The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these states, it purportedly allows distinguishing in an experimentally testable way the predictions of quantum mechanics from those of models of local hidden variables and, ultimately, ruling the latter out. In this paper, we show, however, that the models of local hidden variables constrained by the Bell inequality all share a subtle, though crucial, feature that is not required by fundamental physical principles and, hence, it might not be fulfilled in the actual experimental setup that tests the inequality. Indeed, the disputed feature neither can be properly implemented within the standard framework of quantum mechanics and it is even at odds with the fundamental principle of relativity. Namely, the proof of the inequality requires the existence of a preferred absolute frame of reference (supposedly provided by the lab) with respect to which the hidden properties of the entangled particles and the orientations of each one of the measurement devices that test them can be independently defined through a long sequence of realizations of the experiment. We notice, however, that while the relative orientation between the two measurement devices is a properly defined physical magnitude in every single realization of the experiment, their global rigid orientation with respect to a lab frame is a spurious gauge degree of freedom. Following this observation, we were able to explicitly build a model of local hidden variables that does not share the disputed feature and, hence, it is able to reproduce the predictions of quantum mechanics for the entangled states of two qubits.

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单重态极化状态的局部隐变量模型是否必然受到贝尔不等式的约束？

贝尔不等式被认为是所有局部隐藏变量模型共享的共同约束，旨在描述两个量子位的纠缠状态。由于这些状态的量子力学描述违反了不等式，因此据称它允许以实验可测试的方式将量子力学的预测与局部隐藏变量模型的预测区分开来，并最终排除后者。然而，在本文中，我们表明，受贝尔不等式约束的局部隐变量模型都具有基本物理原理所不需要的微妙但至关重要的特征，因此在实际中可能无法实现测试不等式的实验装置。确实，有争议的特征既不能在量子力学的标准框架内正确实现，甚至与相对论的基本原理相悖。即，不等式的证明需要存在一个优选的绝对参考系（假设由实验室提供），关于该参考系，纠缠粒子的隐藏属性和测试它们的每个测量设备的方向可以是通过实验的一长串实现独立定义。然而，我们注意到，虽然两个测量设备之间的相对方向在实验的每一次实现中都是正确定义的物理量级，但它们相对于实验室框架的全局刚性方向是虚假的规范自由度。根据这一观察，