About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular: (i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography, (ii) how the measurement problem ( "why do we observe no tables in superposition?" ) can be polled in weakly decaying systems, (iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation. These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has.
About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular: (i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography, (ii) how the measurement problem ( "why do we observe no tables in superposition?" ) can be polled in weakly decaying systems, (iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation. These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has.
John St. Bell was a physicist working most of his time at CERN and contributing intensively and sustainably to the development of Particle Physics and Collider Physics. As a hobby he worked on so-called "foundations of quantum theory", that was that time very unpopular, even considered to be scientifically taboo. His 1964-theorem, showing that predictions of local realistic theories are different to those of quantum theory, initiated a new field in quantum physics: quantum information theory. The violation of Bell's theorem, for instance, is a necessary and sufficient criterion for generating a secure key for cryptography at two distant locations. This contribution shows how Bell's theorem can be brought to the realm of high energy physics and presents the first conclusive experimental feasible test for weakly decaying neutral mesons on the market. Strong experimental and theoretical limitations make a Bell test in weakly decaying systems such as mesons and hyperons very challenging, however, these systems show an unexpected and puzzling relation to another big open question: why is our Universe dominated by matter, why did the antimatter slip off the map? This long outstanding problem becomes a new perspective via the very idea behind quantum information.
In 1964 the physicists John St. Bell working at CERN took the 1935-idea of Einstein-Podolsky-Rosen seriously and found that all theories based on local realism have to satisfy a certain inequality, nowadays dubbed Bell’s inequality. Experiments with ordinary matter systems or light show violations of Bell’s inequality favouring the quantum theory though a loophole free experiment has not yet been performed. This contribution presents an experimentally feasible Bell inequality for systems at higher energy scales, i.e. entangled neutral Ҡ -meson pairs that are typically produced in Φ -mesons decays or proton-antiproton annihilation processes. Strong requirements have to be overcome in order to achieve a conclusive tests, such a proposal was recently published. Surprisingly, this new Bell inequality reveals new features for weakly decaying particles, in particular, a strong sensitivity to the combined charge-conjugation-parity (CP) symmetry. Here-with, a puzzling relation between a symmetry breaking for mesons and Bell’s inequality—which is a necessary and sufficient condition for the security of quantum cryptography protocols— is established. This becomes the more important since CP symmetry is related to the cosmological question why the antimatter disappeared after the Big Bang.
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible quantities are not allowed by classical mechanics, a feature that is called as "quantum nonlocality". An experimental observation of those correlations, in other words, a violation of the limits imposed by classical physics, implies the correctness of quantum description and invalidates the classical, local realistic models. The first Bell experiments were proposed by Clauser, Horne, Shimony, and Holt, who invented the most famous Bell's inequality [13]. Later, the Aspect experiments were satisfactory enough for the physics community to be conclusive about the validation of quantum mechanics [1][3][4][2]. Ekert's work on applications of quantum nonlocality to communication resulted in the new field of quantum communication and cryptography, and turned the research program into a practical one [20]. Pitowsky showed a method to find all expressions of limitations due to local realism, all Bell's inequalities, for a given physical scenario. He also proved that the problem is, unfortunately, NP-complete and hence as the scenarios get more complex, they also become computationally intractable [33][34]. Therefore, different methods for the solution of special cases of the problem are necessary. Inequalities found for those special cases can be called classes of Bell's inequalities. For example, Werner and Wolf [41] and Collins, Gisin, Linden, Massar, and Popescu [16] found classes that cover a wide range of scenarios. Our work is a similar kind of effort to produce and study new types of Bell's inequalities.
Abstract John Stewart Bell was one of the most significant physicists of the twentieth century; his work has led to a much enhanced understanding of quantum theory and what it says about the physical universe, particularly about realism, determinism, and locality. This book describes Bell's relatively humble origins and his struggles to obtain secondary and university education. It then describes his work at Harwell, where he made important theoretical contributions to the development of particle accelerators, in particular with his pioneering work on strong focussing. Later, he proved the extremely important CPT theorem. At CERN, Bell made a range of important theoretical contributions to elementary particle physics; these contributions include the physics of neutrinos, the existence of different types of neutrinos, the suitability of gauge theory for all physical interactions, and the Adler–Bell–Jackiw anomaly, which shows how classical symmetries are lost under quantum theory. In his work on quantum theory, he criticized the orthodox 'Copenhagen' interpretation of quantum theory, which did not allow the actual state of the physical world to be analysed. He showed that the famous von Neumann theorem, which claimed to show that 'hidden variables' were not allowed in quantum theory, was incorrect; his famous Bell's theorem, or Bell's inequality, showed that any such variables much be non-local. Bell's work led to greatly increased freedom in the discussion of quantum theory, and the development of quantum information theory.
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates ‘local causality’) became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about themathematical form of the local causality condition and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, in both its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action at a distance, can be articulated in the Everett interpretation. Introduction John S. Bell's last word on his celebrated nonlocality theorem and its interpretation appeared in his 1990 paper ‘La nouvelle cuisine’, first published in the year of his untimely death. Bell was careful here to distinguish between the issue of ‘no superluminal signalling’ in quantum theory (both quantum field theory and quantum mechanics) and a principle he first introduced explicitly in 1976 and called ‘local causality’ [1]. In relation to the former, Bell expressed concerns that amplify doubts he had already expressed in 1976. These concerns touch on what is now widely known as the no-signalling theorem in quantum mechanics, and ultimately have to do with Bell's distaste for what he saw as an anthropocentric element in orthodox quantum thinking. In relation to local causality, Bell emphasised that his famous factorizability (no-correlations) condition is not to be seen ‘as the formulation of local causality, but as a consequence thereof’ and stressed how difficult he found it to articulate this consequence. He left the question of any strict inconsistency between violation of factorizability and special relativity theory unresolved, a not insignificant shift from his thinking up to the early 1980s.
Lying at the heart of quantum mechanics, the notion of quantum superposition causes enormous difficulty in understanding the problem of quantum measurement, which concerns the Einstein-Bohr debate on the conceptual foundations of the quantum theory. According to Bell’s theorem, Einstein’s viewpoint in his debate with Bohr seems to be wrong. In the present paper, a new principle (referred to as the general principle of measurements) is introduced and proved as a mathematical theorem. Based on this principle, various forms of quantum superposition (including quantum entanglement) and the corresponding experiments are scrutinized. The main findings are as follows. (a) Einstein’s viewpoint is correct and Bell’s theorem is problematic. (b) Measurement outcomes of any actual experiment with individual microscopic objects described in a form of quantum superposition, in particular, the experimental results of testing Bell inequalities, are all erroneously explained. (c) Bell inequalities failed to capture the essence of the Einstein-Bohr debate, i.e., whether quantum superposition is legitimate for describing individual microscopic objects. (d) All kinds of quantum superposition violate the general principle of measurements and hence are illegitimate. (e) Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space for describing a single microscopic object, and the mathematical setting will remain essentially unchanged; hidden-variable theories are irrelevant to the real world. (f) After completing quantum mechanics as above, the difficulty in understanding the problem of quantum measurement disappears naturally. Implications of the findings are also discussed.