The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can, in principle, be revealed by measurements. Here we show that this interpretation can, in principle, be falsified if classical systems coexist with other types of physical systems. To make this point, we construct a toy theory that (i) includes classical theory as a subtheory and (ii) allows classical systems to be entangled with another type of system, called anticlassical. We show that our toy theory allows for the violation of Bell inequalities in two-party scenarios where one of the settings corresponds to a local measurement performed on a classical system alone. Building on this fact, we show that measurement outcomes in classical theory cannot, in general, be regarded as predetermined by the state of an underlying reality.

中文翻译：

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与其他系统类型共存的经典系统中的贝尔非定域性

经典理论的现实解释假设每个经典系统都具有明确定义的属性，观察者可能不知道这些属性，但它们仍然是现实的一部分，原则上可以通过测量来揭示。在这里，我们表明，如果经典系统与其他类型的物理系统共存，这种解释原则上可以被证伪。为了阐明这一点，我们构建了一个玩具理论，其中（i）将经典理论作为子理论，并且（ii）允许经典系统与另一种类型的系统（称为反经典系统）纠缠在一起。我们证明，我们的玩具理论允许在两方场景中违反贝尔不等式，其中其中一个设置对应于单独在经典系统上执行的局部测量。基于这一事实，我们表明，一般来说，经典理论中的测量结果不能被视为由潜在现实状态预先确定。