内容来源：https://www.quantamagazine.org/a-strange-quantum-theorem-has-killed-einsteins-reality-20261106/

内容总结：

一项看似抽象的量子定理，最终动摇了爱因斯坦所坚持的“客观现实”观念。文章回顾了这一思想发展过程：爱因斯坦认为，物体拥有独立于观测的固有属性，量子力学中的波函数只是对现实的不完整描述；以玻尔为代表的哥本哈根诠释则主张，量子描述并不对应一个独立的客观量子世界。1964年，贝尔通过思想实验证明，量子力学与“定域实在论”不相容，后续实验也验证了量子力学的预测。2012年，Pusey、Barrett和Rudolph提出PBR定理，进一步排除了“波函数仅代表观测者知识、而现实本身仍然客观存在”这一中间立场。PBR定理表明，在其实验设定下，量子态不能被视为关于某种更深层真实状态的重叠性知识；实验确认后，物理学家被迫在两种极端之间选择：要么接受一种高度反直觉的客观现实，要么放弃客观现实本身。文章指出，PBR并未给出最终答案，但终结了长期以来试图调和量子力学与常识实在论的努力，并推动QBism等新解释的发展；同时，也有研究者试图重新定义“现实”，以寻找更可接受的出路。

中文翻译：

一个奇特的量子定理杀死了爱因斯坦的实在
Samuel Velasco/Quanta Magazine

人类最早的发育里程碑之一是对客体永久性的理解。婴儿通常不到一岁就会明白，当大人在躲猫猫游戏中把手遮在脸上时，大人并没有消失。我们周围的世界远比我们所感知到的要多。

这表明——或者说，至少向阿尔伯特·爱因斯坦表明——世界是“实在的”，意思是世界上的事物具有内在真实的属性，无论任何人怎么想。一个红色台球是红色的，即使在黑暗中也是红的，即使没有人在检查它的颜色。红色是属于球本身的属性，而不是属于某个测量球的设备，也不属于操作测量设备的人的心智。

然而，量子力学——一个经过彻底验证的关于世界如何运作的理论——似乎表明并非如此。该理论的数学在你测量台球的那一刻才把红色赋予它。在此之前，理论只给你一组概率，告诉你球可能是什么颜色。量子力学的主要创始人认为，这种数学反映了现实的本质——在某种意义上，一个单一的、客观的实在并不真正存在。

1935年，爱因斯坦反抗了这种对量子理论的超现实解读，提出了20世纪最著名的思想实验之一。但他的反抗注定失败。1964年，物理学家约翰·斯图尔特·贝尔用他自己的思想实验表明，实在必然比爱因斯坦所假设的更加奇异。随后的工作对贝尔的思想实验进行了检验——并证明他是对的。

然后，在贝尔之后50年，当时还是伦敦帝国理工学院研究生的马修·普西，接手了爱因斯坦实在概念仅存的部分——并且在最初并非有意的情况下——发出了致命一击。

paradigm-shifting定理被称为PBR，以普西和他的学术同伙乔纳森·巴雷特和特里·鲁道夫命名。自2012年PBR发表以来，许多理论家已经接受它排除了我们对实在最常识性的理解。

“从[PBR]问世的那一刻起，人们就知道它将是一个里程碑，”现就职于巴西里约热内卢联邦大学的物理学家雅克·皮纳尔说。

当时，皮纳尔和普西一样，一直沿着爱因斯坦的足迹前行，涉足那些旨在表明客观实在存在、量子力学仅仅描述我们对它的不完整知识的理论。但当PBR定理出现时，皮纳尔记得自己想：“就是这样。这个纲领死了。”

这就是爱因斯坦、贝尔、最终是普西及其合作者如何杀死了我们所知的实在的故事。在三个定理中，他们证明了量子力学与我们感知的世界不相容。而由于一个又一个实验——包括最近对PBR的实现——已经确立了量子力学是基本法则，实在的某些方面不得不被放弃。

剩下的问题是：我们必须放弃多少？

爱因斯坦与实在

在量子力学的发展中发挥了开创性作用之后，爱因斯坦转过身来攻击它。他无法接受它关于实在的说法。

爱因斯坦骨子里知道实在是什么。它是所有客观事实的总和——比如台球的颜色、位置和速度——这些事实存在于它们所描述的物体中，独立于感知和心智。但由维尔纳·海森堡和埃尔温·薛定谔在1920年代中期发展的量子力学，并不处理事实。

量子力学处理的是可能性。它的数学给你一个“量子态”，也称为波函数。这个波函数可以告诉你，例如，在一个测量特定台球颜色的实验中，你有77%的几率发现球是红色的，23%的几率发现它是绿色的。

一个困扰了物理学家一个世纪的问题是：在实验发生之前，球的本质是什么？球有多种颜色吗？没有颜色？颜色的概念没有意义吗？简而言之，是否存在一个实在来支撑我们所经历的客体永久性？

对爱因斯坦来说，答案是显而易见的：当然实在存在；波函数只是没有完全捕捉到它。

在这种观点中，波函数就像天气预报。假设你醒来，你的天气应用告诉你今天有77%的几率下雨，但你还没有看外面是什么情况。然后你拉起百叶窗，看到雨滴落下。在那一刻，你变得100%确定正在下雨。这种从77%到100%的转变是一种纯粹发生在你头脑中的确定性转变。它并不反映某种真实的气象变化。大气是真实的，而你对其状态的（不）确定性是另一回事——是你头脑中信息的反映。

爱因斯坦与他的合作者鲍里斯·波多尔斯基和纳森·罗森（合称“EPR”）提出了一个思想实验，以证明量子态仅仅作为信息的产物而存在。要理解这个思想实验，你需要知道关于波函数的一件奇特的事情：它的数学结构不允许一个物体同时具有位置和动量。

EPR实验涉及两个粒子相互碰撞，然后在一段时间后进行测量，比如其中一个粒子运动了多远。这第一次测量也会告诉你配对粒子运动了多远。EPR论证说，配对粒子的位置必然存在，因为它可以被知道。他们论证说，配对粒子也有动量，因为该属性可以通过类似方式被知道。

关键在于，他们的实验只涉及对一个粒子进行一次测量，而另一个粒子保持未触碰。科学家们论证说，这表明第二个粒子具有在测量之前就已设定且真实的属性。而由于波函数不允许这一点，波函数必然不反映粒子的字面状态；量子态不是实在的。

为了得出这个结论，科学家们做了两个看似不可攻破的假设。首先，他们假设一个粒子可以具有字面状态，即“实在性”假设。其次，他们假设这个字面状态存在于粒子内部而不在其他任何地方，因此改变它的唯一方式就是与粒子相互作用，即“定域性”假设。

但就在EPR之后几个月，海森堡的导师尼尔斯·玻尔试图通过攻击其第一个假设来驳倒爱因斯坦的论证。“不存在量子世界，”玻尔后来 according to his assistant Aage Petersen 说。“只存在一种抽象的量子物理描述。”他的论证类似于断言天气预报是准确的，但大气本身要么不存在，要么不可描述。这种对客观实在的否认被称为哥本哈根诠释。

许多现代量子物理学家批评玻尔对EPR的回应含混而模糊。但玻尔作为量子力学创始人的显赫地位，加上对该理论越来越多的实验支持，使他的许多同代人相信他是对的。物理学家在很大程度上失去了辩论量子态与实在关系的兴趣——而这正是现代“量子基础”领域的核心问题。

“玻尔就像是发生在物理学身上最糟糕的事，”加拿大滑铁卢圆周理论物理研究所的物理学家大卫·施密德说，他青少年时期就痴迷于玻尔-爱因斯坦论战。“他是量子基础[在现代之前]不存在的的原因。”

三十年后，一个重磅定理将重新唤起物理学家的好奇心。

贝尔与定域性

约翰·斯图尔特·贝尔一直对爱因斯坦抱有同情。作为学生，贝尔也难以接受量子力学的超现实性。他想知道，量子力学的预测怎么可能与一个由客观属性构成的真实世界脱节，正如玻尔所主张的那样。

然后，在1952年，贝尔“看到了不可能之事被完成”。他读了大卫·玻姆的著作，后者发展了一种量子力学版本，其中粒子无论测量与否都始终具有真实位置。

“玻姆力学”通过宣布波函数是一种“导波”——一种引导粒子运动的物理对象——来实现这一点。作为世界中的真实事物，这种波有一个令人不快的特征：非定域性。它可以以某种方式变化，从而瞬间扰动一个远处的粒子。

尽管有这一缺陷，导波对贝尔来说是一座灯塔。它允许物理学家论证，与流行的哥本哈根诠释相反，客观实在毕竟存在。“为什么导波图景在教科书中被忽视？”贝尔写道。“难道不应该教授它吗，不是作为唯一的方式，而是作为对盛行自满的解毒剂？”

玻姆的工作启发了贝尔设计一个新的思想实验，这个实验如此简单，以至于适用于所有版本的量子理论，已知的和未知的。跟随爱因斯坦的足迹，他想象两个粒子碰撞后向相反方向飞开。最终，每个粒子会遇到一个执行随机选择测量的设备，测量有两种可能结果。

贝尔想象多次重复这个实验，并用基本算术预测设备可能多久返回匹配的测量结果。他假设每个粒子一开始就有一个状态（爱因斯坦的客观实在观念），并假设设备相距太远，粒子无法相互影响（爱因斯坦的定域性观念）。他计算出，在一个既实在又定域的世界中，粒子匹配的频率相对较低。

然后，用量子力学，贝尔预测两个粒子匹配的频率会高得多。他创造了一个实验检验，可以让量子力学与爱因斯坦版本的实在对决。物理学家在1980年代进行了他的实验，并确认粒子匹配的频率确实超过了爱因斯坦的实在所允许的程度。

贝尔在玻尔失败的地方成功了：他证明了EPR两个关键假设中至少有一个必然是错的。物理学家看到，世界不可能同时是实在的和定域的。某些东西不得不让步。

玻姆力学代表了在权衡中导航的一种极端方式。它通过使波函数成为真实对象来拯救实在，但它要求人们吞下定域性丧失的苦药。哥本哈根立场——什么都不真实——是另一个极端。

在随后的几十年里，一些物理学家意识到存在一条中间道路。贝尔已经表明EPR的假设是错的，但也许爱因斯坦的直觉——波函数类似于我们的知识，就像天气预报——仍然有道理。

“你回去看看[爱因斯坦]写的一切，它超前于时代100年，”施密德说。

寻找一种在不使波函数成为实在的情况下保留客观实在的方法，将引导普西走向PBR定理。而具有讽刺意味的是，PBR定理将有效地终结这一探索。

PBR与信息

像施密德和皮纳尔这样的物理学家无法释怀的是，量子态就是不像一个可理解的物理属性那样行事。

以波函数的一个标志性行为为例，它的“坍缩”。回想那个可能是红色或绿色的台球的例子。在你看向球的那一刻，它的波函数坍缩了，赋予它100%的红色几率。

试图将这一事件解释为物理球的字面变化是令人发狂的。球是否开始为某种无法想象的无色混合物，然后在你瞥它的瞬间，突然跳入100%红色的状态？

“在量子基础这样的领域，你得注意自己的理智，”圆周理论物理研究所从事该领域研究的物理学家吕西安·哈迪说。

但如果你把这一事件解释为你头脑中信息的变化，它就合理得多了。你以为球可能是红色的，看了一眼，得知它确实是红色的。同样的事情发生在你早晨看向窗外时下雨的几率上。爱因斯坦没有完全用这些术语来表达，但现代学者相信这就是他在EPR中所主张的立场。

2004年，圆周理论物理研究所的物理学家罗伯特·斯佩肯斯提出了一个关于简单世界的理论，就像爱因斯坦所想象的那样。在这个理论中，每个粒子都有客观的位置和速度，但实验限制使得无法同时精确测量两者。斯佩肯斯表明，在这样一个世界中——量子态代表对真实属性的不完整知识——他可以产生一长串假定的量子现象：量子“隐形传态”、禁止复制量子态，以及数十种更多现象。他的研究积累了大量新证据，表明如果你把量子态从外部世界移入某人的头脑中，它看起来就没那么奇怪了。换句话说，他表明爱因斯坦的方法尽管假设有缺陷，但仍然有优势。

2011年，斯佩肯斯的工作引起了当时还是研究生的普西的注意。贝尔定理已经吸引了普西，因为它保证量子力学意味着世界确实比爱因斯坦或常识所认为的更加奇异。“我们有了这个理论，它告诉我们不只是我们在想象，”普西说。“这里确实有奇怪的东西需要弄清楚。”

斯佩肯斯的理论暗示，虽然量子力学并非所有的奇异性都能被消除（贝尔定理保证了这一点），但也许其中一些奇异性是因为过于认真对待波函数而产生的幻觉。毕竟，斯佩肯斯的理论在纸面上看起来与完整的量子力学差别不大。在普西用他开发的一种记号重写之后，它只差几个负号。他的合作者——他们是爱因斯坦的同情者——鼓励他尝试升级斯佩肯斯的理论，通过将波函数视为生活在你头脑中的知识状态，尽可能减少怪异之处。

“我花了几天试图做到这一点，然后受够了，”他说。“所以我决定转而证明这是不可能的。”这项工作后来成为PBR定理。

像EPR一样，PBR以精心设计的思想实验的形式探索关于实在的问题。PBR提出了一种奇特的游戏，你可以按照鲁道夫的类比把它想象成庄家和玩家之间的纸牌游戏。首先，庄家从一副牌中抽出26张红牌，从另一副牌中抽出四张A。我们称它们为红牌堆和A牌堆。

接下来，庄家把两堆牌放在桌子下面。他随机从红牌堆或A牌堆中选一张牌。然后他重复这个过程，随机选第二张牌。然后他把两张牌面朝下放在桌上，给玩家一个奇怪的挑战：告诉我这两张牌不是从哪两个牌堆的组合中选出的。

大多数时候，玩家稳赢。假设她翻开两张牌，看到方块2和梅花A。显然，方块2——一张红色非A——来自红牌堆。而梅花A——一张黑色A——来自A牌堆。庄家不可能通过两次从红牌堆选牌或两次从A牌堆选牌来得到这些牌，所以玩家说出这两个选项中的任何一个都肯定能赢。

但假设玩家翻开的是方块A和红桃A，两张红色A。由于两张牌都可能来自任一牌堆，玩家无法排除任何可能性。她可以猜，但只有四分之三的几率猜对。所以在足够多轮之后，她最终必然会输。

这个游戏的意义在于说明真实状态与知识状态之间的根本区别。“方块A”和“红桃A”是牌的真实状态，而“红牌堆”和“A牌堆”是知识状态。玩家有时会输，因为关于每张牌来源牌堆的信息并没有写在牌本身中；它只存在于庄家的头脑中。

这种区别之所以存在，仅仅因为两个知识状态共享真实状态——红色A。这是知识状态的一个基本属性；它们以某种方式“重叠”，使得无法从物理牌上读出其属于哪个牌堆的状态。对比一下，用不重叠的牌堆玩同样的游戏，比如红牌和黑牌。在那种情况下，翻开一张牌就能确定地揭示它来自哪个牌堆。“红牌堆”和“红桃4”都将是牌本身的真实状态。

PBR提出了这个游戏的量子版本，并追问量子态是否可以重叠，以及量子态因此是否可以是知识状态。这个游戏——及其结论——与经典版本共享两个关键假设。它假设牌有真实状态（爱因斯坦的客观实在观念）。它还假设第一张被抽出的牌的真实状态不影响第二张被抽出的牌的真实状态（一个不同于定域性的新假设）。

令人惊讶的是，在游戏的量子版本中，玩家总能赢。为了证明这一点，PBR详细说明了如何组装一台量子机器，由执行简单量子操作（如将经典对象放入量子态）的小装置构成。如果你用这台机器扫描两张牌，它总能排除至少一种牌堆组合。（在一个奇怪的量子特性中，机器做到这一点——事实上需要做到这一点——而无需翻开和观察牌。）

2012年的一个实验表明，这种保证获胜的量子策略确实有效，证明量子态之间没有重叠。因此，鉴于PBR的假设，量子态不是庄家头脑中的知识状态；它们确实是牌本身可扫描的属性。“你可以把[量子态]想象成盖在世界底层状态上的印章，”皮纳尔说。“你改变量子态，你就改变了现实中的某些东西。”

PBR之后的生活

与贝尔一样，PBR已被多次实验证实。例如，去年秋天，英国的研究人员玩了一个扩展版的PBR游戏，发出五张牌而不是两张，使用IBM制造的量子计算机。果然，量子机器总是赢，尽管没有人怀疑它会赢。事实上，研究人员主要用PBR定理来检查量子计算机是否正常运行。量子力学——以及PBR——的有效性被视为理所当然。

“那确实是动机，”领导该实验的剑桥大学物理学家克里斯平·巴恩斯说，“看看量子基础的一个定理是否也能被转化为对真正量子行为的实验探针。”

许多物理学家将PBR理解为量子态必然是实在的——一种存在于粒子、人和行星中的客观属性。如果如此，像坍缩这样看似不可能的事件也必然有某种物理对应物。这种立场相当于走玻姆力学和其他“实在论”诠释的极端道路。正如普西简洁地说的，PBR保证“如果任何东西是实在的，量子态就是实在的。”

但得出量子态肯定是实在的结论是对PBR定理的误解，因为PBR也留下了另一个极端道路的可能性：可能正如哥本哈根学派自玻尔时代以来坚定主张的那样，在某种意义上什么都不真实，包括量子态。量子态完全可能存在于我们的头脑中，与客观实在没有直接联系。在这种情况下，台球的红色将与观察它的行为不可分割地联系在一起——正是这种事态深深冒犯了爱因斯坦。“你真的相信月亮在你没看它的时候不存在吗？”爱因斯坦曾著名地追问他的同事亚伯拉罕·派斯。

PBR没有给我们答案。它所做的，是终结了一个世纪以来与量子力学的讨价还价。通过排除实在为真而波函数不为真的可能性，PBR要求物理学家要么完全接受一个客观但完全超现实的实在概念，要么完全拒绝客观实在。“你是咬子弹，还是试图躲子弹？”普西说。

皮纳尔是少数仍在玩弄中间路线理论的物理学家之一，尽管兴趣日渐消退。PBR促成了他彻底放弃客观实在的选择。他转向了哥本哈根主义的一个现代分支，称为QBism。

QBism断言世界本身可能存在，但量子力学无法描述它。理论真正能做的只是捕捉我们与世界的关系——以及对世界的主观体验。“探戈需要两个人，”皮纳尔说。“没有两个系统，就没有关系。而实在不过是关系而已。”

然而，一些物理学家仍然对两个极端选项——超现实的实在或无实在——感到不满。于是他们开始挑剔实在技术定义中的细节。“也许思考实在状态的正确方式应该更模糊一些，不完全适合这件紧身衣，”普西说。

本着这种精神，哈迪质疑实在是否必然在每个给定时刻都有一个单一的、客观的状态。也许状态可以以某种方式分布在多个时刻。他还没有一个完全成形的方案，但他的目标是提出一个更深层、更普遍的实在概念，同时仍然可辨认。

如果像哈迪这样的弱势一方成功拯救了某种实在概念，那不会完全是爱因斯坦想要的那种；贝尔和PBR保证了这一点。但它可能最终成为爱因斯坦所需要的那种实在——一种具有足够直觉意义、能赢得物理学家心灵和思想的实在，尤其是那些因一生都在关于何为实在的迷宫式辩论中疲惫不堪的人。“它需要具有真理的ring，这样当人们看到它时，就无法忽视它，”施密德说。

英文来源：

A Strange Quantum Theorem Has Killed Einstein’s Reality
Samuel Velasco/Quanta Magazine
One of a human’s earliest developmental milestones is an understanding of object permanence. It generally takes less than a year for a baby to realize that when an adult hides their face behind their hands in a game of peek-a-boo, they don’t cease to exist. There’s more to the world around us than what we perceive.
This suggests — or at least, it suggested to Albert Einstein — that the world is “real,” in the sense that things in the world have properties that are intrinsically true no matter what anyone thinks. A red billiard ball is red, even in the dark, and even if no one is checking its color. The redness is a property belonging to the ball, not to some device measuring the ball, and not to the mind of some person operating the measuring device.
Yet quantum mechanics, a thoroughly validated theory of how the world works, seems to suggest otherwise. The theory’s math assigns redness to the billiard ball at the moment you measure it. Before then, the theory gives you only a set of probabilities telling you what color the ball might be. Key founders of quantum mechanics suggested that this math reflects the nature of reality — that in some sense, a single, objective reality doesn’t really exist.
In 1935, Einstein rebelled against this surreal reading of quantum theory, proposing one of the 20th century’s most famous thought experiments. But his rebellion was doomed. In 1964, the physicist John Stewart Bell showed with a thought experiment of his own that reality had to be stranger than Einstein assumed. Subsequent work would put Bell’s thought experiment to the test — and prove him right.
Then, 50 years after Bell, Matthew Pusey, at the time a graduate student at Imperial College London, took on what remained of Einstein’s notion of reality and — without originally intending to — delivered the killing blow.
Courtesy of Matthew Pusey
The paradigm-shifting theorem became known as PBR, for Pusey and his academic accomplices, Jonathan Barrett and Terry Rudolph. Since the publication of PBR in 2012, many theorists have come to accept that it rules out our most commonsense understanding of reality.
“From the moment [PBR] came out, people knew it would be a landmark,” said Jacques Pienaar, a physicist now at the Federal University of Rio de Janeiro in Brazil.
At the time, Pienaar, like Pusey, had been walking in Einstein’s footsteps, dabbling in theories designed to show that objective reality exists and that quantum mechanics merely describes our incomplete knowledge of it. But when the PBR theorem appeared, Pienaar remembers thinking, “That’s it. The program’s dead.”
This is the story of how Einstein, Bell, and finally Pusey and his collaborators killed reality as we know it. In three theorems, they proved that quantum mechanics is incompatible with the world we perceive. And since experiment after experiment — including a recent realization of PBR — has established that quantum mechanics is the law of the land, something about reality has to go.
The question that remains is: How much do we have to give up?
Einstein and Reality
After playing a pioneering role in developing the theory of quantum mechanics, Einstein turned around and attacked it. He couldn’t accept what it said about reality.
Einstein knew in his bones what reality was. It was the sum total of all objective facts — like the color, position, and velocity of a billiard ball — that exist in the objects they describe, independent of perception and mind. But quantum mechanics, as developed by Werner Heisenberg and Erwin Schrödinger in the mid-1920s, didn’t deal in facts.
Quantum mechanics deals in possibilities. Its mathematics gives you a “quantum state,” also known as the wave function. This wave function can tell you, for example, that in an experiment measuring the color of a particular billiard ball, you will have a 77% chance of finding the ball to be red and a 23% chance of finding it to be green.
Public Domain
The question that has stumped physicists for a century is: What is the nature of the ball before the experiment takes place? Does the ball have multiple colors? No color? Does the concept of color not have a meaning? In short, is there a reality to support the object permanence we experience?
To Einstein, the answer was obvious: Of course reality exists; the wave function just doesn’t fully capture it.
In this view, the wave function is like a weather forecast. Say you wake up and your weather app tells you there’s a 77% chance that it will rain today, but you haven’t looked outside to see what’s going on. Then you raise the blinds and see raindrops falling. In that moment you become 100% certain that it’s raining. This shift from 77% to 100% is a shift in certainty that occurs purely in your head. It doesn’t reflect some real meteorological change. The atmosphere is real, and your (un)certainty about its state is something else — a reflection of the information in your mind.
Einstein, along with his collaborators Boris Podolsky and Nathan Rosen (collectively, “EPR”), came up with a thought experiment to prove that the quantum state exists only as an artifact of information. To understand the thought experiment, you need to know one peculiar thing about the wave function: Its mathematical structure doesn’t allow an object to have a position and a momentum at the same time.
The EPR experiment involved bouncing two particles off each other and, sometime later, making a measurement, such as how far one particle had traveled. This first measurement would also tell you how far the partner particle had traveled. EPR argued that the position of the partner particle had to exist, because it could be known. They argued that the partner particle also had a momentum, because that property was knowable in a similar way.
Crucially, their experiment involved measuring only one particle one time, while the other remained untouched. This showed, the scientists argued, that the second particle had properties that were set and real, even before measurement. And since the wave function doesn’t allow for that, the wave function must not reflect the literal state of the particle; the quantum state is not real.
To reach this conclusion, the scientists had made two seemingly unassailable assumptions. First, they assumed that it was possible for a particle to have a literal state, the assumption of “reality.” And second, they assumed that this literal state existed within the particle and nowhere else, so the only way to change it would be to interact with the particle, the assumption of “locality.”
But just months after EPR, Heisenberg’s mentor, Niels Bohr, tried to shut down Einstein’s argument by attacking its first assumption. “There is no quantum world,” Bohr would later say, according to his assistant Aage Petersen. “There is only an abstract quantum physical description.” His argument was akin to asserting that the weather forecast was accurate but that the atmosphere itself was either nonexistent or indescribable. This denial of objective reality became known as the Copenhagen interpretation.
Public Domain/Paul Ehrenfest
Many modern quantum physicists criticize Bohr’s response to EPR for being confusing and vague. But Bohr’s prominent role as a founder of quantum mechanics, together with the mounting experimental support for the theory, convinced many of his contemporaries that he was right. Physicists largely lost interest in debating how the quantum state relates to reality — the central question in the modern field of “quantum foundations.”
“Bohr is like the worst thing to happen to physics,” said David Schmid, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, who devoured the Bohr-Einstein debates as a teenager. “He’s the reason that quantum foundations didn’t exist” until the modern era.
Thirty years later, a blockbuster theorem would revive physicists’ curiosity.
Bell and Locality
John Stewart Bell always felt sympathy for Einstein. As a student, Bell also struggled to swallow the surreality of quantum mechanics. He wondered how its predictions could possibly be disconnected from a real world made of objective properties, as Bohr had advocated.
Then, in 1952, Bell “saw the impossible done.” He read the works of David Bohm, which developed a version of quantum mechanics where particles always had real positions, regardless of measurement.
“Bohmian mechanics” accomplished this by declaring the wave function a “pilot wave,” a physical object that steered particles around. As a real thing in the world, this wave had one distasteful feature: nonlocality. It could change in such a way that it could disturb a distant particle instantly.
Despite this drawback, the pilot wave was a beacon to Bell. It allowed physicists to argue that, contrary to the popular Copenhagen interpretation, an objective reality existed after all. “Why is the pilot wave picture ignored in textbooks?” Bell wrote. “Should it not be taught, not as the only way, but as an antidote to the prevailing complacency?”
Bohm’s work inspired Bell to devise a new thought experiment, one so simple that it would apply to all versions of quantum theory, known and unknown. Following in Einstein’s footsteps, he imagined two particles colliding and flying off in opposite directions. Eventually, the particles would each encounter a device that would perform a randomly selected measurement, one with two possible outcomes.
Bell imagined repeating this experiment many times and used basic arithmetic to predict how often the devices could possibly return matching measurements. He assumed that each particle had a state to begin with (Einstein’s idea of objective reality) and that the devices were too far apart for the particles to influence each other (Einstein’s idea of locality). He calculated that, in a real and local world, the particles would match relatively rarely.
Then, using quantum mechanics, Bell predicted that the two particles would match much more often. He had created an experimental test that could pit quantum mechanics against Einstein’s version of reality. Physicists carried out his experiments in the 1980s and confirmed that particles really do match more than Einstein’s reality would allow.
Bell had succeeded where Bohr failed: He had proved that at least one of EPR’s two key assumptions had to be wrong. Physicists saw that the world could not be both real and local. Something had to give.
CERN/CC BY 4.0
Bohmian mechanics represented one extreme way of navigating the trade-off. It saved reality by making the wave function a real object, but it demanded that people swallow the bitter pill of nonlocality. The Copenhagen position, that nothing was real, was another extreme.
In the following decades, some physicists realized that there was a middle path. Bell had shown EPR’s assumptions to be wrong, but perhaps Einstein was nevertheless onto something with his intuition that the wave function resembled our knowledge, like a weather forecast.
“You go back and look at everything [Einstein] wrote, and it’s just 100 years ahead of its time,” Schmid said.
The search for a way to preserve objective reality without making the wave function real would lead Pusey to the PBR theorem. And in an ironic twist, the PBR theorem would effectively end that search.
PBR and Information
Physicists like Schmid and Pienaar couldn’t get over the fact that the quantum state just didn’t act like an understandable physical property.
Take one defining behavior of the wave function, its “collapse.” Recall the example of the billiard ball that could be red or green. At the moment you look at the ball, its wave function collapses, giving it 100% odds of redness.
Trying to interpret this event as a literal change in the physical ball is maddening. Did the ball begin as some impossible-to-visualize colorless mixture, and then, in the instant you glanced at it, snap into a state of 100% redness?
“You have to watch out for your sanity in a field like quantum foundations,” said Lucien Hardy, a physicist at the Perimeter Institute who works in the field.
But interpret this event instead as a change of information inside your head, and it makes much more sense. You thought the ball was probably red, looked, and learned that indeed it was. The same thing happens to the odds of rain when you look outside your window in the morning. Einstein didn’t put it quite in these terms, but this position is what modern scholars believe he was advocating for in EPR.
In 2004, Robert Spekkens, a physicist at the Perimeter Institute, laid out a theory of a simple world like the one Einstein had imagined. In this theory, each particle has an objective position and velocity, but experimental limits make it impossible to measure both exactly. Spekkens showed that in such a world, one where the quantum state represents incomplete knowledge of real properties, he could produce a laundry list of putative quantum phenomena — quantum “teleportation,” a ban on copying quantum states, and dozens more. His research amassed a pile of fresh evidence that the quantum state looks a lot less strange if you move it from the external world into someone’s head. In other words, he showed that Einstein’s approach still had advantages, despite its faulty assumptions.
In 2011, Spekkens’ work came to the attention of Pusey, then a graduate student. Bell’s theorem had already hooked Pusey with its guarantee that quantum mechanics means the world really is more bizarre than Einstein, or common sense, would have it. “We’ve got this theory that says we’re not just imagining it,” Pusey said. “There really is something strange to figure out here.”
Spekkens’ theory hinted that while not all of the strangeness of quantum mechanics could be banished (Bell’s theorem guaranteed that), perhaps some of it was an illusion caused by taking the wave function too seriously. After all, Spekkens’ theory didn’t look so different from full-blown quantum mechanics on paper. After Pusey rewrote it in a notation he developed, it differed by only a few minus signs. His collaborators, who were Einstein sympathizers, encouraged him to try to upgrade Spekkens’ theory, minimizing the weirdness as much as possible by treating the wave function as a state of knowledge that lives in your head.
“I spent a few days trying to do that, and got fed up,” he said. “So I decided to prove that it was impossible instead.” That work would become the PBR theorem.
Like EPR, PBR explores a question about reality in the form of an elaborate thought experiment. PBR proposes an odd sort of game that you can imagine as a card game between a dealer and a player, following an analogy of Rudolph’s. First, the dealer pulls the 26 red cards out of one deck of cards and the four aces out of another. Let’s call them the red pile and the ace pile.
Next, the dealer places the two piles of cards under the table. He randomly chooses a card from either the red pile or the ace pile. Then he repeats the process, randomly choosing a second card. He then places the two cards face down on the table and gives the player a strange challenge: Tell me one combination of piles from which these two cards were not selected.
Most of the time, the player is guaranteed to win. Say she turns the two cards over and sees the two of diamonds and the ace of clubs. Obviously, the two of diamonds — a red non-ace — came from the red pile. And the ace of clubs — a black ace — came from the ace pile. The dealer could not have gotten these cards by choosing from the red pile twice, or from the ace pile twice, so the player can definitely win by naming either of those options.
But say the player turns over the ace of diamonds and the ace of hearts, two red aces. Since both cards could have come from either pile, the player has no way of ruling out any possibilities. She can guess, but she has only a 3-in-4 chance of guessing right. And so after enough rounds, she must eventually lose.
The point of this game is to illustrate the fundamental difference between real states and states of knowledge. “Ace of diamonds” and “ace of hearts” are the real states of the cards, while “red pile” and “ace pile” are states of knowledge. The player sometimes loses because information about each card’s pile of origin is not written into the card itself; it lives only in the head of the dealer.
This distinction exists only because the two states of knowledge share real states — the red aces. This is a fundamental property of states of knowledge; they “overlap” in a way that makes the which-pile state unreadable from the physical card. Consider, in contrast, playing the same game with non-overlapping piles, like red cards and black cards. In that case, turning over a card would reveal with certainty which pile it had come from. Both “red pile” and “four of hearts” would be real states of the card itself.
PBR posed a quantum version of the game and asked whether the quantum states could overlap, and whether quantum states could therefore be states of knowledge. This game — and its conclusion — shares two crucial assumptions with the classical version. It assumes that the cards have real states (Einstein’s idea of objective reality). And it assumes that the real state of the first card drawn does not affect the real state of the second card drawn (a new assumption distinct from locality).
The surprise was that in the quantum version of the game, the player could always win. To show this, PBR detailed how to assemble a quantum machine built from doohickeys that perform simple quantum actions like putting classical objects into quantum states. If you scan the two cards with this machine, it can always rule out at least one combination of piles they come from. (In a strange quantum quirk, the machine does this — and in fact needs to do this — without turning over and observing the cards.)
A 2012 experiment showed that this guaranteed-win quantum strategy really works, demonstrating that there is no overlap between quantum states. Therefore, given PBR’s assumptions, quantum states are not states of knowledge in the dealer’s head; they are indeed scannable properties of the cards themselves. “You can think of [the quantum state] as stamped onto the underlying state of the world,” Pienaar said. “You change the quantum state, you change something in reality.”
Life After PBR
As with Bell, PBR has been experimentally confirmed multiple times. Last fall, for instance, researchers in the U.K. played an expanded version of the PBR game, dealing out five cards instead of just two, using a quantum computer built by IBM. Indeed, the quantum machine always won, although no one had doubted that it would. In fact, the researchers had been using the PBR theorem mainly to check whether the quantum computer was functioning properly. The validity of quantum mechanics — and PBR — was taken as a given.
“That was really the motivation,” said Crispin Barnes, a physicist at the University of Cambridge who led the experiment, “to see whether a theorem from quantum foundations could also be turned into [an] experimental probe of genuinely quantum behavior.”
Many physicists have taken PBR to mean that the quantum state must be real — an objective property living in particles, people, and planets. If so, impossible-seeming events like collapse must also have some physical correlate. This stance amounts to taking the extreme path of Bohmian mechanics and other “realist” interpretations. As Pusey pithily puts it, PBR guarantees that “if anything is real, the quantum state is real.”
But to conclude that the quantum state is definitely real is to misunderstand the PBR theorem, because PBR also leaves open the other extreme path: It could be, as the Copenhagenists have steadfastly maintained since the days of Bohr, that in some sense nothing is real, including the quantum state. It’s perfectly possible that the quantum state lives in our minds and has no direct connection to an objective reality. In this case, the redness of the billiard ball would be inextricably linked with the act of observing it — precisely the state of affairs that so deeply offended Einstein. “Do you really believe the moon is not there when you are not looking at it?” Einstein once famously pressed his colleague Abraham Pais.
PBR doesn’t give us the answer. What it does do is end a century of bargaining with quantum mechanics. By ruling out the possibility that reality is real while the wave function is not, PBR requires that physicists either fully embrace the notion of an objective but entirely surreal reality, or fully reject objective reality altogether. “Do you bite the bullet, or do you try and dodge the bullet?” Pusey said.
Pienaar was one of the few physicists who were still playing around with middle-of-the-road theories, though with waning interest. PBR contributed to his choice to give up on objective reality once and for all. He switched to a modern offshoot of Copenhagenism known as QBism.
QBism asserts that the world itself may exist, but quantum mechanics can’t describe it. All the theory can really do is capture our relationship to — and subjective experience of — the world. “You need two to tango,” Pienaar said. “Without two systems, there’s no relation. And reality is nothing but relations.”
And yet, some physicists remain unsatisfied with the two extreme options: a surreal reality or no reality. So they are beginning to pick at the fine print on the technical definition of reality. “Maybe the correct way of thinking about a state of reality is something a bit more woolly, that doesn’t quite fit into this straitjacket,” Pusey said.
In this spirit, Hardy questions whether reality needs to necessarily have a single, objective state at every given moment. Perhaps states could somehow spread out across multiple moments. He doesn’t yet have a fully fleshed-out proposal, but his goal is to come up with a deeper, more general notion of reality that is still recognizable.
If underdogs like Hardy succeed in saving some notion of reality, it won’t quite be the one Einstein wanted; Bell and PBR guarantee that. But it may yet turn out to be the sort of reality Einstein needed, one that makes enough intuitive sense to win the hearts and minds of physicists, especially those fatigued from a lifetime of labyrinthine debates about what is real. “It needs to have the ring of truth, so that when people see it, they can’t unsee it,” Schmid said.