I recently attended a presentation on the fundamentals of quantum mechanics which focused on the most recent experimental tests on Bells Inequality. As part of the introduction the speaker derived Bells Inequality. The speaker made it sound very straightforward and it was, the proof was a piece of cake. However, when I examined the proof later there appeared to me to be what might be a subtle flaw in the logic. A seemingly innocuous assumption that may well be inappropriate is made during the course of the proof. For the sake of allowing me a good nights can someone put me right on this:(adsbygoogle = window.adsbygoogle || []).push({});

The lecturer started by positing that when considering spin 1/2 particles Bell he was unable to derive any LHV (Local Hidden Variable) theorem which was consistent with the results as QM but there are so many possible LHV models to consider that he came to an impasse. He then went on to say: now Bell did something quite brilliant, he ignored quantum mechanics all together and came up with a statistical inequality that must be observed by any LHV system. He was then able to show that the predictions of QM where not consistent with this inequality.

For the next bit its important to understand the Gedankenexperiment:

Two spin one half particles are in a singlet state. Each of the pairs spins are measured by two distant apparatus. Each apparatus is such that it allows two possible measurements -

-A random measurement (each of the apparatus can make an independent spin measurement ie each different than the other) and

-A fixed measurement. ( both apparatus have a setting fixed at say 30 degree)

The inequality is then constructed using the very crucial assumption that measurements made along the fixed axis are negatively correlated. ie when A measures up B measures down. In the non quantum world we can assume this to be correct even when no measurement is made. Hence we can essentially measure each particle twice, once along the random axis and then again along the fixed axis - but we don't actually measure along the fixed axis we just know what the outcome of the correlation will be. However we can not assume this to be true in the quantum world. Each particle can be measured only once by each apparatus, not twice and within the derivation it is assumed that this is possible. It is a subtle point that I haven't seen any discussion of. To sum up, that Bells inequality is violated by quantum experiments is merely due to the fact that it is not appropriate for quantum systems and therefore its violation reveals nothing more than the fact that two concurrent measurements of spin are not possible on the same particle at the same time. Rather than the current interpretation that it somehow invokes the reality of non locality. If the inequality is modified in such a manner as to allow for a distinct and separate measurement of a particle along the fixed axis/setting, then another pair of particles is required which dilutes the expectation values and would likely result in an inequality which is consistent with QM.

Regards

P

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# Bell's Inequality - A misintepretation of probability?

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