Re: Bell's Inequality & Determinism vs Nondeterminism

From: scerir <>
Date: Wed, 3 Oct 2001 16:24:45 +0200

> The point of ATOEs
> is: as long as the computability assumptions hold, any complex universe
> is unlikely, no matter whether Bell's inequality makes sense in it or not.
> From this point of view Bell's inequality and locality are not
> the real issues. The issue is more general. It is determinism vs
> nondeterminism.

Following Jarrett, Shimony, Howard, Cushing, Suppes, van Fraassen, the
original Bell locality condition [for a composite system in a joint state the
joint probability of outcomes for measurements of observables is equal to
the product of the separate probabilities] is equivalent to the conjunction
of two independent conditions: a locality condition and a separability condition.

Locality = Given two systems A and B, space-like separated, the state
of A cannot be influenced by events (measurements) on B, and viceversa.

Separability = Two systems, separated by some spatio-temporal interval,
possess their own separate states, regardless of their previous history,
and the joint state is completely determined by their own separate states.
Now Aspect (et al.) showed that Bell locality condition is not true.
It means either the violation of the locality condition or the violation of the
separability condition (or both).

The violation of locality condition implies superluminal comunication (signaling).
But Eberhard, Page, Ghirardi (et al.) showed that QM implies (just) the
violation of the separability condition.

Notice that a perfect **deterministic** quantum theory (i.e. one in which
the range of any probability distribution of outcomes is the set [0,1]) which
is able to reproduce all QM predictions, implies - for sure - the violation
of the locality condition. Which means: superluminal signals, backward

Locality and determinism are linked (are faces of the same coin).

Received on Wed Oct 03 2001 - 07:28:55 PDT

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