Abstract Examples of violations of Bell inequalities in Special relativity theory (SRT) have led to the need to look for the causes of violations outside of quantum mechanics (QM) and possibly outside of physics. The ability to derive Bell inequalities (BI) from set properties allows us to find the necessary condition for violations: the relativity of sets. At the same time, a necessary condition of a physical theory is the subjective independence (SI) of its propositions. This kind of objectivism, together with the principle of a priori maximum possible ignorance (AMPI), leads to the use of flat spaces in fundamental theories such as QM and SRT, where the principles of SI and AMPI can be implemented. In turn, the measurable quantities represented in spaces turn out to be relative. In this respect, SRT is not much different from QM. This proximity predetermines BI violation in both cases and in both cases the violation of BIs confirms the subject-independent nature of physics. In a classic Gedankenexperiment was demonstrated, that the violation of BI does not contradict the presence of hidden parameters if they are represented by relative quantities. However, the question arises: are relative properties and quantities indeed local?
Abstract Examples of violations of Bell inequalities in Special relativity theory (SRT) have led to the need to look for the causes of violations outside of quantum mechanics (QM) and possibly outside of physics. The ability to derive Bell inequalities (BI) from set properties allows us to find the necessary condition for violations: the relativity of sets. At the same time, a necessary condition of a physical theory is the subjective independence (SI) of its propositions. This kind of objectivism, together with the principle of a priori maximum possible ignorance (AMPI), leads to the use of flat spaces in fundamental theories such as QM and SRT, where the principles of SI and AMPI can be implemented. In turn, the measurable quantities represented in spaces turn out to be relative. In this respect, SRT is not much different from QM. This proximity predetermines BI violation in both cases and in both cases the violation of BIs confirms the subject-independent nature of physics. In a classic Gedankenexperiment was demonstrated, that the violation of BI does not contradict the presence of hidden parameters if they are represented by relative quantities. However, the question arises: are relative properties and quantities indeed local?
‘Experiments violating a Bell inequality [BI] thus leave [‘realists'] no option: the principle of relativity is false [sic]. The world is nonlocal [sic],' Wiseman & Cavalcanti (2015). But we show that even high-school math violates a BI; in fact, all BIs—being inadequate for experiments with highly correlated outcomes—are false. Moreover: under the principle of relativity, elementary math shows that wholistic mechanics (WM)—classical mechanics extended to include Planck's constant—also violates BIs. So, with 3 ways to violate a BI—experiment, high-school math, WM—true-realists find: Bellians are being rather silly, as Bell (1990) half-expected; quantum correlations are wholly explicable via WM in our relativistically local world; the principle of relativity is true, nonlocality false. Importantly: for STEM teachers, and against popular opinion-pieces about quantum nonlocality, our results require no knowledge of QM. Let's see.
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.
Bell's inequalities(1964) provides a quantitative criterion to test the local hidden variable theory(LHVT) versus quantum mechanics(QM).For the first time,it leads to the possibility to experimentally distinguish LHVT and QM.So far,there have been tens of experiments ever since the first experiment by Clauser et al(1972).An overwhelming majority of these experiments are in good agreement with the predictions of QM yet violate those of LHVT.Some loopholes in these experiments are discussed in Section I,followed by a respective summary to 12 experiments between 1972 to 1982 and 31 experiments from 1985 and on in Sections II and III.It is finally pointed out that so far there is not a single experiment to close both the locality loophole and the detection loophole at the same time,but the experimental outcomes are irreversible.Accordingly,theoretical physicists must admit that the present physics foundation is broken,i.e.quantum mechanics is contradiction with special relativity.
Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiments with the experimental results explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to represent quantum information. In the present paper, a new principle, the general principle of measurements, is introduced and proved as a mathematical theorem. Based on this principle, the experiments for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” are scrutinized. The findings are as follows. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental results of testing Bell’s inequality, actually Einstein’s viewpoint is irrelevant to Bell’s theorem. Bell’s inequality failed to capture the essence of the Einstein-Bohr debate. The experimental results of testing Bell’s inequality and the measurement outcomes of various experiments involving “qubit” are all erroneously explained. Without involving hidden variables, quantum mechanics can be completed based on the general principle of measurements by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space, and the mathematical setting can remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the real world. A very regrettable conclusion from the above findings is inevitable: Quantum information has no physical carriers, and all quantum information technologies are not physically realizable.
Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiments with the experimental results explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to represent quantum information. In the present paper, a new principle, the general principle of measurements, is introduced and proved as a mathematical theorem. Based on this principle, the experiments for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” are scrutinized. The findings are as follows. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental results of testing Bell’s inequality, actually Einstein’s viewpoint is irrelevant to Bell’s theorem. Bell’s inequality failed to capture the essence of the Einstein-Bohr debate. The experimental results of testing Bell’s inequality and the measurement outcomes of various experiments involving “qubit” are all erroneously explained. Without involving hidden variables, quantum mechanics can be completed based on the general principle of measurements by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space, and the mathematical setting can remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the real world. A very regrettable conclusion from the above findings is inevitable: Quantum information has no physical carriers, and all quantum information technologies are not physically realizable.