Re: Simpson's Paradox and Quantum Entanglement

Jim Carr (jac@ibms48.scri.fsu.edu)
Thu, 2 Dec 1999 02:31:16 +0100 (MET)

... reduced followups ...

In article <383481b5.22773510@news.prosurfr.com>,
savard@snooze.freenet.eZdZmonton.aZb.cZa (John Savard) wrote:
}
} ca314159@bestweb.net wrote, in part:
} >Given that
} > 1) A and B are complementary
} > 2) A and B are both true XOR A and B are both false
} >then, that 1) contradicts 2) is the essence of Simpson's Paradox.
...

} 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.

In article <813ums$sug$1@nnrp1.deja.com>
ca314159@bestweb.net writes:
>
> You're thrashing here abit.
>
> There is no 'probability Distribution' (PD) after the state
> is measured. It's only active while everything is dynamic
> and not measured and in a very large sense it is only an
> abstraction during that interlude between measurements.

There is. It might be a delta function, or (as suggested by
the remarks above) it could be that B is a measurement of
something like the spin along a different axis than A measured.

> A histogram or barchart is a set of possible states with relative
> frequencies attached to each state, but as such it is not
> interpreted probabilistically. It is just a bunch of
> positive amplitudes distributed over the _space_ of states.

Given that the distinction between amplitudes and probabilities
is an important one, using "amplitude" to refer to a probability
is not a good idea.

> If we interpret this histogram or bar chart probabilistically,
> then we get a "probability _distribution_". If we Fourier
> transform this probabilistically interpreted histogram
> or space-like _distribution_ (spectrum) into
> the time-like domain, we get a "probability density _function_" (PDF)
> or "wavefunction". This is just a time-like Function with a
> probabilistic interpretation just as its complementary
> space-like Distribution was given a probabilistic interpretation.

However, it might be real rather than complex. Where the statistical
assumptions of QM differ from those normally used is at this point,
and the exercise you describe cannot recover the complex phase of
the wavefunction that is responsible for what some consider to be
paradoxes.

-- 
 James A. Carr   <jac@scri.fsu.edu>     | Commercial e-mail is _NOT_ 
    http://www.scri.fsu.edu/~jac/       | desired to this or any address 
 Supercomputer Computations Res. Inst.  | that resolves to my account 
 Florida State, Tallahassee FL 32306    | for any reason at any time. 

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