Abstract In the paper it is demonstrated that Bell’s theorem is an unprovable theorem. The unprovable characteristic has, on the chemical side, repercussions for e.g. spin chemistry and the related magneto-reception studies. We claim that the unprovability of this basic mathematics cannot be ignored by the physics and chemical research community. The demonstrated mathematical multivaluedness could be an overlooked aspect of nature.
Abstract In the paper it is demonstrated that Bell’s theorem is an unprovable theorem. The unprovable characteristic has, on the chemical side, repercussions for e.g. spin chemistry and the related magneto-reception studies. We claim that the unprovability of this basic mathematics cannot be ignored by the physics and chemical research community. The demonstrated mathematical multivaluedness could be an overlooked aspect of nature.
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.
Abstract: The principle of causality occupies an important place in the history of the philosophical interpretation of quantum mechanics from the beginning. In last consequence, today’s Copenhagen dominated acausal interpretation of quantum mechanics casts doubt upon traditional views in the philosophy of nature and demands the revision of the principle of causality at a fundamental level of theoretical description in physics. Testing the mathematical and logical consistency of the quantum mechanical description of nature i. e. especially such as non-locality has become a subject of an ongoing dispute and research. 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 by the help of 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 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, accept Bell's theorem or the CHSH-inequality as correct,
The most prominent version of Bell’s theorem consists of the Bell-CHSH inequality and a quantum-mechanical example that violates it. The inequality is shown to rest on the non-trivial presupposition that the values of elementary spin quantities are scalars, and not, e.g., vectors. In the version considered, the theorem’s argument succeeds for scalars and fails for vectors. However, the reference to vector values can be motivated by the physics of spin. Hence, recognizing the presupposition suggests a critical reassessment of the theorem.
An analysis of both the original and the CHSH Bell inequalities is presented. Two additional mathematical assumptions are identified in the theorem. These are: all variables in the inequalities have a field algebraic structure, and all variables have measurability as a mathematical property. This means the variables are of metric-type, mathematically indistinguishable from those of classical theories. The consequences of attributing the violation of Bell’s theorem to these assumptions are examined.
In a recent article [], Genovese and Piacentini analyzed recent experiments measuring what they call “the entire Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) parameter.” They claimed those experiments may have implications for interpreting loophole-free tests of the Bell-CHSH inequality. We explain that the Bell-CHSH inequality is not based on the entire Bell parameter, so these experiments are unrelated to their empirical tests and cannot close any eventual loopholes that might still persist. We point out that the physical meaning of these new experiments measuring the entire Bell parameter could be interpreted differently.
Bell inequalities represent a milestone for contemporary physics, both for quantum foundation investigations and technological applications (e.g., quantum communication and entanglement certification). Although loophole-free tests have been recently performed, a strong debate is still ongoing on the actual meaning of Bell inequality tests, for example, on the possible additional hypotheses and eventual loopholes to be included in Bell's theorem, as well as on the implications for certain interpretations of quantum mechanics. A recent work [S. Virzì , ] challenges some of the statements appeared in this debate, achieving an experimental estimation of the entire Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) parameter from a single entangled pair owing to a weak-interaction-based measurement approach. Here, we analyze the implications of this result for quantum mechanics foundations investigation, illustrating how it can tackle some of the aforementioned interpretations of Bell inequality tests and, more in general, of quantum mechanics itself.