42 Bell's Inequalities — Foundations and Quantum

Časlav Brukner, Marek Żukowski

Louis Vervoort

Here we show that spin-lattices can serve as a test object for quantum foundations and quantum information theory, revealing unsuspected properties. We propose a (thought) experiment on such lattices that mimics the Bell- experiment and calculate the outcomes and the Bell inequality. It appears that for a wide range of geometries the Bell- inequality is violated, even if these lattices are local according to the usual definitions. Some spin-1/2 lattices can even violate the Bell inequality more than the Tsirelson bound. We argue that there is no consensual explanation for this result. We make the link with problems in quantum foundations and quantum information theory.

H. E. Andås

J. V. Corbett, Dipankar Home

The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of Bell's inequality necessarily implies nonlocality because of the measurement problem. The differences in the implications of deterministic and stochastic formulations of Bell's inequality are highlighted. The reality condition used in Bell's inequality is shown to be a generalisation of Einstein's later form of realism.

E. C. G. Sudarshan, Tony Rothman

Ilija Barukčić

Today, quantum-mechanical concepts i.e. such as non-locality refer to some mathematical foundations, especially to Bell’s inequality and the Chsh inequality. Experimental data, analyzed while using Bell’s inequality or the Chsh inequality, favor a quantum mechanical description of nature over local hidden variable theories (often referred to as local realism). In general, the use of mathematically inconsistent methods can imply a waste of money, time and effort on this account. Under some certain conditions (the assumption of independence) Bell’s theorem and the Chsh inequality are already refuted. The purpose of this publication is to explore the terra incognita, the interior logic that may lie beyond Bell’s original theorem and the Chsh inequality and to refute both Bell’s original theorem and the Chsh inequality under any circumstances by the proof that we can derive a logical contradiction out of Bell’s inequalities. Thus far, if you accept Bell’s theorem or the Chsh inequality as correct, then you must accept too that +0 = +1, which is a logical contradiction. Bell’s theorem and the Chsh inequality are refuted in general. In this insight, it appears to be necessary to revisit the very foundations of quantum theory and of physics as such.