Tests of Bell's inequality are essential to determining if my approach is correct and to motivating the research need to develop my approach. Thus it is useful to briefly review the history that led to Bell's inequality.

In the early 1930's von Neumann published a paper that claimed to prove that no more complete theory could be consistent with the predictions of quantum mechanics[33,34]. Two years later Einstein, Podolsky and Rosen, in a classical paper frequently referred to today as EPR , argued that quantum mechanics is an incomplete theory because properties that are conserved absolutely such as momentum must have some objective reality to them and does not model this objective reality[15]. Einstein later argued in a famous series of debates with Bohr

that the that there must be additional hidden variables that provide a more complete description of a quantum mechanical system. In the early 1950's Bohm published what he called a ```hidden'' variables theory' that was nonlocal but deterministic and consistent with the predictions of [6]. This suggested there was something wrong with von Neumann's proof. At the time Bohm felt that his theory was different than at some point and thus escaped von Neumann's proof but this apparently is not true and it is the nonlocal nature of Bohm's theory that allows it to reproduce the predictions of in a deterministic model.

showed that von Neumann's assumptions were too
restrictive[4]. Bell felt it
was not possible to prove the general result von Neumann claimed
and started looking for additional constraints that might allow one
to distinguish between and hidden variable theories. Influenced by
Bohm's work, he developed an inequality that the statistics of
events with a space-like separation must obey in any *local*
hidden variables theory. (Events are space-like separated if they are close enough in time and
far enough apart in space so that no signal traveling at the speed
of light can go from one to the other.)

Bell proved predicts this inequality is violated[3]. In the 1970's Eberhard

derived Bell's result without reference to local hidden variable
theory, it applies to all local theories[12,13]. Eberhard also showed that the
nonlocal effects predicts cannot be used for superluminal
communication. Eberhard assumed a statistical law known is
contrafactual definiteness in his derivation. That is he assumed
that he could average over all the *possible* outcomes of a
*single* experiment. Previously Stapp had argued that Bell's
inequality was evidence that this property does not hold for
quantum mechanical effects[30].
This assumption is a standard one in statistical analysis. Some
argue that the uncertainty principle is a reason for doubting this
principle for quantum effects. How can there be a definite outcome
for an experiment not performed in ? The reason one can make such
arguments is the claim that probabilities are irreducible in .
There is no mathematics of irreducible probabilities and reason to
doubt that one can develop such mathematics. Thus one can argue
that probabilities in are something different than in classical
mechanics and completely outside of any known mathematics. In
theory one can ascribe any property one wants to probabilities in .
Thus, for example, Youssef has argued that probabilities in are
complex and not real valued[40].

I doubt all of this. I think the difference between classical and is in the conceptual framework of the theories as discussed in Section on page

and not in basic principles of mathematics or statistics.

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