In this work a general relativistic generalization of Bell inequality is suggested. Namely,it is proved that practically in any general relativistic metric there is a generalization of Bell inequality.It can be satisfied within theories of local (subluminal) hidden variables, but it cannot be satisfied in the general case within standard quantum mechanical formalism or within theories of nonlocal (superluminal) hidden variables. It is shown too that within theories of nonlocal hidden variables but not in the standard quantum mechanical formalism a paradox appears in the situation when one of the correlated subsystems arrives at a Schwarzschild black hole. Namely, there is no way that black hole horizon obstructs superluminal influences between spin of the subsystem without horizon and spin of the subsystem within horizon,or simply speaking,there is none black hole horizon nor "no hair" theorem for subsystems with correlated spins. It implies that standard quantum mechanical formalism yields unique consistent and complete description of the quantum mechanical phenomenons.
In this work a general relativistic generalization of Bell inequality is suggested. Namely,it is proved that practically in any general relativistic metric there is a generalization of Bell inequality.It can be satisfied within theories of local (subluminal) hidden variables, but it cannot be satisfied in the general case within standard quantum mechanical formalism or within theories of nonlocal (superluminal) hidden variables. It is shown too that within theories of nonlocal hidden variables but not in the standard quantum mechanical formalism a paradox appears in the situation when one of the correlated subsystems arrives at a Schwarzschild black hole. Namely, there is no way that black hole horizon obstructs superluminal influences between spin of the subsystem without horizon and spin of the subsystem within horizon,or simply speaking,there is none black hole horizon nor "no hair" theorem for subsystems with correlated spins. It implies that standard quantum mechanical formalism yields unique consistent and complete description of the quantum mechanical phenomenons.
It is proved that Bell's inequality can be traced back to a classical probabilistic formula that is invalid clearly, while the spin correlation formula in quantum mechanics to a formula that has confirmed both by facts and quantum mechanics. Two misunderstandings about Bell's theorem are pointed out: Firstly, the hidden variable theory Bell's used is a special one, but it is regarded as a general form of such theories. Secondly, there are two outcomes obtainable from Bell's hypotheses: one is compatible with quantum mechanics and the other leads to Bell's inequality. Unfortunately, the former is regarded as a property of local hidden variable theory, while the latter as self-evident. G. Lochak has revealed the first misunderstanding, and thereby he pointed out that Bell's inequality has nothing to do with locality, but he did not find the second one, so that he still analyzed this problem starting from hidden variable theory, which is actually irrelative to Bell's inequality. (The Journal of American Science. 2005;1(2):42-50).
The phenomenon of nonlocality in quantum mechanics is one of its most fundamental features and is most strikingly exemplified in the discussion of the Einstein, Podolsky and Rosen (EPR) type of experiment. The generality of Bell's inequality and the results of experiments done up to now show that local hidden-variable theories are ruled out as a means to resolve the famous EPR paradox. What remains for further consideration are the nonlocal and the Einstein-separable hidden-variable models. Finally, an alternative and possibly successful approach in trying to 'explain' nonlocality might involve ideas of backward causation.
Bell’s inequality can be traced back to a classical probabilistic formula that is invalid clearly, while spin correlation formula in quantum mechanics to a formula that has confirmed both by facts and quantum mechanics. Bell’s two misunderstandings about Bell’s theorem are pointed out: Firstly, the hidden variable theory Bell’s used, which is a special form of such theories, is regarded as a general one. Secondly, there are two theses obtainable from Bell’s hypotheses; one is compatible with quantum mechanics, the other leads to Bell's inequality. Unfortunately, the former is regarded as a property of local hidden variable theory, while the latter as self-evident. G.Lochak has revealed the first thesis, and thereby he pointed out that Bell’s inequality has nothing to do with locality, but he did not find the second one, so that he still analyzed this problem starting from hidden variable theory, which is actually without regard to Bell’s inequality.
Like classical theory,quantum theory including non-relativistic quantum mechanics and relativistic quantum field theory has adopted locality description.But,essentially,quantum theory is a space nonlocality theory dressed by locality description.Since EPR paradox,Bell inequality,GHZ theorem,Hardy theorem and Cabello theorem were proposed,there have been a lot of theoretical and experimental works about the space nonlocality route along Bell-GHZ-Hardy-Cabello.Up to now the experimental results all support quantum theory.However,the essence of the space nonlocality characteristics of quantum theory has not been discovered yet,nor can the existence of hidden variables be denied,a situation that keeps attracting more attention and consideration to this hot issue.Here we generalize this route concisely and specify the related ideas,definition and theorem systemically.At last we give a detailed comment on this route.
Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a–c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.
A factual inconsistency of the nonlocality theory is demonstrated via a careful analysis of the conceptual and formal contents of Bell's theorem and the inequalities associated with it. The conceptual inconsistency of the theory follows from the consideration that it is, in principle, impossible to formulate quantum mechanics in terms of local hidden variables. The formal inconsistency of the nonlocality theory follows from the facts that: (i) nonlocality is not a physical property that can be represented by a function or an operator; (ii) it is impossible to derive Bell's inequality in a mathematically consistent way; and (iii) Bell's definition of locality is incorrect. Therefore, Bell's theorem cannot serve as the foundation for the introduction of the nonlocality notion in quantum mechanics.