标题： 解决薛定谔对爱因斯坦-波多尔斯基-罗森悖论的分析：一个不完备性准则和现实的弱元素 显示英文标题

标题： Resolving Schrödinger's analysis of the Einstein-Podolsky-Rosen paradox: an incompleteness criterion and weak elements of reality

摘要： 爱因斯坦-波多尔斯基-罗森（EPR）悖论被提出作为量子力学对物理现实描述不完整的论据。 然而，该论点所基于的前提可以通过贝尔实验进行检验。 在本文中，我们从薛定谔对EPR的回应角度来审视EPR悖论。 薛定奇指出，悖论的相关状态使得可以同时测量$\hat{x}$和$\hat{p}$，一个通过直接测量，另一个通过间接测量。 薛定奇的分析具有及时的重要性，因为最近的一项实验实现了宏观原子系统的这些相关性。 不同于原始论点， 薛定奇的分析适用于测量设置已经确定的实验时期。 在此背景下，一组局部实在性假设（未被贝尔定理否定）意味着$x$和$p$是同时精确定义的。 因此，可以提出另一种EPR论点，基于一组（可能是不可检验的）前提，认为量子力学是不完整的。 当系统被放大时，可以引入宏观实在性，这些前提被称为弱宏观实在性（wMR）。 在本文中，我们提出了一种实现薛定奇思想实验的方案，其中场正交相位幅度$\hat{X}$和$\hat{P}$取代了位置和动量。 假设wMR，我们推导出量子力学不完整的标准，表明该标准对于当前实验是可行的。 薛定奇提出的问题得到了解决。 通过基于客观场（$Q$基于）的量子力学模型进行模拟，我们展示了同时预定值对于$\hat{X}$和$\hat{P}$的放大效应。这些值可以被视为现实的弱元素，类似于贝尔的宏观可测性。 显示英文摘要

摘要： The Einstein-Podolsky-Rosen (EPR) paradox was presented as an argument that quantum mechanics is an incomplete description of physical reality. However, the premises on which the argument is based are falsifiable by Bell experiments. In this paper, we examine the EPR paradox from the perspective of Schrodinger's reply to EPR. Schrodinger pointed out that the correlated states of the paradox enable the simultaneous measurement of $\hat{x}$ and $\hat{p}$, one by direct, the other by indirect measurement. Schrodinger's analysis takes on a timely importance because a recent experiment realizes these correlations for macroscopic atomic systems. Different to the original argument, Schrodinger's analysis applies to the experiment at the time when the measurement settings have been fixed. In this context, a subset of local realistic assumptions (not negated by Bell's theorem) implies that $x$ and $p$ are simultaneously precisely defined. Hence, an alternative EPR argument can be presented that quantum mechanics is incomplete, based on a set of (arguably) nonfalsifiable premises. As systems are amplified, macroscopic realism can be invoked, and the premises are referred to as weak macroscopic realism (wMR). In this paper, we propose a realization of Schrodinger's gedanken experiment where field quadrature phase amplitudes $\hat{X}$ and $\hat{P}$ replace position and momentum. Assuming wMR, we derive a criterion for the incompleteness of quantum mechanics, showing that the criterion is feasible for current experiments. Questions raised by Schrodinger are resolved. By performing simulations based on an objective-field ($Q$-based) model for quantum mechanics, we illustrate the emergence on amplification of simultaneous predetermined values for $\hat{X}$ and $\hat{P}$. The values can be regarded as weak elements of reality, along the lines of Bell's macroscopic beables.