Re: Simpson's Paradox and Quantum Entanglement

Christian Borgelt (borgelt@iws.cs.uni-magdeburg.de)
Thu, 25 Nov 1999 01:34:11 +0100 (MET)

What about looking up the classical reference:

Hans Reichenbach.
Logical Foundations of Quantum Mechanics.

It is still available from Dover Publications.

In this book Reichenbach also develops a multi-valued logic
to deal with quantum phenomena. From it stems the Reichenbach
implication that is sometimes used in fuzzy logic.

Regards,

Chris

-----------------------------------------------------------------------
Christian Borgelt

Otto-von-Guericke-University of Magdeburg
Department of Knowledge Processing and Language Engineering
Research Group Neural and Fuzzy Systems

Universit"atsplatz 2 Phone : +49.391.67.12700
D-39106 Magdeburg Fax : +49.391.67.12018
Germany E-mail: borgelt@iws.cs.uni-magdeburg.de
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H. Mark Hubey writes:
> > > either A and B are lacking in
> > > concrete meaning, or the "givens" are themselves false. You are
> > > missing whatever part it has that makes it really paradoxical, if any.
> > >
> > > Quantum-mechanically, a particle can have a state such that "A has
> > > spin up" is neither true nor false, but subject to a probability
> > > distribution. But once A is observed, if B is observed later, B may
> > > have its own probability distribution, or it may correlate with A in
> > > some fashion. But it can't, after observation, be both spin up and
> > > spin down, either.
>
> I created some 4-valued logics to fiddle with problems of this type.
> For example, one has T, F and B (both, true and false), B' and the other
> has T,F and N (neither false nor true), N'. These can be made to
> collapse
> to the standard T/F logic.
>
> The spin is unknown before the measurement so the statement "it has
> spin up or down" is neither true nor false, and then it collapses to
> the T/F as as soon as the measurement is made.
>
> OR the spin could actually be oscillating and that is what makes
> the state unknowable. When the measurement is made then it catches
> the spin at that particular moment.
>
>
> > So, measuring a single spin-up particle collapses
> > both its PD in the space-like domain and its PDF in the
> > time-like domain and all the other states are then "false"
> > (in this case there is only one other state in the binary
> > state-space of up and down spins, so that the spin-down
> > state is instantly "false" when the spin-up state is
> > measured as "true")

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