**Stephen Paul King** (*stephenk1@home.com*)

*Sat, 20 Nov 1999 14:36:53 -0500*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**I.Vecchi: "[time 1010] Re: [time 1009] [Fwd: Simpson's Paradox and Quantum Entanglement]"**Previous message:**Stephen Paul King: "[time 1008] Turing Machines vs. Real-World Computers [was: Colors of Infinity and Mathematical Reality] by Bill Dubuque"**Next in thread:**I.Vecchi: "[time 1010] Re: [time 1009] [Fwd: Simpson's Paradox and Quantum Entanglement]"

Hi All,

Robert Fung is making some great points!

Later,

Stephen

**attached mail follows:**

It is like _any_ paradox in terms of contradiction;

much in the same sense that 'solving' one NP-complete

problem, will 'solve' the rest.

Paradoxes form a class and any solution on one paradox

gives a clue for solving others simultaneously and

instantaneously.

*> either A and B are lacking in
*

*> concrete meaning, or the "givens" are themselves false. You are
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*> missing whatever part it has that makes it really paradoxical, if any.
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*>
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*> Quantum-mechanically, a particle can have a state such that "A has
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*> spin up" is neither true nor false, but subject to a probability
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*> distribution. But once A is observed, if B is observed later, B may
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*> have its own probability distribution, or it may correlate with A in
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*> some fashion. But it can't, after observation, be both spin up and
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*> spin down, either.
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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.

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.

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.

The Fourier transform (or more generally, an orthonormal transform):

turns functions into distributions, and vice versa.

Both the PD and the PDF "collapse" when _a single_ measurement

is made into _a single_ state of all the possible states.

You can take that single state measured and add it into

your PD (or its corresponding PDF) to increase its

forecasting ability in future measurements.

_Empirically_, we never really know for sure how large a

state space is, but experimentation can indicate it's size

probabilistically speaking. This empircal and so this

non-deterministic approach leaves open the possibilities of

measuring a state that was never before considered part of the

state space (a hidden variable).

_Theoretically_, we might try to do better and deterministically

define the state space size. But quantum mechanics does not use

this approach (as Einstein was wanting to say to Bohr)

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")

This is the usual consideration for superpositions of

states (or phasors in state space...) and their corresponding

wavefunction phases in time within the time-domain.

But, entanglement is an additional problem when you consider

not just the state-space of a single particle, but the

state space of two particles that interacted and so their

PD's and PDF's have some memory of that event as if they

were two bell's (or impulse response functions[1]) that

once clanged together and when separated, they maintained

a "memory" of that event in their separate sets of PDs and PDFs.

Those separate memorys are what allow the two particles

to be non-locally correlated, or "entangled".

Those memories however tend fade away (decohere) after a while.

But they should be maintainable, by a _local_ resonant

communications between the entangled particles.

Of what use that may be to quantum cryptography &c.,

I am not concerned with, as I think there are more significant

implications than that.

[1] have a look at the "perturbation" methods

and "Green's" functions in this context.

Sent via Deja.com http://www.deja.com/

Before you buy.

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**Next message:**I.Vecchi: "[time 1010] Re: [time 1009] [Fwd: Simpson's Paradox and Quantum Entanglement]"**Previous message:**Stephen Paul King: "[time 1008] Turing Machines vs. Real-World Computers [was: Colors of Infinity and Mathematical Reality] by Bill Dubuque"**Next in thread:**I.Vecchi: "[time 1010] Re: [time 1009] [Fwd: Simpson's Paradox and Quantum Entanglement]"

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