Bell's Inequality and Quantum Gravity: On the Incompleteness of Quantum Mechanics and General Relativity

Vasil Dinev Penchev

WU Xin-zhong

This paper examines the history of Bell’s inequality from EPR argument to Bell’s papers, and the influence of Bell’s inequality on the frontier exploration of quantum mechanics. It is found that Bell’s inequality has some hidden assumptions that are different from EPR argument. Along Schrodinger’s idea that the measurement process of the EPR experiment requires time, Karl Hess and his follows treat time as a time order parameter, by extending the method of space-time geometry analysis of relativity to the localized geometry analysis of quantum states, it is believed that the reasoning of Bell’s inequality does not meet the requirements of the completeness of EPR argument. Analyzing the non locality of gravitational energy in general relativity makes it necessary for us to seek a more localized expression of relativistic gravitational theory. Based on local realism, exploring new interpretations and expressions of quantum mechanics may open up new avenues for studying quantum gravity. We found that Lorentz almost discovered the incompleteness of general relativity but erroneously insisted on the concepts of ether and absolute space, just as Einstein correctly discovered the flaws in the non local representation of quantum mechanics based on outdated determinism.

Hooman Moradpour, S. Jalalzadeh, Hamid Tebyanian

This study delves into the validity of quantum mechanical operators in the context of quantum gravity, recognizing the potential need for their generalization. A primary objective is to investigate the repercussions of these generalizations on the inherent nonlocality within quantum mechanics, as exemplified by Bell’s inequality. Additionally, the study scrutinizes the consequences of introducing a nonzero minimal length into the established framework of Bell’s inequality. The findings contribute significantly to our theoretical comprehension of the intricate interplay between quantum mechanics and gravity. Moreover, this research explores the impact of quantum gravity on Bell’s inequality and its practical applications within quantum technologies, notably in the realms of device-independent protocols, quantum key distribution, and quantum randomness generation.

Norbert Wiener, Dirk Jan Struik

Ernst Schmützer

L. E. Ballentine, Jon P. Jarrett

Special relativity demands a locality principle (no instantaneous action at a distance); locality implies Bell’s theorem; quantum mechanics violates Bell’s inequality, therefore, quantum mechanics contradicts relativity! Or so it would seem. It is shown, however, that the locality principle needed for Bell’s theorem is stronger than the simple locality that is needed to satisfy the demands of relativity and that quantum mechanics satisfies the latter. The stronger locality principle is equivalent to the conjunction of simple locality and predictive completeness, and it is the latter principle that fails. The notion of predictive completeness is weaker than, and is implied by, the completeness criterion of Einstein, Podolsky, and Rosen. But the quantum mechanical state description is not only incomplete but incompletable, for any local complete state description would satisfy Bell’s inequality and disagree with experiment.