulness
proved in countless examples in physics. It invited many people to take the
space defining the wavefunction (i.e., a Hilbert space) to be the
probability space, also. Experiments are usually done in ordinary space.
However, quantum mechanics interprets the experiments in a Hilbert space. If
a physicist picks up a strange Hilbert space, a biological organism may have
a curious intersection between being alive and dead there.
Cheers,
Koichiro
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Received on Tue May 30 23:53:24 2006
