物理学 1935

能认为量子力学对物理实在的描述是完备的吗？

阿尔伯特·爱因斯坦、鲍里斯·波多尔斯基、内森·罗森

若测量一个粒子便锁定其远方伙伴，量子理论必不完备。

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In depth · the introduction

在这边测量一个粒子，它远方的伙伴仿佛在同一瞬间就打定了主意——这条联系，爱因斯坦无法忍受，并以此论证：量子理论一定漏掉了什么。

核心想法

量子力学说，一个粒子在你测量之前，并没有确定的位置或动量——只有概率。爱因斯坦，连同波多尔斯基与罗森，认为这不可能是故事的全部。他们设想：两个粒子一同诞生、再被送往远方，命运彼此锁死——你为其中一个测出什么，立刻就知道另一个相匹配的答案。

他们布下的陷阱是这样的。假设你通过测量粒子 A，就能完全确定地预测粒子 B 的结果，而根本不去碰 B。那么 B 想必早已具有那项性质——它是实在的，早在你去看之前，就好端端待在那里。可量子力学偏偏拒绝预先给 B 赋予那个确定值。于是 EPR 断言：这套理论必定不完备——其中一定有它略去未提的隐藏细节。爱因斯坦希望实在是定域的（没有瞬时的超距影响），而且是确定的。量子力学，这两样似乎都给不了。

它是如何诞生的

到 1935 年，爱因斯坦帮着建起了量子理论，却已对它那幅世界图景生出不信任。在普林斯顿高等研究院安顿下来的他，与两位年轻些的同事——鲍里斯·波多尔斯基和内森·罗森——合作，要把这份不安，化成一个谁也挥之不去的论证。文章由波多尔斯基执笔，结果，他在正式发表前把它透给了报界——《纽约时报》登出了标题，而爱因斯坦对那种说法颇为恼火。

据说，量子力学的伟大旗手尼尔斯·玻尔，为此投入了数周的紧张工作，又以一模一样的标题发文回击。他论证道：EPR 那种「粒子独立于你如何选择测量、自身便拥有种种性质」的想法，对纠缠系统根本不适用。这场争论就这样搁了三十年：对同一组方程的两种精彩解读，却没有一个实验能在它们之间作出裁决。

它为何重要

EPR 做成了一件罕见的事：他们把一个关于实在的哲学问题，变成了一个精确、可回答的问题。他们本想揭露量子力学的一个破绽。结果，1964 年，物理学家约翰·贝尔找到了一条路，把他们的思想实验变成一个真实的检验——而其后数十年的实验，交出了一个爱因斯坦会深恶痛绝的判决：自然界确实如方程所言那般离奇；EPR 所盼望挽救的那个安稳的、定域而确定的世界，并不存在。

他们的诚实，正是关键所在。在他们的假设之下，EPR 的逻辑完美无缺；落空的，是其中一条假设——影响不能跑得比分离的速度更快——而自然界不肯遵守它。少有哪篇旨在赢得争论的论文，错得如此富有成果。

一个可以想象的画面

想象一双手套，被分装进两个密封的盒子，运往地球的两端。打开其中一个盒子，看到一只左手套，你立刻就知道：远处那个盒子里装的是右手套——没有任何信号传过去；答案早在出发时就被封了进去。爱因斯坦希望纠缠粒子正是这样：答案在源头就已决定，只是被藏了起来。

可量子粒子偏偏不符合这幅图景。对手套，你只能查「左还是右」，如此而已。对纠缠粒子，你却可以在最后一刻，挑选去问哪一个问题——而无论你怎么挑，远方伙伴的答案，都吻合得太过完美。任何一双事先封好的手套，都变不出这个戏法。正是这道落差，被贝尔变成可检验的，最终了结了争论。

它的位置

这篇论文，是量子力学的奠基——普朗克、玻尔、海森堡、薛定谔——与量子信息时代之间的枢纽。它把纠缠凝结为一个概念，催生了贝尔 1964 年的定理，并引出克劳泽、阿斯佩与蔡林格那些赢得 2022 年诺贝尔奖的实验。爱因斯坦所拒斥的那份离奇，如今正驱动着量子密码学与量子计算机。在本馆中，它紧挨着它所质疑的工作，以及它无意间播下的种种技术。

The original document

Original source text

A. Einstein, B. Podolsky, N. Rosen · Physical Review 47 (1935): 777–780 · Received March 25, 1935

Abstract

In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system.

In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.

§1 — The condition of completeness and the criterion of reality

Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness. The second question is thus easily answered, as soon as we are able to decide what are the elements of the physical reality.

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.

[ … ]

§2 — The two-particle thought experiment

Suppose now that we have two systems, I and II, which we permit to interact … after which the systems no longer interact. We assume that the states of the two systems … are known. We can then calculate … the state of the combined system. … By measuring either A or B we are in a position to predict with certainty, and without in any way disturbing the second system, either the value of the quantity P (that is p_k) or the value of the quantity Q (that is q_r). In accordance with our criterion of reality, in the first case we must consider the quantity P as being an element of reality, in the second case the quantity Q is an element of reality. But, as we have seen, both wave functions … belong to the same reality.

Previously we proved that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that two physical quantities, with noncommuting operators, can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2).

We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. … This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this.

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

Institute for Advanced Study · Princeton, New Jersey · received March 25, 1935