The Quantum Conspiracy: What Popularizers of QM Don't Want You to Know

量子阴谋：量子力学科普者不愿让你知道的真相 Garret指出，量子力学的流行表述（尤其是哥本哈根诠释中的波函数坍缩概念）在逻辑上存在缺陷，因为它们暗示了超光速信号传递和逆因果关系。通过双缝干涉、偏振滤光片和量子擦除等实验，他揭示了波函数坍缩只是一种光学子系综过滤假象，而非不可逆的物理过程。结合薛定谔方程和冯·诺依曼熵的数学原理，Garret证明了测量与量子纠缠具有完全相同的数学形式。最终，他提出了一种“零世界”量子信息论诠释，得出结论认为：连贯、客观的经典宇宙感知并非源于物理实体，而是因为宏观观察者忽略了他们所测量的纠缠目标。 量子力学的标准哥本哈根诠释在科学上是站不住脚的，因为不连续、不可逆的波函数坍缩与薛定谔方程连续、时间可逆的数学性质相矛盾。 (11:52) 测量与量子纠缠在数学上是完全相同的物理现象，这意味着测量表现为一个平滑的连续统一体，而非非此即彼的二元对立。 (34:55) 量子擦除器并没有改变过去；它们通过光学手段将子系综过滤为条纹和反条纹，二者叠加后表现为表面上的非干涉，并通过需要经典信道来重构图案，从而维护了相对论因果律。 (38:12) 在量子信息论（“零世界”诠释）下，经典现实是通过求偏迹排除被观察粒子而产生的幻象，使得宏观观察者表现为没有底层形而上学关联物的相关性。 (48:58)

Software engineer Dr. Ron Garret argues that popular accounts of quantum mechanics rely on a flawed concept of physical wave function collapse that implies impossible faster-than-light signaling. Instead, Garret asserts that measurement and entanglement are mathematically identical continuous processes best understood through quantum information theory without assuming an objective classical reality. The Collapse Fallacy and Faster-Than-Light Signaling (25:14) Popular explanations explain the loss of interference in double-slit experiments as an abrupt, irreversible collapse of the wave function caused by measurement. Garret argues that physical collapse contradicts the Schrödinger equation, which is continuous, deterministic, and time-reversible. Furthermore, combining collapse with entangled pairs generates what he terms the Einstein-Podolsky-Rosen-Garret (EPRG) paradox. If measuring one slit apparatus collapsed the wave function of an entangled photon across the universe, an experimenter could toggle interference fringes on and off to transmit faster-than-light Morse code. Conversely, if measuring one side left the remote pattern intact, an observer would possess which-way knowledge while retaining interference, violating basic quantum principles. Garret uses this dilemma to demonstrate that the standard physical collapse narrative is untenable. Measurement as Entanglement in Continuous Mathematics (34:55) Garret resolves the EPRG paradox by showing that quantum interactions involve no physical collapse. When a particle interacts with an apparatus, their joint state evolves continuously into an entangled superposition. Evaluated mathematically, the wave function of a particle interacting with a which-way detector is structurally identical to the wave function of an entangled particle pair. Consequently, measurement is not a binary, disruptive collapse, but a continuous interaction governed by detector reliability. Interference disappears because detector states become orthogonal—canceling the mathematical cross-terms—not because a wave physically shatters. In Garret's formulation, entanglement does not merely trigger measurement; entanglement and measurement are the exact same phenomenon. Resolving Signaling via Sub-Ensemble Filtering (38:12) Garret demystifies the quantum eraser by evaluating its wave function normalization. When paths are marked with orthogonal polarizations, interference vanishes; adding a downstream 45-degree polarizing filter restores it. Garret explains that this filter does not alter the past. Instead, it absorbs or deflects half the photons while transmitting the other half, which display interference fringes. Crucially, the rejected photons form an identical set of out-of-phase "anti-fringes." When combined unfiltered, fringes and anti-fringes sum into a uniform, featureless distribution. In an entangled setup, recovering the hidden fringes requires correlating local hits with remote measurement records transmitted over a classical, subluminal channel. Because fringes remain imperceptible without classical data, faster-than-light signaling is prevented. Quantum Information and the Zero-Universe Reality (48:58) Garret advocates for Quantum Information Theory, framing physical systems using von Neumann entropy. Using complex amplitudes allows quantum entropy to take on negative values. While two independent classical coins have two bits of joint entropy, an entangled particle pair possesses zero total entropy alongside two bits of mutual information, indicating the particles are "super-correlated." When an ancilla particle entangles with a macroscopic apparatus of 10^23 particles, applying the mathematical partial trace operator to the measured particle cancels the negative entropy. The remaining apparatus displays classical correlation. Garret calls this the "zero-universe" interpretation: consistent physical reality is an illusion that emerges because observers trace out and ignore the quantum systems they interact with. Garret concludes that human observers are "correlations without correlata," composed of informational bits rather than classical physical matter. While measurement remains unitary and theoretically reversible, un-entangling a macroscopic environment of 10^23 particles is practically impossible, creating the persistent appearance of classical irreversibility. Garret notes that while an Everettian Many-Worlds interpretation is mathematically tenable, he prefers the information-theoretic view, while openly leaving unresolved thermodynamic questions about multiverse mass-energy conservation to professional physicists.

前谷歌工程师兼前NASA研究员Ron Garret指出，通俗科学将量子测量解释为客观波函数坍缩不仅与连续可逆的量子数学方程相矛盾，还会导致超光速通信的逻辑悖论。他主张从量子信息论的视角重新审视量子力学：测量在数学上等同于纠缠，客观的单一经典现实并非独立实体，而是宏观系统忽略被测对象后显现的信息关联。 坍缩假说的逻辑破绽与数学矛盾 (11:52) 哥本哈根诠释将干涉条纹的消失归因于测量行为对微观粒子造成了不可逆的物理扰动，迫使波函数发生不连续的物理坍缩。然而，Garret指出，薛定谔方程本质上是一个偏微分波动方程，其数学结构完全连续、时间对称且确定性可逆，在基本数学形式中不存在任何不连续机制或内在随机性。将复数振幅模方平方转化为实数概率密度的波恩定则（Born rule），纯粹是一种极为成功的计算技巧，缺乏深层的物理机制推导。 此外，双缝干涉图样的产生与消失完全取决于“路径信息”在原则上是否可知。即使粒子未直接与探测器发生物理接触，仅在单缝处设置探测器并通过排除法推导出未触发探测器的粒子路径，干涉条纹也会立即消失。这种非接触性的影响表明，假设存在局域物理坍缩的传统解释在根本上与底层的连续性物理定律相悖。 EPRG悖论与量子擦除的虚假超光速 (25:14) 为了揭示流行叙事的破绽，Garret提出了“爱因斯坦-波多尔斯基-罗森-加勒特”（EPRG）思想实验：将一对处于自旋纠缠的粒子分别导入左右两套双缝装置。若左侧的路径测量能瞬间摧毁右侧的干涉图样，由于干涉是宏观可见的光斑条纹，观测者便能通过在左侧反复放置和撤去探测器，实现跨越宇宙的瞬时摩尔斯电码通信；反之，若右侧干涉不消失，则违背了“已知路径必无干涉”的量子基本定律。即使试图将纠缠本身视为初始破坏干涉的测量，引入量子擦除器恢复纠缠同样会再次触发超光速信号传递。 Garret解释，破解该悖论的关键在于认清量子擦除的物理本质。以45度偏振片构成的量子擦除实验为例，它并未物理性地修改过去或抹去既成事实，而是过滤掉了半数光子：透过的光子产生干涉条纹，被阻挡或偏转的光子则构成相位相反的“反条纹（anti-fringes）”。未被过滤时，条纹与反条纹重叠抵消，呈现为均匀的光斑。在纠缠实验中，右侧屏幕的干涉条纹必须与左侧远程探测器的测量记录相匹配才能显现，这一比对过程严格依赖以光速或亚光速传输的经典通信信道，因此根本不存在超光速通信。 测量即纠缠：消除干涉的数学统一 (34:55) 传统科普常将量子测量视作寻常操作，而将量子纠缠渲染为不可思议的神秘现象。Garret强调，两者的数学形式完全一致。在含探测器的双缝系统中，复合态波函数由粒子路径与探测器状态的直积叠加构成；展开计算概率密度时，交叉干涉项受到探测器本征态重叠狄拉克括号（如⟨DU|DL⟩）的调制。当探测器足够可靠且不发生自发状态跃迁时，该内积项为零，导致交叉项消失，从而在数学上消除了干涉图样。这证明测量并非非此即彼的突变，而是一个随着探测器可靠性连续变化的平滑过程。 剥离符号差异后，这一含有探测器的状态方程与一对自旋反相关的纠缠粒子波函数结构毫无二致。Garret指出，纠缠之所以会破坏双缝干涉，是因为从数学层面而言纠缠就是测量本身。流行叙事中所谓“幽灵般的超距作用”，在数学形式上不过是全同的关联方程在空间维度上的投射。 量子信息熵与“零宇宙”诠释 (42:59) 基于量子信息论（QIT），Garret提出了被称为“零宇宙（Zero-Worlds）”的全新诠释。在经典信息论中，香农熵衡量系统的随机性，两个独立系统的互信息为零；而在扩展至复数域的量子信息论中，冯·诺依曼熵（Von Neumann entropy）允许负熵的存在。处于完全纠缠状态的双粒子系统，其总熵为零，互信息却达到2比特，呈现出超越经典极限的“超相关（super-correlated）”。 当引入由被测粒子、探测粒子及宏观测量仪器（约10²³个粒子）构成的三体系统时，对被测粒子执行偏迹（partial trace）数学操作——即在观测中忽略被测对象本身，正负熵项便会相互抵消。此时，剩余的宏观仪器系统在数学上退化为具备1比特经典熵的硬币与传感器模型，显现出完全的经典确定性。Garret援引物理学家David Mermin的观点指出，物理观察者本质上是“没有相关物的相关性（correlations without correlata）”。宏观测量的单向不可逆性并非源于物理定律的时间不对称，而仅是因为在实践中无法将散逸至10²³个环境粒子中的纠缠信息逐一逆转。因此，客观一致的宏观现实并非预先存在的形而上学实体，而是源于我们作为由经典比特构成的图灵机观察者对测量目标的数学忽略。 Garret总结指出，在数学上多世界诠释与“零宇宙”信息论诠释同样成立，唯一被量子数学明确否决的是“单一经典宇宙”的存在。他坦承由于多世界分支在实际时间尺度内永久不可逆，且在多宇宙质量与能量守恒的分割机制上存在尚未解决的理论分歧，自己更倾向于将现实视作高精度量子信息模拟。同时，他承认关于量子理论是否属于局域理论的判定取决于定义标准，而人类大脑作为依托经典规则运行的认知系统，在直觉上理解复数底层的量子全貌始终存在根本局限。

## Background 本讲座由 Google TechTalks 于 2011 年 1 月 12 日在 YouTube 平台发布，主讲人为前 NASA 喷气推进实验室研究员、前 Google 早期工程师 Ron Garret 博士。视频简介指出，费曼曾有名言称没人真正懂量子力学，但这更多是科普书为了销路而营造的神秘感；基于早已破产的哥本哈根诠释会导致超光速通信谬误，而本场讲座旨在基于量子信息论（QIT）提供一种替代视角，揭示测量与纠缠实为同一种物理现象。 ## TL;DR Ron Garret 针对流行科普中波函数坍缩与哥本哈根诠释的漏洞展开剖析，指出如果传统测量坍缩模型成立，就会在自旋纠缠与量子擦除实验中推导出超光速传递信号的悖论。他通过初等代数拆解薛定谔方程与带探测器的双缝实验展开式，证明在纯粹连续且时间可逆的底层量子数学中，量子纠缠与宏观测量本质上是完全同构的物理过程。进一步借助将香农熵扩展至复数域的冯·诺依曼熵，Garret 说明测量只是一场宏观的多体纠缠，通过对被测系统求偏迹忽略原粒子从而呈现出经典确定的表象，进而引出放弃独立客观实在、将现实视作纠缠信息网络的“零宇宙诠释”。 ## Atmosphere & style 现场氛围既有工程师特有的极客幽默与务实较真，又洋溢着打破权威神话的思辨锋芒。Garret 随手拿出价值数十美元的铅笔芯和偏振片在讲台上做低成本物理演示，口吻亲切随和且充满自嘲，但在推演公式和逻辑反驳时又极为犀利干脆。问答环节中观众与物理学家频频抛出尖锐质疑，Garret 既能机智交锋，又能在触及质能守恒与宇宙学前沿盲区时坦然举手认输，整场演说在轻松的极客脱口秀外壳下包裹着深邃震撼的科学启蒙张力。 ## Bulletin - [11:52](https://www.youtube.com/watch?v=dEaecUuEqfc&t=712s) 哥本哈根诠释中的“波函数坍缩”在物理学上已被证实站不住脚；若其实体存在，将允许超光速通信并导致因果律逆转。 - [34:55](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2095s) 纠缠与测量在底层数学结构上完全同一：测量只是微观粒子与由大量粒子构成的宏观系统发生纠缠的过程，而非不可逆的外力破坏。 - [38:12](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2292s) 量子擦除器并未改变过去或重塑干涉，它仅是通过偏振过滤分离出了互补的正干涉条纹与反干涉条纹，二者原本并在屏幕上叠加抵消。 - [52:04](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3124s) 基于量子信息论的“零宇宙诠释”指出，客观形而上学现实只是一种错觉，宇宙本质上是运行在复数底层上的量子关联网络（没有相关物的相关性）。 ## Key takeaways - [00:00](https://www.youtube.com/watch?v=dEaecUuEqfc&t=0s) 科普读物所宣传的“量子不可理解性”存在误导，量子力学的理解难度并不高于相对论，误解主因在于过时的哥本哈根诠释被过度灌输。 - [02:50](https://www.youtube.com/watch?v=dEaecUuEqfc&t=170s) 经典世界观认为测量只是读取预先存在的客观实在，但现代物理实验已证明这种独立的客观实体假设并不成立。 - [09:03](https://www.youtube.com/watch?v=dEaecUuEqfc&t=543s) 在双缝实验中引入无相互作用测量（单缝探测）依然会摧毁干涉条纹，表明粒子系统具有全局波动态。 - [29:43](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1783s) 薛定谔方程的动力学演化是完全确定性、连续且时间可逆的，数学上根本不存在瞬时不可逆的波函数坍缩机制。 - [25:14](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1514s) “EPRG 思想实验”揭示了传统叙事的悖论：若测量瞬间改变远端状态，将导致超光速摩斯密码信道的产生，直接破坏狭义相对论。 - [32:12](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1932s) 干涉条纹的数学起源于复数概率振幅交叉项相加可能产生的负值，引入探测器后交叉项的大小直接由探测器自身的可靠性决定。 - [34:55](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2095s) 双缝实验加入探测器后的复合波函数与两粒子纠缠态公式完全同构，证明纠缠就是一种摧毁干涉的原始测量。 - [38:12](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2292s) 利用纠缠粒子复现干涉条纹必须依赖亚光速的经典信道传递筛选数据，因此绝不存在跨空间的超光速信号传递。 - [47:00](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2820s) 复数扩展后的冯·诺依曼熵允许出现负熵，使得纠缠粒子对具备超越经典极限的“超级关联”，而整体系统总熵为零。 - [49:04](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2944s) 宏观测量的确定性表象来自于对被测系统求偏迹（数学上忽略被测粒子），这使得多粒子纠缠网络退化为经典的信息关联。 - [52:04](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3124s) 宏观测量的“不可逆性”只是热力学与工程实践的限制，因为解开以光速扩散至上百亿粒子的纠缠网络在现实中无法做到。 - [55:18](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3318s) 单一经典宇宙在数学上已被证伪；在数学相容性上，只有无穷分裂的“多宇宙诠释”与否定实体宇宙存在的“零宇宙诠释”站得住脚。 - [55:18](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3318s) 人类思维依托于经典实数图灵机逻辑，而底层现实由复数支撑的量子纠缠驱动，这一认知错配是人类直觉难以理解量子特性的根源。 ## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=dEaecUuEqfc&t=0s) 讲座开场与背景介绍 Arthur Gleckler 为活动作开场主持，向在场听众隆重介绍了主讲人 Ron Garret 博士。Ron Garret 是 Google 极早期的员工（大约在 2000 年加入），身兼多项重要工程的开创者：他是 Google AdWords 第一个版本的首席工程师，编写了 Google 最初的计费系统（billing system），并且是 Google 翻译控制台（Google Translation Console）的原作者。在此之前，他曾在位于帕萨迪纳的 NASA 喷气推进实验室（JPL）工作长达 15 年，专注于人工智能与机器人技术。Gleckler 开玩笑称，希望以后能劝说 Garret 再回 Google 做一场分享，专门讲讲当年如何在距离地球 2.5 亿英里之外远程调试航天器的经历。 随后，Ron Garret 登台接过麦克风。他首先向大家打趣并澄清，本次讲座的标题《量子阴谋：量子力学科普家不希望你知道的秘密》在发布后引发了不小的骚动（kerfuffle）。他解释道，这个标题纯属半开玩笑（tongue-in-cheek），“据我所知，并不存在真正的阴谋”，但大众在科普读物中看到的量子力学描述，与物理学界底层的真实情况之间确实存在着巨大的脱节，而这场讲座的目的正是要打破这一鸿沟。Garret 坦承自己并非物理学家，而是一名软件工程师。当得知台下坐着几位真正的物理学家时，他笑着说请大家监督并确保自己“保持诚实”。 ```mermaid flowchart TD accTitle: 测量认知链路示意图 accDescr: 展示从物理系统到人类头脑认知心智模型的单向测量流程。 subgraph S1["物理交互与数据捕获"] A["物理系统 (System)"] -->|"传感器/相机采集"| B["原始数据 (Data)"] B -->|"输入终端"| C["计算机处理与屏幕显示"] end subgraph S2["感知与心智映射"] C -->|"光子进入视网膜"| D["人类眼睛感知"] D -->|"神经信号构建"| E["大脑心智图像 (Mental Image)"] end E -.->|"真的对应物理现实吗？"| A ``` Garret 回忆了自己探索这个课题的渊源：大约 20 年前，他在《科学美国人》（Scientific American）上读到一篇关于量子力学的文章，当时的第一反应就是“这绝对不可能是对的”。为了搞明白究竟是怎么回事，他花了整整 10 年的时间，最终在加州理工学院（Caltech）找到了一位物理学家为他解惑，指出科普读物中的说法确实是错误的。那一瞬间，一切豁然开朗，量子力学在他眼中变得无比清晰顺畅。他提到有人曾对他说过“量子力学遵循怪异守恒定律”（quantum mechanics obeys the law of conservation of weirdness）。Garret 承认量子力学的确挑战人类直觉，但坚决反对将其视为不可理喻的玄学： > “但我认为，量子力学在根本上并不比相对论更令人费解，而如今大多数技术人员理解相对论似乎毫无困难。” ### [02:50](https://www.youtube.com/watch?v=dEaecUuEqfc&t=170s) “测量”的本质与空间时间的一致性 在正式切入量子理论之前，Garret 邀请观众共同深思一个看似朴素的基础哲学与科学问题：“‘测量’某件事物到底意味着什么？”在日常实验中，我们测量一个系统的属性：传感器（例如相机）捕捉数据，送入计算机并在屏幕上渲染，光线映入我们的眼帘，最终在大脑中构建起一个心智图像（mental image）。但这引出一个根本性的拷问：我们凭什么认定头脑中的心智图像真的对应着底层的客观物理实在？ 我们相信这一点的唯一线索，在于测量的结果在不同空间与时间中表现出了惊人的一致性与可重复性。Garret 用手中的绿色激光笔现场互动提问这束光是什么颜色，观众齐声回答“绿色”。正是这种时空上的一致性构成了人类理解世界的基础。然而，这种规律本身就是一个未解的深层次谜团。Garret 引用了爱因斯坦的名言： > “宇宙最令人难以理解的事情，就是它是可以被理解的。” 对于这种时空一致性，有一种极为合情合理的传统解释：测量结果准确反映了某种底层客观存在的形而上实在（metaphysical reality）。换言之，外部世界是真实独立的实体，测量只是从中读取预先存在的信息，而客观实在本身确保了前后测量结果的统一。然而，Garret 随即抛出惊人论断：现代科学已经能够证明“这种客观实在观根本不是真的”。为了让听众理解这一点，他准备带领大家深入“兔子洞”，并承诺会一步步抽丝剥茧，确保大家最终能安全走出来重获启迪。讲座的推进路线清晰分为四步： 1. 回顾主流科普书（如亚马逊畅销书或《连线》杂志）中常见的标准量子力学叙事； 2. 证明该传统叙事为何必定是错误的——如果它成立，将允许超光速通信，进而破坏相对论； 3. 用初中代数和基础算法概念拆解量子力学真实的底层数学； 4. 基于真实的数学构建全新叙事，揭示测量与纠缠的本质。 ### [06:18](https://www.youtube.com/watch?v=dEaecUuEqfc&t=378s) 双缝干涉实验与波粒二象性 Garret 快速切入量子力学最具代表性的双缝实验（two-slit experiment）。当相干激光穿过平行的双缝投射到屏幕上时，屏幕上会出现明暗相间的干涉条纹，这雄辩地证明了光具有波动性，能像水波一样发生自我干涉。但在微观尺度下，该实验揭示出两个颠覆常识的怪异特性： 1. **单个粒子的离散撞击**：如果将光源强度调至极低，让光子一个一个穿过，最初探测器屏幕上只会出现零星散落的单点感光斑痕；只有当粒子数量不断累积，这些离散随机的点才会渐渐重叠、显现出清晰的明暗干涉条纹。无论用光子还是电子做该实验，底层的物理现象都一模一样。 2. **“增加路径反而变暗”的反直觉现象**：在单缝开放时，屏幕中央是明亮的；然而当平行打开第二条狭缝后，屏幕上原本单缝照射时处于亮斑的特定位置，反而变成了完全漆黑的暗纹。原本有光照射的地方，仅仅因为人类多提供了一条光可以通行的路径，光反而消失了，这就是波的相消干涉。 为了打破“量子现象极其精密高深、必须在昂贵专业实验室才能观察”的刻板印象，Garret 拿出了自己随身制作的简易道具：几根用普通透明胶带粘在一起的铅笔芯，以及一支普通的激光笔。铅笔芯之间留有极其微小的缝隙。当他把激光打在铅笔芯上时，光束瞬间在前方扩散开来，肉眼即可直接辨认出干涉条纹。Garret 兴奋地邀请大家在演讲结束后走上前亲自观察，以此证明量子干涉绝非飘渺的抽象理论，而是日常可见的实在效应。 ### [09:03](https://www.youtube.com/watch?v=dEaecUuEqfc&t=543s) 路径探测与干涉条纹的消失 面对上述现象，人类的机械论直觉本能地试图寻找经典的物理机制予以解释：或许光子和电子是实打实的经典粒子，拥有确定的空间位置和运动速度，只是它们在运动过程中被某种未知的底层导波推着走；而粒子落点看似随机，也许只是因为某些人类尚未掌握的隐藏物理变量在作祟。然而，量子实验完全封死了这种经典解释的退路。 检验这一设想的方法是追踪粒子的真实路径：在粒子飞向屏幕形成干涉图案的过程中，它究竟穿过了两条狭缝中的哪一条？物理学家可以在狭缝处加装粒子探测器。但致命的转折随之出现：一旦我们在狭缝处进行了测量、成功获取了粒子的“哪一条路径”（which-way）信息，屏幕上的干涉图案便会瞬间烟消云散，退化为两团经典的叠加分布。这种“一测就变”的现象构成了量子力学的波粒二象性（wave-particle duality）核心特征。 更深刻的怪异之处在于所谓的无相互作用测量（interaction-free measurement）。为了摧毁干涉条纹，实验人员甚至根本不需要在两条缝上都安装探测器，只需在其中一条缝上放置探测器即可：如果该探测器没有触发响铃，逻辑上就能确凿断定粒子必然穿过了另一条狭缝。在那条没有被放置任何探测器的狭缝中，粒子本身从未与任何探测仪器发生哪怕一个光子的物理碰撞或相互作用，然而干涉条纹依然全盘瓦解。Garret 强调，这意味着粒子似乎“知道”另一侧存在着探测器： > “因此，必定有某种东西同时存在于两个狭缝中，才能产生干涉。” - **演讲中穿插的现场插曲**：在讨论波粒二象性期间，视频会议（VC）系统中传来了远程参会者的杂音，现场工作人员示意提醒，Garret 随即在讲台上微笑着转达并请求远程听众将麦克风静音。 ### [11:52](https://www.youtube.com/watch?v=dEaecUuEqfc&t=712s) 测量对干涉的破坏与哥本哈根诠释的漏洞 在量子力学中，任何提供两条不同路径并在不获知具体路径的情况下将粒子重新汇聚的实验，都会产生干涉条纹；而一旦做出任何能够探知粒子到底走了哪条路径的修改，干涉条纹就会立即遭到破坏。这种性质是普遍存在的，适用于现实宇宙中未经核反应涉及的绝大多数粒子（本质上就是光子和电子）。从表面上看，这似乎还可以用直觉解释：粒子系统微小且脆弱，也许物理上根本不可能做到在测量时不扰动系统，正是这种扰动摧毁了干涉，使波函数发生“坍缩”并表现为粒子。这正是著名的哥本哈根诠释的核心观点。 然而，哥本哈根诠释中的“波函数坍缩”在先验逻辑和数学上存在重大疑点。坍缩被描述为一种不连续且不可逆的过程——一旦获知粒子穿过了某个狭缝，时间就无法倒退去撤销这一结果。但纵观量子力学的底层数学架构，其中没有任何不连续的成分，而且整个数学体系在时间上完全是可逆的。因此，坍缩假说与量子力学描述宇宙运作的数学规律存在根本性的冲突。针对这种假设，Ron Garret 指出： > “And more than that, all the math is actually time reversible so we can make a--hypothesize that this collapse happens, but this is fundamentally at odds with the mathematics of what quantum mechanics--of how quantum mechanic says that our universe works.”（不仅如此，所有的数学在时间上实际上都是可逆的，所以我们可以假设这种坍缩发生，但这与量子力学本身所描述的宇宙运作数学规律存在根本冲突。） ```mermaid flowchart LR accTitle: 哥本哈根诠释与量子数学特性的矛盾 accDescr: 对比传统哥本哈根诠释中波函数坍缩的物理特征与量子力学底层数学规律的根本冲突。 subgraph Copenhagen["哥本哈根诠释假说"] A["观测导致波函数坍缩"] --> B["不连续过程"] B --> C["不可逆过程"] end subgraph Math["量子力学底层数学架构"] D["连续演化"] E["时间完全可逆"] end Copenhagen -.->|"根本冲突"| Math ``` ### [14:11](https://www.youtube.com/watch?v=dEaecUuEqfc&t=851s) 量子擦除实验与偏振片现场演示 为了证明波函数坍缩即便存在也是一个远比表面更微妙的现象，Ron Garret 引入了第二个量子谜题——“量子擦除器”（Quantum Eraser）。在抽象化的双缝模型中，粒子源发出粒子并分流至两条路径，汇聚后在亮暗干涉条纹处分别设置探测器；一旦在某条支路上引入某种测量，条纹便会弥散退化为单缝时的弥散图案。但量子擦除实验表明，如果所做的是某种特定的“原始测量”（proto-measurement），物理上是可以在事后将其信息“擦除”的，从而让干涉条纹重新恢复。 为了让听众亲眼目睹信息擦除的机制，Ron Garret 现场拿出了价值约 30 美元的偏振片（与偏光太阳镜材质相同）进行演示。当两片偏振片的光轴平行时可以透光，正交旋转到 90 度时则完全遮蔽光线；若在两片正交偏振片中间插入一片 45 度的偏振片，原本被挡住的光竟奇迹般地重新透过。随后，他展示了一种高阶材料——偏振旋转器（Polarization Rotator），它可以将特定偏振方向的光直接旋转 90 度而不产生传统实验中明显的亮度损失。 通过这种旋转，两条光路被赋予了不同的偏振态，从而构成了“哪条路径”（which-way）测量，按哥本哈根诠释这本应导致波函数坍缩。但随后通过在下游放置 45 度滤镜过滤，路径信息被抹除，两路光的差异大幅缩小。尽管由于廉价实验器材角度未完全对齐导致少量光线泄露，但擦除效果肉眼可见。Ron Garret 强调，在时间序列上，擦除发生在测量之后，若用激光照射即可观察到干涉图案消失后又重新出现。这证明波函数坍缩并非某种粗暴且不可逆的机械破坏。面对若没有真正坍缩所带来的逻辑推论，他直接引出了宏观态叠加的困境： > “Quantum mechanics says that this cat is in a quantum superposition of being alive and dead which is intuitively absurd but as far as we can tell, that's really what happens.”（量子力学表明这只猫处于一种既死又活的量子叠加态之中，这在直觉上极其荒谬，但就我们目前所知，事实确实如此。） - 现场道具包括普通偏振片与偏振旋转片，总成本仅约 30 美元。 - 偏振片正交（90 度）时透光量为零，中间插入 45 度偏振片可打破正交阻断重新透光。 - 时间序列明确：光沿特定方向行进，擦除操作严格发生在测量操作之后。 - 若摒弃坍缩假说，则不得不直面薛定谔的猫（Schrödinger's cat）所代表的宏观叠加难题。 ### [20:45](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1245s) 第三谜题：自旋纠缠与“鬼魅般的超距作用” 在讨论完叠加与擦除之后，Ron Garret 引出了第三个核心量子谜题——量子纠缠（Entanglement）。虽然大众科普往往将纠缠描述为边缘附属现象，但它揭示了现实最诡异的本质。现场展示了一张通过紫外激光照射自发参量下转换晶体（Beta Barium Borate，简称 BBO，偏硼酸钡晶体）产生纠缠光子对的真实彩色照片。该晶体吸收一个高能紫外光子，将电子激发至高能级，电子分两步跃迁回基态，从而释放出两个能量较低的可见光子。 由于能量守恒与动量守恒等基本物理定律，产生的两枚光子具有严格的互补关联：若一侧射出的是能量偏低的红光光子，另一侧必然匹配一枚能量偏高的蓝光光子；而在空间重叠的交叉区域，光子波长相同，并在空间发射位置与偏振方向上形成高度对称的匹配。当这对光子被发送至宇宙两端进行测量时，无论以偏振还是空间位置作为物理量进行分流，其测量结果在宏观统计上展现出完美的“反关联”（anti-correlated）——右侧探测器若在上通道检测到光子，左侧探测器必定在下通道检测到光子。 讲到探测器方位的代号时，Ron Garret 开玩笑地指出由于英文中“左”（Left）与“下”（Lower）的首字母都是 L，给口头讲解带来了不少口误麻烦。这种跨越空间间隔的瞬时必然关联，正是爱因斯坦当年深恶痛绝并讽刺为“鬼魅般的超距作用”（Spooky action at a distance）的现象。Ron Garret 强调，这在现代物理学中早已不是争论中的猜想，而是无可辩驳的既成实验事实： > “This is what the--what Einstein famously called, 'Spooky action at a distance.' If you take this phenomenon, this isn't controversial, this is an experimental--an undeniable experimental result, this really [happens]...”（这就是爱因斯坦那句名言所说的‘鬼魅般的超距作用’。这种现象毫无争议，是一个不可否认的实验结果，它确实存在……） ```mermaid flowchart TD accTitle: 自发参量下转换与量子纠缠测量 accDescr: 紫外激光通过BBO晶体下转换产生两个能量与偏振反关联的光子，并分别发送至空间两侧进行测量。 subgraph Generation["纠缠光子生成 (BBO晶体)"] UV["紫外激光 (UV Laser)"] --> Crystal["偏硼酸钡晶体 (BBO)"] Crystal -->|"一步激发，两步跃迁"| Pair["纠缠光子对 (Pair)"] end subgraph Distribution["守恒定律与空间分离"] Pair -->|"动量/能量守恒"| LeftPhoton["光子 A (向左传播)"] Pair -->|"动量/能量守恒"| RightPhoton["光子 B (向右传播)"] end subgraph Measurement["空间两端测量"] LeftPhoton --> DetL["左侧探测器: 检出 [下/Lower]"] RightPhoton --> DetR["右侧探测器: 检出 [上/Upper]"] DetL <-.->|"完美反关联 / 鬼魅超距作用"| DetR end ``` ### [23:38](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1418s) 超光速通讯的幽灵与量子随机性的“遮羞布” 如果波函数确实不发生坍缩，那么传统科普中描绘的图景将导向一个极其惊人的结论。正如 Ron Garret 指出的那样，直到最近（比如去年六月的《连线》杂志 Wired），主流媒体依然在宣称：“当测量其中一个光子的量子状态时，另一个光子即使相隔遥远的距离，也会立刻做出响应并改变。”在狭义相对论的框架下，这种瞬间发生的超距作用理应是不可能的，因为任何超光速的信息传递都意味着信号可以在时间中逆行，进而彻底破坏因果律并引发逻辑灾难。 为了维护因果律，传统解释搬出了一面关键的“盾牌”——量子随机性。在纠缠实验中，观测者根本无法控制光子究竟会落在上方还是下方的探测器中；它完全是随机决定的。虽然一旦我们看到自己这边的光子落在上方探测器，就能瞬间断定远在宇宙另一端的同伴一定会看到光子落在下方探测器，但在这两点之间并没有发生真正的信息传输。数学上也可以证明利用这种现象无法传递信息。然而，Ron Garret 在这里话锋一转，抛出了关键转折：这个看似严密的“不可超光速通信”证明，实际上存在一个致命的漏洞。 - 传统理论认为测量造成的瞬间状态改变因“量子随机性”而无法用于发送信号。 - 相对论禁止超光速通信，因为超光速信号等同于向过去传递信息并摧毁因果链条。 - Ron Garret 强调数学证明中关于不可传递信息的结论其实隐藏着漏洞。 --- ### [25:14](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1514s) “爱因斯坦-波多尔斯基-罗森-加勒特”佯谬 Ron Garret 带领听众总结了第一阶段讲到的所有物理事实：分束/合束实验会产生干涉条纹；任何路径测量都会摧毁干涉；存在某种弱“原初测量”可以在事后被擦除以恢复干涉；纠缠粒子对之间的测量结果呈现严格的反相关。随后，他半开玩笑地提出了自己设计的思想实验——“爱因斯坦-波多尔斯基-罗森-加勒特（EPRG）佯谬”： ```mermaid flowchart LR accTitle: EPRG 思维实验图示 accDescr: 展示自旋/偏振纠缠光子源向左右两端分别发射光子进入双缝实验并进行测量的思想实验结构 Source["纠缠光子源<br/>(Down Converter)"] subgraph LeftSide ["左侧观测区"] L_Slit["双缝装置 / 分束器"] L_Det["路径探测器<br/>(测量开关)"] end subgraph RightSide ["右侧观测区"] R_Slit["双缝装置 / 分束器"] R_Screen["干涉屏幕<br/>(肉眼可直接观测)"] end Source -->|"光子 A"| L_Slit Source -->|"光子 B"| R_Slit L_Slit --> L_Det R_Slit --> R_Screen ``` 在这个实验中，中间的参量下转换器向左右两边分别发送纠缠光子，两端各有一套双缝干涉装置。核心问题在于：**如果在左侧测量光子的路径，是否会摧毁右侧的干涉图样？** 1. **如果答案是“会”**：那么人类就实现了超光速通信。因为干涉条纹是肉眼可见的宏观现象，不需要任何精密的单光子探测器就能直接识别。左侧的人只需反复装上、撤下探测器，遥远宇宙另一端的干涉条纹就会随之出现和消失，从而实现莫尔斯电码的瞬间跨星际传输。这显然违背相对论。 2. **如果答案是“不会”**：那么我们通过纠缠推导出了右侧光子的确切路径信息，但右侧却依然存在干涉条纹。这又直接违背了量子力学的核心基石——不可能在获知粒子路径的同时还能观测到干涉。 3. **第三种可能性（全场物理学家的直觉）**：如果系统从一开始就根本没有干涉条纹呢？也许纠缠本身就是一种不可逆的原初测量，早就把干涉毁掉了。但 Garret 指出，这依然无法摆脱超光速通信的噩梦：纠缠是一种极其脆弱的物理属性，在实验中极易被破坏。只要我们在左侧加入量子擦除器摧毁纠缠，右侧原本没有干涉的地方就会凭空出现干涉条纹，这依然构成了一套超光速摩斯密码发射器。 由此，Garret 宣布现有的量子力学传统叙事彻底破产。面对现场听众“为什么从没有人真正做过这个实验”的疑问，Garret 直截了当地回答：“因为所有物理学家都知道结果会是什么。等我讲完接下来这部分，你们也会确信那个结果，以至于根本不需要再费力去做这个实验了。” > “This is a thought experiment... I've dubbed the Einstein-Podolsky-Rosen-Garret paradox.” —— Ron Garret - 经典量子力学逻辑陷入死结：若左侧测量影响右侧，则存在超光速信号；若不影响，则违反波粒二象性互补原理。 - 即使假定初始无干涉，通过单侧量子擦除重现干涉条纹同样能构建超光速信道。 - 针对听众关于实验装置的提问，Garret 补充说明这类实验可使用 Mach-Zehnder 干涉仪、斯特恩-盖拉赫装置或偏振分束器（PBS）实现。 --- ### [29:43](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1783s) 走出兔子洞：薛定谔方程背后的纯粹数学 为了理清这一死结，Garret 带着听众“钻进兔子洞的更深处”，从最底层的数学方程式重新审视物理现实。他向听众展示了著名的薛定谔波动方程（Schrödinger wave equation），并指出方程式中的自由变量是波函数 $\psi$。该偏微分方程所描述的本质就是经典波动的传播规律，这也是粒子在实验中表现出波动特性的根源所在。 波动力学展现出几个极为关键的数学本质：方程的演化过程是**连续的**、**时间对称的（时间可逆）**，并且是**完全确定性的**。在整个薛定谔方程的严格数学中，根本找不到任何坍缩机制的影子，也完全没有哪怕一丁点内在的随机性。而将波函数（复数）取模平方得到在特定时空坐标发现粒子的概率（实数），在物理学历史上根本没有任何先验的物理原理解释；Garret 尖锐地将其评价为：“它纯粹是一个 hack（技术窍门），但却是一个管用得不得了的 hack。” > “The dynamics are continuous, time-symmetric, fully deterministic and hence, reversible, and so there's no place where you can find anything that resembles collapse in this math.” —— Ron Garret - 薛定谔方程的动力学演化具备时间可逆性与严格确定性。 - 波函数值本身是由复数构成的概率振幅，可正可负甚至带有虚数部分；唯有通过取模平方运算后才会转化成可测量的实数概率。 - 粒子之所以会产生相消干涉，正是因为两个模长大于零的复数振幅矢量方向相反时，叠加结果可以精确抵消为零。 --- ### [32:12](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1932s) 双缝干涉与探测器介入的数学展开 Garret 随后用物理学专业文献中的标准数学语言还原了双缝实验的真实演化机制。设光子通过上方狭缝到达探测器的概率振幅为 $\psi_U$，通过下方狭缝的概率振幅为 $\psi_L$。归一化后的总态矢可以写为： $$\psi_{total} = \frac{\psi_U + \psi_L}{\sqrt{2}}$$ 计算光子被检测到的总概率需要对总振幅取模平方。这就像初中代数中展开 $(A + B)^2$ 一样简单： $$P = |\psi_{total}|^2 = \frac{1}{2}\left(|\psi_U|^2 + |\psi_L|^2 + \psi_U^* \psi_L + \psi_U \psi_L^*\right)$$ 公式前两项 $|\psi_U|^2$ 和 $|\psi_L|^2$ 是正实数概率的总和，而包含共轭交叉乘积的后半部分则是典型的“干涉项”。由于两个不同的复数相乘相加后其实部可能为负数，因此它能将某些区域的概率削减为零，这就是量子干涉条纹在数学上的真正起源。 当我们在系统中加入路径探测器时，数学形式发生了关键变化。整个系统的态不仅包含光子，还必须纳入探测器的物理状态：包含“光子在上方且探测器指示在上方”的联合振幅，以及“光子在下方且探测器指示在下方”的联合振幅。再次对该联合态进行取模平方计算，展开后同样会出现形如交叉项的表达式。然而，这里出现了一个利用狄拉克括号（Bra-ket notation）书写的微小内积项。Garret 向听众解释道，这个复杂的符号本质上描述的是：探测器在没有任何外界干扰的情况下，自发地从“指示粒子在上方”翻转为“指示粒子在下方”的物理振幅。 > “So this sum can be negative. So this is where the interference comes from. This is the mathematical manifestation of interference in quantum mechanics.” —— Ron Garret - 干涉条纹是由复数概率振幅的交叉项相加可能产生负值所导致的。 - 引入探测器后，干涉项的保留与否在数学上完全取决于探测器自身不同指示态之间的内积重叠程度。 - 测量过程并非不可捉摸的神奇外力，它在数学上只是粒子态与宏观仪器态共同构建的复合张量体系。 ### [34:55](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2095s) 测量的本质：概率干涉与纠缠数学的同一性 在推导探测器对双缝干涉影响的公式时，交叉项的大小取决于探测器的可靠性（reliability）。如果探测器工作正常，探测器自发在状态间发生错误翻转的概率幅（例如自发从探测上缝状态 $U$ 翻转为探测下缝状态 $L$，或反向翻转）均为零，这就使得原本引起概率干涉的交叉项直接归零。这就是数学上“测量摧毁干涉概率”的机制。更关键的是，数学清楚地表明，测量并不是一个非此即彼的二分法状态（dichotomy），而是一个连续谱（continuum）：我们可以测量得非常轻微，也可以测得相当充分但不完全精准；干涉条纹的减弱程度是连续变化的，完全取决于测量的可靠度。 ```mermaid flowchart LR accTitle: 纠缠态与双缝测量态的数学等价性 accDescr: 展现双缝测量态公式与两粒子纠缠态公式如何映射为完全相同的物理数学形式。 subgraph DoubleSlit["带探测器的双缝系统"] DS["(上缝粒子 ⊗ 探测器上) + (下缝粒子 ⊗ 探测器下) / √2"] end subgraph Entangled["纠缠粒子对系统"] EPR["(|左上⟩ ⊗ |右下⟩ + |左下⟩ ⊗ |右上⟩) / √2"] end DS <-->|"数学本质完全等同"| EPR ``` 当把目光转向纠缠粒子对（Entangled Particles）的数学描述时，物理学论文中常见的纠缠态公式表现为：左粒子处于“上”态且右粒子处于“下”态的概率幅，与左粒子处于“下”态且右粒子处于“上”态的概率幅相叠加，再除以根号 2。尽管各种波函数符号（如狄拉克符号的坚线与尖括号）看起来晦涩且带有记号戏法，但只要还原其物理涵义——左粒子对应上/下，右粒子对应下/上——其结构与带探测器的双缝实验状态方程完全一致，仅仅是标签有所不同。对此，Ron Garret 指出，所谓的“EPRG 悖论”前半部分至此得到了解答：纠缠其实就是一种摧毁干涉的原始测量（proto-measurement）。 > “According to the math, entanglement and measurement are the exact same phenomenon, the math is exactly the same, and that is why entanglement destroys interference because entanglement is measurement.” —— Ron Garret - 探测器探测可靠性与系统态的交叉干涉幅直接关联，测量是一个连续物理量。 - 纠缠态的波函数数学表达与“粒子态 ⊗ 探测器态”的双缝波函数形式完全同构。 - 物理学普及中常将测量描绘为可直观理解的日常事物，而将纠缠视为神圣神秘的量子谜团，但数学本质上二者是同一个现象。 --- ### [38:12](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2292s) 量子擦除器真相：条纹从未被擦除，只是被过滤 针对所谓“利用量子擦除器（Quantum Eraser）重新恢复干涉图样”的说法，Ron Garret 通过偏振滤光状态方程进行了拆解。假设入射光为垂直偏振，上缝的光子偏振态被旋转 90 度变为水平偏振，下缝保持垂直偏振，此时系统处于已被测量且无干涉的状态。若在光屏前加入一个 45 度的偏振滤镜进行“擦除”，光子态会投射到水平加垂直的叠加轴向，这在几何向量上即对应 45 度偏振。 然而，一旦代入概率幅的归一化计算，原本公式分母上的根号 2 变成了 2，导致总概率计算结果不再是 1，而是变成了 1/2。这意味着有一半的光子“失踪”了。这并非数学错误，而是 45 度滤镜客观阻挡并过滤掉了这半数光子。那些被阻挡的光子处于正交的 $H - V$ 轴向，波函数中带有一个负号。这两组光子各自都会自我干涉：通过滤镜的光子形成了明暗相间的干涉条纹（fringes），而未通过滤镜的光子同样产生干涉，但形成的是完全反相的“反条纹”（anti-fringes）——前者的亮斑精确落在后者的暗斑位置，二者叠加在一起，肉眼或屏幕整体感官上就呈现为平滑无干涉的弥散斑。因此，量子擦除器并未擦除任何既有历史，也没有创造出新的干涉，它只是从原本就并存的条纹与反条纹中过滤出了一组。 ```mermaid flowchart TD accTitle: 量子擦除器条纹反相抵消示意图 accDescr: 说明通过 45 度滤镜的光子与被阻挡光子分别形成条纹与反条纹，合并后呈现无干涉。 Photons["45度偏振过滤前<br>(条纹 + 反条纹并存)"] Passed["通过滤镜的光子 (50%)<br>正条纹 (明暗相间)"] Blocked["被阻挡的光子 (50%)<br>反条纹 (明暗互补)"] CombinedScreen["未做区分的整体屏幕检测<br>呈现为完全无干涉图案"] Photons -->|"通过 45° 轴"| Passed Photons -->|"被 H - V 轴阻挡"| Blocked Passed -.->|"在经典未分离时叠加"| CombinedScreen Blocked -.->|"在经典未分离时叠加"| CombinedScreen ``` 在 EPR 实验中同样可以重现这种条纹复现，但必须借助亚光速的经典信道传递信息。实验者必须在一侧记录每个光子是在上探测器还是下探测器被捕获，并在另一侧记录光子在屏幕上的位置，然后通过经典信道把记录传递过去进行数据筛选过滤。只有把对应“上”的光子挑出来，干涉条纹才会浮现；把对应“下”的光子挑出来，反干涉条纹也会浮现。不传输经典信息，这种条纹根本无法显现。 > “And that is the last nail in the coffin. I was very disappointed when I learned this 10 years ago because I was really counting on winning a Nobel Prize and taking over the world but, oh, well, this is the next best thing.” —— Ron Garret --- ### [42:28](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2548s) 从哥本哈根到零世界假说：量子力学的各派诠释 确认了“纠缠即测量”之后，便能从软件工程师的视角构建一种更清晰、更符合直觉的量子力学理解体系。Garret 回顾并对比了主流的量子力学诠释： | 诠释名称 | 核心主张 | 局限性 / 演讲者评价 | |:--- |:--- |:--- | | **哥本哈根诠释 (Copenhagen)** | 波函数在测量瞬间发生坍缩 | 最流行但科学上站不住脚（Scientifically untenable），波函数并不存在真实坍缩。 | | **多世界诠释 (Many-Worlds)** | 任何粒子产生多重可能路径时，整个宇宙分裂 | 数学逻辑完全自洽，但对人类直觉的索求代价过高，令人情感上难以接受。 | | **交易诠释 (Transactional)** | 由华盛顿大学的 John Cramer 提出，认为麦克斯韦方程组的逆时间解具有实体物理真实性 | 鲜为人知但十分有趣，引入逆时间解能解决很多矛盾，但过于小众且复杂。 | | **零世界诠释 (Zero-Worlds)** | 基于量子信息论（QIT），用复数拓展经典信息论，认为纠缠是信息关联 | 演讲者极力主推的观点，数学自然，无需凭空分裂宇宙。 | Ron Garret 强调，在软件工程师的思维看来，量子信息理论（Quantum Information Theory）是理解微观世界最优雅的工具。它不需要哥本哈根诠释凭空捏造的波函数坍缩，也不需要多世界诠释那样每次分裂出无数个实体宇宙，而是通过信息与熵的数学结构，直截了当地说明量子态的本质。 > “So Copenhagen is the most popular but as we've seen it, it's scientifically untenable. There just is no collapse.” —— Ron Garret --- ### [44:19](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2659s) 经典信息论基础：香农熵与信息重叠 为了铺垫量子信息论，Ron Garret 快速梳理了经典香农信息论的核心概念。一个系统 $A$ 的香农熵（Shannon Entropy）反映了系统内部的随机度（randomness），其定义为系统处于各状态概率与概率对数乘积的负总和： $$H(A) = -\sum P(A_i) \log P(A_i)$$ 为了便于直观理解，假设系统以均等概率处于 $N$ 个状态之中，那么系统的熵就简化为 $\log(N)$。若状态数 $N=1$（系统状态完全确定），熵为 0；若系统具有等概率的 2 个状态，以 2 为底计算对数，信息量即为 1 bit 的随机度。 ```mermaid flowchart LR accTitle: 经典信息熵与互信息文氏图示意 accDescr: 展示两个独立系统 A 与 B 的熵、互信息及条件熵在文氏图中的构成关系。 subgraph VennDiagram["经典系统文氏图 (独立抛硬币例子)"] A["系统 A 自身熵: 1 bit"] B["系统 B 自身熵: 1 bit"] I["互信息熵 I(A; B): 0 bit<br>(交集重叠为零)"] end A --- I B --- I ``` 基于香农熵，可以进一步引出联合熵（Joint Entropy）、条件熵（Conditional Entropy）以及互信息熵（Information Entropy / Mutual Information）。互信息衡量的是系统 $A$ 中包含多少关于系统 $B$ 的信息，其数值介于 0 到 1 之间：0 代表两系统完全独立无关联，1 则代表完全关联。 这些量可以用文氏图（Venn Diagram）直观呈现：左圆代表系统 $A$ 的总熵，右圆代表系统 $B$ 的总熵，两个圆重叠相交的部分就是互信息熵，而圆内排除重叠剩下的区域则是条件熵。以掷两枚互不相关的硬币为例：硬币 $A$ 具有 1 bit 随机性，硬币 $B$ 具有 1 bit 随机性，由于彼此独立，交集互信息为 0。整个系统共有 4 种等概率状态，系统的联合熵为 $\log_2(4) = 2$ bit，两枚硬币的信息量呈现出最简单的经典独立相加特征。 - 香农熵度量系统内在的随机性大小；状态等概率时熵为 $\log(N)$。 - 两个完全独立的双态系统各自拥有 1 bit 随机度，联合总熵为 2 bits。 - 互信息表示系统间信息重合度，经典图景下互信息受限于两系统的局部独立熵。 ### [047:00] 冯·诺依曼熵与负熵：纠缠态的“超级关联” 为了理解量子信息，Ron Garret 首先从经典硬币系统进行对比：如果两枚硬币互不干涉，一枚硬币完全不包含关于另一枚硬币的信息；但如果引入一个正常工作的传感器来检测硬币的正反面，系统就拥有 1 bit 的信息熵，因为传感器和硬币之间具有完美的、无方向性的双向关联（硬币的状态完全决定传感器的读数，反之亦然），整个系统仅有“正面+传感器报正面”或“反面+传感器报反面”这两种状态。随后，Garret 指出，若将这套数学推导从实数域扩展到复数域，就会得到著名的冯·诺依曼熵（von Neumann entropy，记为 $S$）。 在复数体系下，信息熵的取值不再被限制在 0 与 1 之间，甚至不再局限于正实数，而是可以出现负数。Garret 展示了纠缠粒子对的熵图，其中出现了奇怪的“-1 bit”负熵，而一个粒子对另一个粒子所包含的量子信息量则达到了 2 bit。这意味着纠缠粒子在数学上表现出一种“比完美关联还要好”的“超级关联”（super correlated），而整个纠缠系统的总熵之和却恰好为零，即系统内部完全不存在内在的随机性。 - 经典传感器与硬币系统中，信息熵为 1 bit，两者完全互补且相互包含完整信息。 - 引入复数后计算冯·诺依曼熵，系统的局部熵可以为负实数。 - 纠缠粒子对的相互信息量达到 2 bit，总系统熵相加为 0。 - “They have become super correlated and the total entropy of this system, the sum of all these numbers, is zero.” —— Ron Garret 强调纠缠粒子之间具有超越经典极限的超级关联性。 --- ### [049:04] 测量机制的本质：对被测粒子的偏迹（Partial Trace）与宏观表象 ```mermaid flowchart LR accTitle: 测量系统与部分迹运算流程 accDescr: 展示被测系统粒子与辅助粒子纠缠，再扩散至宏观仪器，并通过求偏迹忽略原粒子从而呈现经典关联的过程。 subgraph QuantumCore["量子微观层"] Q["被测系统 (粒子 Q)"] A["辅助粒子 (Ancilla A)"] end subgraph Macroscopic["宏观测量环境"] M["测量仪器 (10^23 个粒子)"] end Q <-->|"纠缠 (Entanglement)"| A A <-->|"纠缠扩散"| M Q -.->|"执行偏迹 (Trace Out 忽略 Q)"| Classic["呈现经典相关性 (像硬币与传感器一样确定)"] ``` 当测量发生时，微观粒子实际上是与一个由大量粒子构成的宏观系统发生了纠缠。Garret 用一个由三个相互纠缠的粒子组成的韦恩图来剖析这一机制：粒子 A 与 C 之间有 1 bit 熵，A 与 B 之间有 1 bit 熵，且中间伴随着复杂的负熵结构。若将粒子 C 设为被测目标，粒子 A 和 B 视作测量仪器，并暂时“忽略”被测粒子 C，在数学运算上这恰恰等价于量子力学中的“偏迹”（trace operator）操作。 奇妙的事情发生了：当忽略粒子 C 并擦去相关边界后，正 1 和负 1 相互抵消变为 0，剩下的测量仪器在信息论层面上完全等价于前述的“硬币与传感器”经典系统——两个展现出完美经典关联的表象粒子。Garret 提醒观众回忆讲座开始时大家一致确认屏幕上某物是绿色的实验：这种一致性并非源于外部存在一个客观反映出来的物理实体，而是因为我们在观测中忽略掉了被测物理实体本身。这一规律可以扩展至任意宏观系统，即粒子 Q 与一个辅助粒子（ancilla A）纠缠，A 再与包含 $10^{23}$ 个粒子的宏观探测器纠缠，其整体的信息论熵图与三粒子模型毫无二致。 - 宏观测量本质上是量子系统与环境/测量仪器发生的多粒子纠缠。 - 数学上的“求偏迹”（tracing out）对应了在认知上“忽略被测粒子”，此时抵消掉负熵，显现出经典的 1 bit 确定性关联。 - 无论宏观系统包含多少粒子（哪怕达到 $10^{23}$ 个数量级），其熵分布模型均可等效为三粒子纠缠图。 - “So, this is now the mathematical description of a quantum measurement.” —— Ron Garret 总结道，这就是纯量子力学视角下对“测量”的数学描述。 --- ### [052:04] 不可逆的假象与“零宇宙诠释”（Zero Universe Interpretation） 既然测量纯粹是由量子纠缠构成的，而基本量子物理规律都是严格幺正可逆的，那么经典测量在物理上理论上也必定是完全可逆的。Garret 解释道，我们在现实中之所以无法“撤销”一次测量，并非因为物理法则不可逆，而是因为要撤销它，就必须解开在宏观系统中已经以光速蔓延开来的庞大纠缠网络。若要抹去全场观众脑海中关于“看到绿色物体”的记忆，就必须把所有四散的光子和相互作用粒子全部抓回并重新干涉相消，这在工程实践上绝无可能，从而导致了宏观测量看似不可逆的单向幻觉。 从这一结论出发，Garret 引申出了哲学意义上的“零宇宙诠释”（Zero Universe Interpretation）。如果承认这套物理图像，就必须彻底放弃“存在一个独立的客观形而上学现实以保证不同时空观测一致性”的信念；恰恰相反，物理世界是“没有相关物的相关性”（correlations without correlata，引用 David Mermin 的名言）。我们根本不是由硬质原子构成的，而是由比特（量子信息）构成的，人类的思维好比运行在量子计算机上的模拟程序。正如爱因斯坦所感叹的“宇宙最不可理解之处在于它是可理解的”，量子力学以一种极其激进的代价解释了宇宙的可理解性：我们所感知的客观物理实在其实只是一种错觉。“鬼魅般的超距作用”与让我们觉得时空在时间流逝中保持一致的“时间上的鬼魅作用”没有任何区别，它们均由同一种物理机制——量子纠缠——所驱动。 - 测量的不可逆性纯粹是热力学与宏观复杂性带来的实践困难，微观底层是完全可逆的。 - 信息的扩散以光速向外成指数级扩张，使得宏观相干性撤销（抹除观测历史）在工程上不可能实现。 - 人类不是经典粒子实体，而是量子信息网络中的节点，是“没有相关物的相关性”。 - “Quantum mechanics actually predicts a comprehensible universe but at the cost of forcing you to believe that what you perceive as physical reality is not actually real it's actually an illusion.” —— Ron Garret 犀利地指出，量子力学确实解释了宇宙的可理解性，代价是必须承认客观物理现实只是一种幻觉。 --- ### [055:18] 问答环节：经典大脑与量子实相的鸿沟，以及多宇宙与零宇宙之辩 演讲结束后，Garret 引用了一句日本禅宗大师的禅语作为尾声并开放提问，其间他还开玩笑打趣道：“糟糕，物理学家们开始离席退场了。”现场观众随即抛出深度疑问：既然在三粒子模型中拿掉被测粒子能还原出经典传感器模型，那如果把第三个粒子保留在分析中，世界又该如何理解？Garret 回答，这所有模型都是数学工具，如果保留第三个粒子，你看到的就是未经遮蔽的底层客观现实——纯粹的量子世界。而人类之所以觉得量子力学极其难以理解，是因为我们的大脑在运行逻辑上是经典的图灵机，只能处理实数构成的经典比特，但底层宇宙却是由复数支撑的量子计算机，这种认知结构与底层逻辑的错配导致直觉上的裂痕永远无法弥合。 紧接着，另一位听众站起来为“多世界诠释”（Many-Worlds Interpretation）辩护，提出薛定谔方程是线性的，死猫与活猫随时间演化各自独立互不干扰，因此单宇宙诠释可能无法满足需求。Garret 立刻纠正对方：“不是单宇宙（One），是零宇宙（Zero）。这个区分极其重要。”Garret 阐明，数学清晰地证明了“单一经典宇宙”是绝对站不住脚的伪命题（那就是已经破产的哥本哈根诠释）；从数学相容性来看，“多宇宙”与“零宇宙”同样完全成立，选择哪一个更多是哲学品味问题。在多世界诠释中，分裂出的其他宇宙在概率和时空上将永远无法被我们访问；面对听众以“从太阳背面飞走、永远超出光锥的光子是否真实存在”作比，Garret 指出该类比存在漏洞：远去的光子理论上仍有可能被宇宙某处的镜子反射回来，但在完全正交退相干的多宇宙之间，这种相互作用的通道是彻底切断的。 | 诠释类型 | 宇宙数量状态 | 数学与物理上的有效性 | 核心评价与哲学代价 | |:--- |:--- |:--- |:--- | | **哥本哈根诠释** | 单一经典宇宙 (One Universe) | **不可行 (Untenable)** | 假定存在单一客观现实与波函数坍缩，会导致超光速通信佯谬。 | | **多世界诠释 (MWI)** | 无穷多分立宇宙 (Multiple Universes) | **可行 (Tenable)** | 承认线性叠加并存，但分裂出去的宇宙永远无法被验证或访问。 | | **量子信息论诠释** | 零宇宙 (Zero Universe) | **可行 (Tenable)** | 认为不存在实体宇宙，现实是纠缠关联构成的幻觉与模拟。 | - 人类思考依赖实数与经典状态机，而底层实在由复数和量子纠缠主导，这造成了永恒的直觉冲突。 - 哥本哈根式的单一经典物理世界在数学上已被证明是不可能的。 - 多宇宙诠释在数学上与零宇宙诠释一样站得住脚，但二者在形而上学假设的简洁度上存在分野。 - “Multiple universes are just as tenable, according the math, as zero universes. The only thing that's not tenable is one classical universe...” —— Ron Garret 明确强调，多宇宙和零宇宙在数学上都成立，唯独单一经典宇宙绝对不成立。 ### [59:37](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3577s) 多世界诠释与信息论视角的抉择 在探讨量子力学的多世界诠释时，Ron Garret 指出数学计算明确无误地表明，一旦另一个宇宙分裂出去，它就再也不可能回来了，没有任何物理手段能将其复原。台下一位听众随即插话提出异议，认为在经历漫长的特征回归时间后它们仍会交汇，Garret 幽默地回应道，在任何人类具有实际现实意义的时间跨度内这都不会发生。他分析称，如果是从宇宙学的宏观维度来思考，多世界诠释确实是一种站得住脚的理论假说；但如果人们需要的是一个能够解释日常生活体验、理解自我存在本质的故事，他个人更倾向于信息论的观点。 Garret 坦言自己更愿意相信当下所处的宇宙本质上是一场极高品质的模拟，不过他也承认这种世界观的选择纯属“个人品味”。在这个框架下，人们无需纠结于无穷无尽分裂开去的平行实体，而是可以将注意力集中在信息本身的处理与呈现机制上。 > “If you want a story that you can help you to understand how the universe works in terms of your everyday life and what your fundamental nature is, I personally find that I gravitate more towards the information theoretic point of view and believing that I--the universe that I exist in is a very good high-quality simulation.” —— Ron Garret --- ### [01:00:39](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3639s) 多宇宙中的质能守恒与认知边界 现场观众抛出了一个尖锐的物理问题：多重宇宙分裂时是否遵循质能守恒定律？Garret 非常坦率地承认这超出了自己的专业领域，必须将问题留给专业物理学家。随后台下有观众补充道，自己曾向多世界诠释的支持者请教过同样的问题，得到的答案是质量能量并没有凭空翻倍，而是在分裂时被实质性地一分为二了。 听到这个解释后，Garret 现场推演道，这或许意味着在数学层面上，即便经典宇宙中的总质量被均匀减半，所有物理定律和相对观测量依旧能保持完全一致的运行结果。不过台下随即有听众反驳指出，如果宇宙整体真的每次分裂都在稀释质量，为什么身处当前宇宙中的我们从未观测到质量有逐渐流失衰减的迹象？面对观众之间层层深入的辩论，Garret 笑着举手认输，坦承探讨已经彻底超越了自己的知识极限，展现出务实而坦诚的科学态度。 > “So in that, we are now beyond the limits of my knowledge of this stuff.” —— Ron Garret - **多世界分裂的质能假说**：有理论支持者认为平行宇宙并未凭空增生能量，而是将总体质量平分至各个分支中。 - **现实观测的悖论感**：身处单一分支中的观测者并未察觉到质量或能量浓度的渐进式削弱。 - **讲者的求实态度**：Garret 并不强行圆场，而是公开承认在深入的宇宙学守恒定律面前自己需要向专业学者请教。 --- ### [01:02:04](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3724s) 推荐阅读资源与量子局域性之辩 在演讲接近尾声的问答环节中，针对那些被该理论激发起强烈好奇心、渴望进一步钻研的观众，Garret 给出了具体的学习途径。他提到自己在互联网上公开发表了相关的研究论文，同时极力推崇著名物理学家 N. David Mermin 的著作《Boojums All the Way Through》。Garret 解释说，虽然 Mermin 在书中并未直接阐述这套完全相同的观点，但他以极其通俗易懂的方式讲解了贝尔不等式（Bell's inequality），这对于理解量子本质量度至关重要。此外，Garret 还表示欢迎大家发邮件与他联系，他非常乐意引荐听众去结识加州理工学院（Caltech）那些真正奠定本次演讲理论基石的一线研究人员。 最后，一位听众提问道，这种诠释是否构成了一个纯粹的局域理论（所有相互作用均以光速在局域传播）？Garret 解答称，它归根结底仍然是标准的量子力学，而量子力学是否具有纯粹局域性在物理学界本身就是一个充满争议的论题。这完全取决于人们如何界定“纯粹局域”：在经典物理的语境下它显然不是局域的，但在量子力学的语境下它又是局域的。Garret 总结道，自己今天介绍的视角并没有在这个悬而未决的问题上提供额外的定论，并随即感谢全场观众，圆满结束了整场演讲。 > “It's quantum mechanics. And whether quantum mechanics is purely local is the subject of debate.” —— Ron Garret - **推荐论文与著作**：Ron Garret 本人撰写的相关理论论文，以及 David Mermin 浅显阐释贝尔不等式的名著《Boojums All the Way Through》。 - **理论来源**：加州理工学院（Caltech）研究学者的前沿量子信息理论成果。 - **局域性（Locality）辨析**：经典观念下量子纠缠看似违背局域实在性，但在量子信息论或严格量子表述中，它并不违反相对论的光速因果传递限制。 ## Notable quotes > [34:55](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2095s) According to the math, entanglement and measurement are the exact same phenomenon, the math is exactly the same, and that is why entanglement destroys interference because entanglement is measurement. — Ron Garret > [55:18](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3318s) Multiple universes are just as tenable, according the math, as zero universes. The only thing that's not tenable is one classical universe... — Ron Garret > [52:04](https://www.youtube.com/watch?v=dEaecUuEqfc&t=3124s) Quantum mechanics actually predicts a comprehensible universe but at the cost of forcing you to believe that what you perceive as physical reality is not actually real it's actually an illusion. — Ron Garret > [42:28](https://www.youtube.com/watch?v=dEaecUuEqfc&t=2548s) So Copenhagen is the most popular but as we've seen it, it's scientifically untenable. There just is no collapse. — Ron Garret > [29:43](https://www.youtube.com/watch?v=dEaecUuEqfc&t=1783s) The dynamics are continuous, time-symmetric, fully deterministic and hence, reversible, and so there's no place where you can find anything that resembles collapse in this math. — Ron Garret > [11:52](https://www.youtube.com/watch?v=dEaecUuEqfc&t=712s) And more than that, all the math is actually time reversible so we can make a--hypothesize that this collapse happens, but this is fundamentally at odds with the mathematics of what quantum mechanics--of how quantum mechanic says that our universe works. — Ron Garret > [00:00](https://www.youtube.com/watch?v=dEaecUuEqfc&t=0s) 但我认为，量子力学在根本上并不比相对论更令人费解，而如今大多数技术人员理解相对论似乎毫无困难。 — Ron Garret > [09:03](https://www.youtube.com/watch?v=dEaecUuEqfc&t=543s) 因此，必定有某种东西同时存在于两个狭缝中，才能产生干涉。 — Ron Garret ## Mentioned Ron Garret, Arthur Gleckler, Google, Google AdWords, Google Translation Console, NASA Jet Propulsion Lab, Caltech, Richard Feynman, Albert Einstein, David Mermin, John Cramer, Scientific American, Wired, Beta Barium Borate, Schrödinger wave equation, Schrödinger's cat, Boojums All the Way Through, Bell's inequality, Mach-Zehnder 干涉仪, Stern-Gerlach 实验 ## Video description Google Tech Talk January 6, 2011 Presented by Ron Garret. ABSTRACT Richard Feynman once famously quipped that no one understands quantum mechanics, and popular accounts continue to promulgate the view that QM is an intractable mystery (probably because that helps to sell books). QM is certainly unintuitive, but the idea that no one understands it is far from the truth. In fact, QM is no more difficult to understand than relativity. The problem is that the vast majority of popular accounts of QM are simply flat-out wrong. They are based on the so-called Copenhagen interpretation of QM, which has been thoroughly discredited for decades. It turns out that if Copenhagen were true then it would be possible to communicate faster than light, and hence send signals backwards in time. This talk describes an alternative interpretation based on quantum information theory (QIT) which is consistent with current scientific knowledge. It turns out that there is a simple intuition that makes almost all quantum mysteries simply evaporate, and replaces them with an easily understood (albeit strange) insight: measurement and entanglement are the same physical phenomenon, and you don't really exist. Slides are available here: https://docs.google.com/a/google.com/present/edit?id=0AelF4upZ7VjZZGM1eGttOGJfNDNkenFtNnFkaw&hl=en Link to the paper: http://www.flownet.com/ron/QM.pdf About the speaker: Dr. Ron Garret was an AI and robotics researcher at the NASA Jet Propulsion Lab for fifteen years before taking a year off to work at Google in June of 2000. He was the lead engineer on the first release of AdWords, and the original author of the Google Translation Console. Since leaving Google he has started a new career as an entrepreneur, angel investor and filmmaker. He has co-founded three startups, invested in a dozen others, and made a feature-length documentary about homelessness. [Source](https://www.youtube.com/watch?v=dEaecUuEqfc)

[34:55] Ron Garret: According to the math, entanglement and measurement are the exact same phenomenon, the math is exactly the same, and that is why entanglement destroys interference because entanglement is measurement. [55:18] Ron Garret: Multiple universes are just as tenable, according the math, as zero universes. The only thing that's not tenable is one classical universe... [52:04] Ron Garret: Quantum mechanics actually predicts a comprehensible universe but at the cost of forcing you to believe that what you perceive as physical reality is not actually real it's actually an illusion. [42:28] Ron Garret: So Copenhagen is the most popular but as we've seen it, it's scientifically untenable. There just is no collapse. [29:43] Ron Garret: The dynamics are continuous, time-symmetric, fully deterministic and hence, reversible, and so there's no place where you can find anything that resembles collapse in this math. [11:52] Ron Garret: And more than that, all the math is actually time reversible so we can make a--hypothesize that this collapse happens, but this is fundamentally at odds with the mathematics of what quantum mechanics--of how quantum mechanic says that our universe works. [0:00] Ron Garret: 但我认为，量子力学在根本上并不比相对论更令人费解，而如今大多数技术人员理解相对论似乎毫无困难。 [9:03] Ron Garret: 因此，必定有某种东西同时存在于两个狭缝中，才能产生干涉。

[34:55] Ron Garret: According to the math, entanglement and measurement are the exact same phenomenon, the math is exactly the same, and that is why entanglement destroys interference because entanglement is measurement. [55:31] Ron Garret: Multiple universes are just as tenable, according the math, as zero universes. The only thing that's not tenable is one classical universe, that's--that's the only thing that the math tells you unambiguously does not exist. [52:04] Ron Garret: spooky action at a distance' is no more and no less mysterious than the 'spooky action across time' that lets us perceive the universe as consistent from one moment to the next. [52:04] Ron Garret: We are not made of atoms we are actually made of bits.

[0:00] >> [0:22] GLECKLER: Hi everyone. I'm Arthur Gleckler and I'm happy to introduce Dr. Ron Garret [0:27] here, who's going to be speaking about quantum mechanics today. He's a former Googler from [0:32] the very early days of the company, around 2000. He was the lead engineer on the first [0:37] release of AdWords and the original author of the Google translation console. He also [0:43] wrote the first billing system that Google used. Also, for many years, he worked at the [0:48] NASA Jet Propulsion Lab in Pasadena, specializing in AI and robotics. I'm hoping to convince [0:53] him to come back and talk about his experiences, debugging spacecraft 250 million miles from [0:59] the earth. Here's Ron. >> GARRET: Thanks. So I'm told that my abstract [1:09] caused a little bit of a kerfuffle so let me start out with a couple of disclaimers [1:14] upfront to kind of manage expectations. The title of the talk was intended to be tongue-in-cheek. [1:20] There is no actual conspiracy, at least, as far as I know but there is a fairly big disconnect [1:25] between what you read about quantum mechanics in the popular press and what the actual underlying [1:30] truth is, and that's what this talk is about. I am not a physicist. Do we have any actual [1:35] physicists in the crowd? Oh, boy, okay. You can make sure you keep me honest. I'm a software [1:44] engineer. I came upon this about actually 20 years ago when I read an article in Scientific [1:50] American and I thought, "This can't possibly be right." And it took me 10 years to finally [1:55] find a physicist at Caltech who could explain to me why in fact it wasn't right and at that [2:01] point, everything just kind of clicked and quantum mechanics made a lot more sense to [2:04] me than it did before. And that's what this talk is about. It's about--it's about a different [2:08] way to think about QM that hasn't gotten very much attention and dispels this idea that [2:17] quantum mechanics is sort of intractably weird. Somebody has said to me once that quantum [2:23] mechanics obeys the law of conservation of weirdness. And to a certain extent, that is [2:28] true. There is a certain amount of--quantum mechanics extracts a toll on your intuition [2:33] and some of that will never go away. But I don't think that quantum mechanics needs to [2:38] be fundamentally any more incomprehensible than, say, relativity which most technical [2:44] people seem to have no trouble wrapping their brains around nowadays. So with that sort [2:50] of expectation management out of the way, I want to start out by inviting you to think [2:54] about the question, "What does it mean to 'measure' something?" So, imagine that we're [3:00] sitting here doing some experiment. We have some system--let me grab a pointer--that we [3:08] want to measure some property of it so we have some, you know, sensor here like a camera, [3:12] and it gathers some data and we feed it to a computer, and that data shall pop up from [3:16] the screen, and we look at that with our eyes, and we form some mental image in our head, [3:21] and how do we know that this mental image that we form in our head actually corresponds [3:25] to underlying physical reality? Well, one indication that we have of this is that we [3:32] can do experiments more than once and observe that we get consistent results. So, for example, [3:37] what color is this? >> Green. [3:39] >> GARRET: Green, yes. So we can observe through our common everyday experience that the results [3:48] of measurements are consistent across space and time. And, I mean, this is really a very [3:54] reliable aspect of our universe, but it's actually a very deep mystery why this is so. [4:01] And Einstein famously said that, "The most incomprehensible thing about the universe [4:05] is that it is comprehensible." We can actually do experiments and get results that are consistent [4:10] across space and time and we don't really know why that, any inherent reason, why that [4:16] should be the case. Now, there is one very plausible sounding explanation of why this [4:22] is the case, and that is that the results of these measurements are actually an accurate [4:26] reflection of some underlying metaphysical reality. That reality, that there really is [4:31] a universe out there and when we measure it, we're getting back actual information about [4:37] that underlying physical reality. And that is the reason why these measurements are consistent [4:41] because reality sees to it that that's the case. Well, it turns out that we can demonstrate [4:48] that that's not true. I'm about to lead you down a rabbit hole but my purpose in leading [4:55] you down this rabbit hole is to do it in such a way that you can find your way back out [4:59] again. So I'm going to do it very carefully, step by step, and tell you in advance where [5:03] we're going. I'm going to start out by reviewing the usual QM story. What you will read if [5:08] you go to a popular account of quantum mechanics that you read, you know, pick up at Amazon [5:14] or a bookstore or read about it in Wired or whatever. I'll then show you how that story [5:23] can't possibly be true, because if that story were true, it would lead to a violation of [5:27] relativity, in particular, it would lead to faster-than-light communication. And it doesn't [5:31] do this in the usual way that most people think that it leads to faster-than-light communication, [5:35] it does it in a more subtle way that really hasn't gotten a lot of attention. So you physicists [5:39] in the room, bear with me. Then, I'm going to walk you through some of the actual underlying [5:47] mathematics of quantum mechanics, in a way that is accessible to anyone who knows--can [5:53] do basic algebra and knows what algorithm is. And finally, tell a new story based on [6:02] our understanding of what the underlying mathematics actually says about what's really going on [6:06] and hopefully we'll achieve enlightenment at the end of that. So, is there anybody here [6:13] who has not heard of the two-slit experiment? All right, good. I will just blast through [6:18] this very quickly. So, we have a--this is--you have a laser that shines through two-slits, [6:25] and you get an interference pattern that shows that light is a wave and can interfere with [6:32] itself like any other wave. And there are two strange things about this. If you look [6:40] at the results of this experiment with very low intensity light, what you find is, and [6:46] this isn't showing up very well, but this top image here shows just some dots scattered [6:53] randomly. And then dots get denser and denser and denser until down here at the bottom you [6:57] have a dense enough pattern of dots that you can start to see this interference pattern [7:01] start to emerge. And this is an actual photograph of laser light going through a single slit [7:08] and going through two slits. And you can see this interference pattern here, this is actual, [7:13] an actual photograph of the same experiment, this particular one happened to be done with [7:17] electrons but the underlying physics is the same. And the--the thing to notice here is [7:24] that the total amount of light that you get in this pattern when there are two slits is [7:29] brighter than the overall amount of light that you get with one slit which is what you [7:34] would expect but that there are some places here where you have these dark bands that [7:40] were bright up here when you only had one slit. And this is the interesting part that [7:44] you want to kind of focus your attention on because what this means is that there's a [7:49] spot here where light was shining and then you open up an extra path for light to get [7:54] to the screen and that spot goes dark. And that is the manifestation of interference. [8:01] But the strange thing about it is that this is not a continuous phenomenon, it's an accumulation [8:06] of all these particles. Now, I can actually--I used to think that this was a fairly subtle [8:13] experiment that you need a specialized equipment to conduct this experiment. It turns out it's [8:18] not true, you can actually do this experiment yourself. These are some pencil leads that [8:23] I've taped together with scotch tape and this is an ordinary laser pointer. And if I pass [8:29] these, and there's just some very narrow gaps between these leads, so you can actually see [8:32] this happen if I pass the leads in front of this pointer, you can see the light start [8:38] to spread out. And if you're close enough, you can actually see the interference bands. [8:44] I don't think you can see it in the back. But if you're interested, after the talk, [8:48] come up, I'll give you a closer look at it. You can actually see the interference pattern. [8:51] The point here is that this is not a subtle phenomenon and it's not something that you [8:56] need expensive equipment to reproduce. This is an everyday experience for modern humans, [9:03] at least. Okay, so this is not yet intractably weird, because there are all kinds of explanations [9:11] that we can postulate about how this might be happening. So, for example, photons and [9:16] electrons might be real particles that have real locations and velocities like our intuitions [9:20] about particles that might be pushed around by some kind of underlying wave. And--oh, [9:26] I forgot to mention--whoops--the location where these particles accumulate is random, [9:33] there's no known way to predict other than statistically where these particles are going [9:40] to end up on the screen. So, the randomness might just be due to some underlying real [9:47] physical property that we just don't know how to measure. But it turns out we can eliminate [9:52] this possibility as well. And the way we do that is by asking--by trying to track the [9:57] path of a particle and ask with--on its way to the screen, on its way to producing this [10:03] interference pattern, which of these two slits did it go through? And we could do that. We [10:07] can add detectors to the slits and we can measure which of the two slits a particle [10:12] went through. But it turns out that when we do that the interference pattern goes away [10:16] and the phenomenon that we were trying to get a better grip on has changed. And it turns [10:24] out that this is an inherent feature of quantum mechanics, that any modification that we make [10:29] to this experiment that allows us to determine, even in principle, which of these slits this [10:35] particle went through destroys the interference. This is the famous wave particle duality, [10:45] any modification that allows us to determine even in principle--yeah? [10:47] >> You ask people in the VC to mute their mics so... [10:54] >> GARRET: So, I've been asked to ask the people on the VC to mute their mics, did I [10:59] get that right? Okay. Okay, anyway, so the conclusion from this observation is that something [11:08] has to be--something has to be at both slits in order to produce interference. And the [11:13] reason we know that is because we don't actually need both of these detectors, one of them [11:18] is enough, because if we have one detector and it fails to register that we know the [11:24] particle went through the other slit. Now, that particle going through the other slit, [11:29] it never interacted with anything, the particle never interacted with anything, but because [11:34] it allows us to know where the particle was even though we didn't actually measure it, [11:38] that's enough to destroy the interference and so this particle that's over here must [11:43] somehow have known that we were looking over here even though the particle itself wasn't [11:46] there. So, something must have been there to be able to tell that we had a detector [11:52] here, but we don't know what that is. Now, it turns out, this is again, this is a universal [11:59] property of quantum mechanics. It holds for any kind of particle--in practice, that means [12:04] photons and electrons because that's all there is in this universe unless you start getting [12:09] into nuclear physics. And any kind of measurement, and any kind two-slit experiment, any experiment [12:14] where you provide two different paths for the particle to potentially go down and bring [12:18] it back together without knowing which way it actually went will produce interference [12:23] and any modification that you make that lets you figure you out where it went will destroy [12:26] that interference. Now, this is still not intractably weird because we can still tell [12:32] a reasonable story about why this might happen. So, maybe measurement does something to this [12:37] system. These are after all very small particles and very delicate systems and so maybe it's [12:41] just physically impossible to make a measurement without disturbing the system in a way that [12:45] is the cause of the destruction of this interference. Maybe the wave function collapses and becomes [12:51] a particle somehow, this is the famous Copenhagen interpretation of quantum mechanics. But it [12:58] turns out that we can rule out that possibility as well. And the way we rule out that possibility [13:04] is by asking, "How and when does this collapse, this purported collapse, happen?" Collapse [13:11] has a number of features that ought to make us very suspicious of it just at priority [13:17] without even doing any experiments. It's a discontinuous and nonreversible phenomenon [13:23] that once you know that a particle has gone through one slit or the other, you can't go [13:27] roll back time and undo that. And if you look at the mathematics of quantum mechanics, which [13:33] we'll get to later, there's nothing in the math that's discontinuous. And more than that, [13:39] all the math is actually time reversible so we can make a--hypothesize that this collapse [13:46] happens, but this is fundamentally at odds with the mathematics of what quantum mechanics--of [13:52] how quantum mechanic says that our universe works. So we can actually do better than that. [13:56] We can actually do an experiment to show that collapse, if it happens, is a much subtler [14:04] phenomenon than it would've first appear and this is the famous--this is the quantum mystery [14:11] number two, the famous quantum eraser. Now, I--this is a two-slit experiment that I have [14:15] now reduced to something more abstract. So we have some particle source, this can be [14:21] photons or electrons. We have some abstract way of splitting up particles so that it has [14:27] two different paths to go down and some abstract way of recombining that particle so that both [14:35] of those paths end up in the same place so that we get interference. And here notionally, [14:38] we have one detector at one of these dark fringes and another one at a bright fringe [14:45] so that if we introduce some kind of an abstract measurement on one of these branches then [14:51] the interference pattern fusses out, that we now have the path, the amount of light, [14:58] in each detector. So now we don't have fringes anymore, we have the spread-out pattern that [15:02] we saw and the single slit version of the experiment. Like I said, there are lots of [15:09] different ways that you can do this--actually, let me go on to the next one. So it turns [15:14] out that you can erase this, that there are physical ways that if this measurement, certain [15:20] kinds of proto measurements, that you can do here, you can then go back and erase after [15:25] the fact and restore the interference. And here's a concrete example of that. If we depolarize [15:32] light and--I'm actually going to show you this in just a second, so bear with me if [15:36] you don't understand what I'm about to say, you use polarized light and you do the measurement [15:40] by rotating that light 90 degrees and then erase it by filtering it 45 degrees, that [15:46] is an actual concrete example of a quantum eraser. And I can't show you the interference [15:51] part of it but I can show you the erasure part. So what I have here is some Polaroid [15:58] film, this is the same stuff that you find in polarized sunglasses. And, I first want [16:03] to convince you, has anyone not played with this stuff before? Okay, so again, real quick. [16:10] If the--if the axis of the film are aligned then you can see through it. Can everybody [16:16] see through this? And if I rotate it at 90 degrees then you can't see through it anymore [16:22] and that effect is independent of the absolute orientation of the film so the light that's [16:27] going through to your eyes starts at unpolarized over here, it gets--passes through this film [16:33] and becomes polarized, let's say in this direction, and I can demonstrate then that it has become [16:39] polarized in that direction by filtering it out using a filter at 90 degrees. And there's [16:45] also this cool adjunct to the experiment that you can do by adding a filter at 45 degrees. [16:51] If you put it in front or behind, nothing happens which is pretty much what you--what [16:54] you'd expect. But if you slide this in between, then suddenly you can see through it again. [17:01] Pretty cool, huh? And the reason for that is because if you start out with polarized [17:09] light and you filter it at 45 degrees then some of it gets through and it's now polarized [17:13] in this direction. And now I can do the same operation again, which is now the relative [17:18] orientation of these two are 45 degrees so some of it gets through again. But that's [17:23] not what I want to show you, that's not the cool part. Cool part is this stuff. This is [17:32] what they didn't show you, what they didn't show you in high school. This film is actually [17:36] a polarization rotator. If I'd stick this in here, I can actually take this light that's [17:45] polarizing this direction, I can rotate it to 90 degrees that it's polarizing the same [17:49] direction as this film. And the thing to notice here is that the apparent brightness here [17:56] in the center is the same as it is up here. There's before, if we did the high school [18:01] version of the experiment--whoops--you've gotten quite a bit of loss. [18:18] So, I really can take--I can take light and I can polarize it and I can take that polarized [18:22] light and I can rotate it by 90 degrees and so I can create two different paths so I can [18:30] tell which way the light went through. I can tell whether the light is going through here [18:33] or whether the light is going through here. Actually, let me back up a step. My claim [18:38] is, without this filter, it's a little hard. My claim is that the light that's coming out [18:43] of here is different than the light that's coming out of here, so I can tell which way [18:46] it went. And the way that I can demonstrate that to you is with this measurement apparatus [18:52] that lets me filter out this light and tell which way it went. So this is a measurement. [18:58] This should collapse the wave function according to the Copenhagen interpretation. But I can [19:04] undo this, and the way I undo it is by filtering at 45 degrees. And now, I have to ask you [19:12] for a little bit of suspension of disbelief because this is not high precision optical [19:17] equipment and my angles aren't aligned just right. And if you look very closely, you will [19:21] actually be able to tell the difference between these two paths, but the difference is now [19:24] much less than it was before. See that? Oh, I'm sorry. I didn't realize there are people [19:36] over there. Okay, I'll just show you all this at close range afterwards. So there's a measurement. [19:43] There's an erasure of that measurement. The light is going this way so the--in time, the [19:47] erasure has to happen after the measurement. And if I actually had a laser to shine through [19:53] this, I can demonstrate to you that the interference would go away and would come back. So again, [20:00] these are not subtle effects and they're not effects that you necessarily need high precision [20:05] equipment to reproduce, it's an everyday experiment. This is $30 worth of polarizing film. So this [20:14] leaves us with the philosophical conundrum that is embodied by Schrodinger's cat. If [20:21] there's no collapse, then if we set up a radioactive source that triggers some kind of a mechanism [20:28] that will break a bottle of poison that will kill a cat that's in a sealed box, can this--what [20:34] happens? Quantum mechanics says that this cat isn't a quantum superposition of being [20:38] alive and dead which is intuitively absurd but as far as we can tell, that's really what [20:45] happens. So if that's not intractably weird enough for you, this is the third quantum [20:53] mystery entanglement which is usually described as sort of an ancillary phenomenon to all [21:00] these other mysteries. And, oh, yes. It's sort of--oh, by the way, has everybody seen [21:06] this picture? Has anybody not seen this picture before? Okay. This is what the production [21:12] of quantum entangled photons really looks like. You take a--this is not--this is not [21:17] an actual photograph, this is a drawing. But this is an actual photograph of the output [21:20] of one of these gadgets. There's an ultraviolet laser that shines through a crystal of some [21:25] material called beta barium borate, details don't matter, and this crystal has this interesting [21:31] property that it will absorb photons of ultraviolet light and reemit them in--and that it'll kick [21:36] an electron up to an excited state, and then that electron will drop back down to its ground [21:41] state and it will do it in two steps. And so it will kick up in one step, down in two, [21:45] and in the process of coming back down, it will emit two photons instead of one so what [21:51] comes out of this system is visible light. And the photons always come out in pairs and [21:57] they come out in matched sets because of fundamental conservation laws. We have law--conservation [22:03] of energy and momentum and so--and electron--a photon that, say, comes out over here is a [22:11] red, photon will be matched by one that comes out over here as a blue photon, and the same [22:17] thing over here. And in the middle, you get this band where you get photons that come [22:22] out at the same wavelength and it just matched in position so a photon over here will be [22:26] matched by one over here. And they'll also be matched in polarization as it turns out. [22:33] So this is the way it's depicted conceptually. You have these ultraviolet lasers. It's called [22:39] a down convert--this crystal is called a down converter, and you send these photons off [22:45] to opposite sides of the universe and what--and then you measure some property out of them. [22:50] Let's say, we split them according to polarization or position them in, it doesn't matter, any [22:55] quantum state variables, as long as you can filter them that way and what you find is [22:58] that they're perfectly anti-correlated because of the conservations laws. So if you get a [23:02] photon up here, on the right side of the experiment at the upper detector, that will always be [23:07] matched by a photon over here on the left side of the experiment at the down detector. [23:13] An unfortunate artifact of the English language that words "left" and "lower" both start with [23:19] a letter L so I'm going to switch back and forth between them. This is what the--what [23:27] Einstein famously called, "Spooky action at a distance." If you take this phenomenon, [23:32] this isn't controversial, this is an experimental--an undeniable experimental result, this really [23:38] does happen, combine that with a fact if there is no collapse with the wave function and [23:43] the inescapable conclusion seems to be that as it was put in Wired as recently as last [23:50] June, that when an aspect of one photon's quantum state is measured, the other photon [23:55] changes in response even when the two photons are separated by large distances. And this [24:01] would seem to be impossible because it would seem to violate relativity because it's an [24:06] instantaneous effect and we know that we can't communicate information faster than light, [24:10] because if we could do that then we could communicate information back within time and [24:14] that would cause all kinds of problems with causality and just be a horrible mess. So [24:21] these instantaneous effects are supposed to be impossible but there is one thing that [24:25] comes to save us and that is this quantum randomness. We don't actually have any control [24:30] over whether the photon on one side ends up at the upper detector or the lower detector [24:35] and so we can't actually send information up here to there, we know that if we see the [24:40] photon up on the upper detector over here, then our counterpart across the universe must [24:45] have seen it at the lower detector over there but we haven't transmitted any information [24:50] from A to B. And you can actually prove this mathematically that it's impossible to transmit [24:57] information using this phenomenon. But it turns out that the proof of the impossibility [25:04] has a loophole. So that is the end of step one. I'm now going to on the step two and [25:14] show why the story that I've just told you can't possibly be true. So let's summarize [25:20] and take stock. A split/combine experiment produces interference. Any which-way measurement [25:25] destroys that interference, there's some which-way that the proto measurements that we can go [25:30] back and erase after the fact and restore the interference and measurements on entangled [25:35] particles are perfectly anti-correlated. So the quantum conspiracy is that all of these [25:43] things cannot possibly be true and here's why. So this is a thought experiment. This [25:50] experiment has not actually been done that, again, with tongue slightly in cheek, I've [25:55] done the Einstein-Podolsky-Rosen-Garret paradox, and it's two-slit experiments that are fed [26:04] by quantum entangled photons produced by one of these down converter setups in the middle, [26:11] and I want you to consider the question of if we measure on the left, do we destroy the [26:15] interference on the right? So, if the answer is yes, then we have faster-than-light communication [26:23] because this interference is a macroscopic effect. It's really easy to see if you have [26:28] interference or not. You just look at it with your eyes. You don't need any kind of delicate [26:33] detectors or anything so you just measure over here and take measurement away, measure, [26:40] take the measurement away, and over there on the other side of the universe, this interference [26:43] pattern will come and go and you can send Morse code instantaneously. That's obviously [26:47] impossible, so the answer must be no. But if the answer is no, then we know the position [26:52] of one particle but we have interference regardless and that contradicts the fundamental principle [26:59] of quantum mechanics, which is that we can't know the position of the particle and still [27:04] have it interfere. Now, this is not yet an iron-clad argument. There is one other possibility [27:13] that I have not mentioned here. Can anybody think of what it is? Any of the physicists [27:20] in the crowd? Oh, good. So, this one last possibility, and that is that if there was [27:24] no interference to begin with. It might be that entanglement sort of counts as one of [27:29] these subtle proto-measurements that destroys the interference so we didn't have any interference [27:34] to begin with. But it turns out that doesn't get us out of this faster-than-light conundrum [27:38] because, fine, if that's the case, then we can still produce faster-than-light communications [27:43] by putting in a quantum eraser and destroy the entanglement. Entanglement is a very--is [27:47] a very delicate property. Physicists work very hard to produce it and maintain it. It's [27:52] very easy to destroy. So, just destroy the entanglement and produce interference where [27:56] there was none before and, again, we have a faster-than-light signal-ly mechanism. Now, [28:03] that is a very compelling argument that the story that I have told you, the usual quantum [28:08] story is wrong. That argument is, in fact, correct. The story that I have told up until [28:14] now is, in fact, wrong, and that's why. >> You said this experiment hasn't been done, [28:21] why not? >> GARRET: Because all physicists know what [28:24] the outcome will be. And I'm about--I'm about to tell you what the outcome will be. And [28:29] by the time I finish telling you, you will be convinced enough that the outcome is what [28:32] I tell you that it will be that you won't need--feel the need to do the experiment either. [28:38] I promise you--hmm? >> GLECKLER: Why don't you repeat the question. [28:40] >> GARRET: Oh, I'm sorry. The question was, why hasn't this experiment been done. Yeah? [28:44] >> So the entanglement is about polarization, in which way it goes through a splitter, is [28:55] that about exactly the same polarization, we know they're the same? [28:57] >> GARRET: That's right. So, I assuming here, like I said, there are lots of different ways [28:59] that you can do the split-combine experiments. You can use some thing called a Mach-Zehnder [29:03] interferometer. You can use something called a Stern-Gerlach device. You can, you know, [29:06] lots of different ways. When I talk about polarization, the way that the splitting is [29:09] done is with the device called the polarizing beam splitter, which is exactly like one of [29:14] these, except instead of just absorbing half the photons and letting half the--half of [29:18] them go through, it reflects them. So it look like a mirror, a half-silvered mirror, and [29:24] what comes out this direction is photons that are polarized one direction and what gets [29:30] reflected at the other direction are photons that are polarized in the opposite direction. [29:36] Okay, so we are now in the depths of the rabbit hole and now, it's time to find our way back [29:43] out. We're going to do some math. Don't panic, it will not be as bad as you think. This is [29:50] the mathematics of quantum mechanics right here. This is the famous Schrodinger wave [29:56] equation. It's--this is the free variable here is this thing called psi. Psi is the [30:03] quantum wave function and it obeys the dynamics of this partial differential equation, which [30:09] those of you who are proficient in partial differential equations, will recognize as [30:12] a wave equation like any other equation that describes waves, and that's why these particles [30:20] seem to propagate like wave because this is the map that describes how they propagate. [30:26] The point here is that these, the dynamics of this thing, are continuous and time-reversible. [30:33] All wave equations have continuous time-reversible dynamics. And the second part of quantum mechanics [30:40] is that you take this quantum wave function, which is a function of position and time and [30:46] is a complex number, you take the norm, the magnitude of that complex number and square [30:51] it, and that gives you the probability of measuring a particle at this position X at [30:57] a time T. That's really all you need to know about the mathematics of quantum mechanics. [31:03] There are some things to note about this. There is this distinction between the underlying [31:08] amplitudes, which are complex numbers, and the probabilities, which are of where we find [31:13] these particles, which is the only thing that we can measure which are real numbers. And [31:19] the reason that particles can interfere is because complex numbers with magnitudes greater [31:24] than zero can add to zero. You can have a complex number that points off in this direction, [31:28] another complex number that point off in that direction. They always have magnitudes greater [31:32] than zero but they can add and destructively interfere. The dynamics are continuous, time-symmetric, [31:38] fully deterministic and hence, reversible, and so there's no place where you--there's [31:43] no place you can find anything that resembles collapse in this math. And no randomness either, [31:49] by the way. Going from amplitudes to probabilities by taking this wave function and squaring [31:58] it has no physical justification or whatsoever. It's purely a hack. But it's a hack that works [32:04] really, really well. So here's what the actual math looks like for the two-slit experiment. [32:12] This is, and if you go to actual papers on quantum physics you won't find this in the [32:17] popular press, this is what you will find in physics journals. This is--or physics texts--this [32:25] is the state, the amplitude of the photon being at the upper detector. This is the amplitude [32:31] of photon being at the lower detector and we have to divide by the square root of two [32:35] in order to make the total probability come out to be one. So to figure out the probability, [32:44] we take this number, which is a complex number, and take the modules and square it. And when [32:49] we do that, it's almost exactly the same as just squaring A plus B in 8th grade algebra [32:54] class, you get A squared plus B squared plus AB plus BA. You have to take these complex [32:59] conjugates because they're complex numbers, and the square root of negative one pops in [33:02] there to do some weird things, those kind of details don't matter. The point is this [33:07] is a complex number, psi U is a complex number. Its magnitude is a real number and when you [33:13] square it it's a positive real number. So here we have a positive real number, here [33:17] we have another positive real number, the sum of those two has to be a positive real [33:22] number. But over here we have two different complex numbers and two different complex [33:27] numbers that were multiplied together so this sum can be negative. So this is--this is where [33:32] the interference comes from. This is the mathematical manifestation of interference in quantum mechanics. [33:39] That's what it looks like in terms of Greek symbols. So, what happens when we add detectors? [33:45] Well, when we add detectors, the amplitude starts to look like this. We have the amplitude [33:51] for the photon to be at the upper detector times the amplitude for the detector to be [33:56] in the state where it shows that the particle is at the upper detector and the same thing [34:01] at the lower detector. So this is just the mathematical description of that. And when [34:07] you--when you--when you take the amplitude to that and square it, here's what you get, [34:11] same thing as before, psi U squared plus psi L squared. And this, which looks an awful [34:17] lot like an interference term, right, which is weird because I just got though telling [34:24] you that if we have a detector that we know--tells us which way the particle went, that destroys [34:29] the interference. Well, there's this subtle difference here between what we have now-what [34:34] we have before, and that's this weird notation here, which is called the rock--bracket notation. [34:39] You don't need to concern yourself with it. Just take my word for it when I tell you that [34:43] this quantity here is the amplitude for the detector to spontaneously switch between indicating [34:51] that the particle is at the upper slit and the lower slit. In other words, it's a measure [34:55] of the reliability of the detector. That just comes out when you do the math. And if the [35:02] detector is working properly, that value--oops--this--this value is the amplitude for it to spontaneously [35:14] switch between UNL and spontaneously switch between L and U, those are both zero so this [35:19] term goes away. That's the math of how measurement destroys probability. And the interesting [35:27] thing about this is that measurement is a continuum. It's not a dichotomy. The math [35:32] tells us that we can measure just a little bit or we can measure mostly but not quite. [35:37] And we have vary--it's a varying levels of interference that we get depending on whether [35:45] the measurement that we're making is reliable or not. That's what the math says. So what [35:52] about entanglement? Well, this is, if you go to a physics paper that talks about entangled [35:58] particles, this is what you will see as the mathematical description of a pair of entangled [36:04] particles. What this means is that you have an amplitude for the particle on the left [36:09] to be in the up state and the particle on the right to be in the down state superimposed [36:15] with an amplitude for the particle on the left to be in the down state and the particle [36:18] on the right to be in the up state; again, divided by the square root of two. Now, this [36:24] looks a lot like the--or the unmeasured two-slit description. But there's some notational sleight [36:34] of hand going on here because this is shorthand for this and it's an unfamiliar notation. [36:42] This vertical bar, followed by the bracket, this is a term. So you got--this is a quantum [36:48] wave function here. This is another quantum wave function here. This is the wave function [36:51] for the upper particle. This is a wave function for the lower particle. Another way to write [36:59] that is--you don't have to use arrows, that's just a notational convenience, so I could [37:03] call this the left upper particle and the right downward particle, and the left downward [37:08] particle on the right upper particle. And this is just another way of writing this Psi, [37:13] this quantum wave function. So this and this are the same thing in different notations. [37:20] And this should now look familiar. This is exactly the same as--oops--as this, the two-slit [37:31] experiment with the detector, module of a few labels. And so, that is now the answer [37:39] to the first part of the EPRG Paradox. In fact, entanglement does count as a proto-measurement [37:46] that destroys interference. But it's actually much deeper that that. According to the math, [37:53] entanglement and measurement or the exact same phenomenon, the math is exactly the same, [37:59] and that is why entanglement destroys interference because entanglement is measurement. And I [38:05] have a lot more to say about that later in the talk. So okay, so there's no interference [38:12] but now what about this last--the idea of creating the interference using a quantum [38:17] eraser. So let's take another look at our--I'm running little short on time so I'm just going [38:23] to blast through this. This is what the state equation looks like for the quantum eraser [38:32] after the so-called measurement but before erasure. So you have an upper photon that's [38:36] horizontally polarized because we've--let's assume we start with a vertically polarized [38:44] light going in here and we measure by rotating 90 degrees. So we have now the upper photon [38:50] rotated from vertical to horizontal and the lower photon still vertical and this you will [38:57] now--you should recognize as a measured and therefore non-interfering state. And it turns [39:03] out that if you filter now at 45 degrees this is the state function, the quantum wave function, [39:10] that you end up with. You now have a photon that's either in the upper or lower slit and [39:16] that's either horizontally or vertically polarized, and this kind of makes sense because if you [39:21] think of these as vectors and you have a horizontal polarization plus a vertical polarization, [39:26] that's a 45-degree polarization, which is exactly what you would expect to see if we're [39:31] filtering it 45 degrees, right? But remember the square root of two term here that I told [39:38] you was there in order to make the total probability to come out to be one? Now, that's a two root [39:44] though, and if you run the math on this you find out that the total probability is not [39:49] one, it's one-half. So either we've made a mistake or half our photons have gone missing. [40:00] Well, in fact, half our photons have gone missing which is also shouldn't be too surprising [40:04] because we filtered--we put this 45-degree--we put this filter in place. This filter is filtering [40:11] out half the photons that go through it. If it--if they come in at 45 degrees then half [40:15] of them come out polarized this way and the other half get blocked. So it turns out that [40:23] the other half, the half that didn't get through, have a different wave function that has a [40:28] negative sign over here, which again, makes intuitive sense because the filter lets these--the [40:33] filter is at 45 degrees so it lets this axis through and this axis, which is the H minus [40:40] V axis it blocks. And these photons interfere with themselves and these photons also interfere [40:49] with themselves. So the photons that passed through the filter display interference fringes [40:56] and the photons that don't pass also display interference but it turns out that they're [40:59] anti-fringes. They're exactly like the bright spots in the interference fringes for the [41:06] photons that got filtered out, exactly lined up with the dark spots of the fringes for [41:11] the photons that were let through. And they sum together to produce what we perceived [41:16] when we look at it as non-interference. So this quantum eraser doesn't actually erase [41:21] anything and it doesn't produce interference, it just filters out interference that was [41:25] actually already there all along. And it turns out that we can actually do this in the EPR [41:31] experiment too. And the way that we--but in order to do it, we have to transmit classical [41:35] information from one side of the other in order to do the filtering. The way it works [41:39] is you make a record of all the photons that you collected over here and keep it in order [41:44] so you've got this record of first photon was at the upper detector, the second photon [41:48] was at the down detector, and so on and so forth, and over here you keep track of which [41:52] photons ended up where on your screen, and then you take this record and you transmit [41:57] it over here by some classical slower-than-light channel. And you look at all the up photons [42:02] and sure enough there's an interference pattern, and you look at all the down photons and sure [42:05] enough there's an interference pattern. But the only way to see that is to take classical [42:09] information and move it from here to here. And that is the last nail in the coffin. I [42:17] was very disappointed when I learned this 10 years ago because I was really counting [42:21] on winning a Nobel Prize and taking over the world but, oh, well, this is the next best [42:28] thing. So the take-home message up to this point is measurement and entanglement are [42:35] the same phenomenon, and what you will find in many, many accounts and even some professional [42:42] accounts, is that they're completely different. That measurement is this common everyday thing [42:48] that we can sort of intuitively grasp and entanglement is the quintessential quantum [42:54] mystery and in fact they are really the exact same thing. Now, having come to that realization [42:59] we can now tell a different story about quantum mechanics that to my software engineer's mind [43:06] is much more intuitively pleasing than any of the other competing alternatives. So Copenhagen [43:13] is the most popular but as we've seen it, it's scientifically untenable. There just [43:17] is no collapse. Their--the next most popular interpretation is the so-called "many worlds" [43:26] interpretation where it says that anytime that a particle can go multiple ways, the [43:29] entire universe splits and the math actually supports that, but I personally find that [43:37] that takes a heavier toll on my intuition than I'm really willing to concede. There's [43:43] another thing that nobody's ever heard of called the "transactional" interpretation [43:46] by fellow named Cramer at the University of Washington. Actually, if you're really interested [43:49] in this stuff, I encourage you to take a look at because it is kind of interesting. It postulates [43:54] that the backwards in time solution for Maxwell's equation are physically real and if you make [44:00] that assumption then you can explain a lot of stuff, but I don't have time to get into [44:05] that. What I want to talk about here is the quantum information theory which I have dubbed [44:09] the "zero-worlds" interpretation of quantum mechanics. It's an extension of classical [44:14] information theory with complex numbers and if you run through that math you get some [44:19] very interesting results. So here is a lightning introduction to classical information theory. [44:24] It's the study of this quantity called the Shannon entropy of a system A, which can be [44:30] in any one of a number of classical states, and it's defined as the sum of the probability [44:35] that the system is in sum state A times the log of that probability and then you take [44:40] a negative sign. And intuitively, it's a measure of the amount of randomness that's in the [44:44] system A. So just to simplify things for the purpose of this talk, if the system has an [44:51] equal probability of being in one of N states, then the entropy is just the log of N. So [44:57] when N is one and the system is definitely in one state then the entropy is zero. And [45:03] if it can be in one of two states with equal probability and we take this log base two, [45:08] we measure information content in bits, then it has one bit of randomness in it. You can [45:17] define all kinds of other derived quantities like the joint entropy of multiple systems [45:21] and the conditional entropy, and this quantity here which is called the information entropy [45:25] which is a measure of how much information a system A contains about a system B, and [45:31] the interesting thing to note about it is it's the sum of some of these other quantities [45:35] that had been defined up here. And the information entropy ranges between zero and one, where [45:44] zero means that this system has no--system A has no information about system B, they're [45:49] completely uncorrelated, and one means that they're perfectly correlated. So for example, [45:56] because they're sums we can describe these quantities as Venn diagrams. So this circle [46:02] here on the left is system A and this circle on the right is the system B, and the total [46:11] entropy is contained inside these circles, the total entropy for each system, and the [46:16] information entropy is here in the intersection, and that leaves the conditional entropy out [46:21] here because the information entropy is the system's individual entropy minus the conditional [46:31] entropy, just simple addition. This is the important part. If we flip two coins so that [46:39] they're completely independent of each other, this is what the numbers end up looking like. [46:43] The conditional entropy, the coin A has one bit of randomness and coin B has one bit of [46:50] randomness so the total entropy in the system is two bits of randomness. The system as a [46:54] whole of these two coins can be in one of four states, the log of four is two, and there's [47:00] no information that one coin contains about the other. By way of contrast, if we have [47:06] a coin with a sensor, just looking at that coin telling us whether it's landed heads [47:10] or tails then--and the sensor is working properly, then we have one bit of information entropy [47:16] because the sensor gives us perfect information about the coin and vice versa by the way. [47:23] The coin gives us perfect information about the sensor, there's no directionality here, [47:27] and the total entropy in the system is one bit so it's only going to be in one of two [47:31] states, heads and sensor says heads, or tails and sensor says tails. If we extend, do the [47:37] same math again except using complex numbers instead of real numbers then you end up with [47:45] something called the Von Neumann entropy which is called S and this hairy-looking equation [47:52] over here, which I don't have time to go into, but the intuition is kind of the same as it [47:56] was before when we talked about how interference was produced. Because we're now dealing with [48:01] complex numbers rather than real numbers, the information entropy is no longer restricted [48:07] to the range zero and one. And, in fact, entropies are no longer restricted to be positive real [48:13] numbers, they can be negative. And this turns out to be, if you do the math, the entropy [48:20] diagram for a pair of entangled particles. You get a negative bit of entropy over here. [48:29] And the information entropy, the amount of information that one particle quantum information [48:33] now, that one particle contains about the other is two bits. So you can think about [48:38] two entangled particles, the math is telling us that these particles are now, somehow, [48:44] better than perfectly correlated. They have become super correlated and the total entropy [48:51] of this system, the sum of all these numbers, is zero. There's no randomness. That's not [48:58] yet the cool part. What happens when we take a measurement? Well, when we take measurement, [49:04] we have a particle that becomes entangled with a macroscopic system of particles. So [49:09] what happens if we have three mutually entangled particles? You end up with a Venn diagram [49:14] that looks like this and if we assume a two-state system then the actual numbers come out looking [49:24] like this. You've got one bit of information entropy between A and C, one bit between A [49:30] and B, and you've got this negative, this weird negative entropies over here and it's [49:35] all kind of mind-boggling. But let's imagine that this particle down here is the one that [49:43] we're measuring and this is our--these two particles here are our measurement apparatus. [49:49] And let's look just at the measurement apparatus and ignore the fact that we're actually measuring [49:53] a particle here. So we're going to take this particle C, we're just going to throw it out [49:59] for a minute. It turns out that ignoring C is exactly what is represented by this trace [50:08] operator here that ends up showing up in the math. Look what happens. This one bit of information [50:20] entropy--we lose this boundary so this one, the negative one, cancel out and become a [50:25] zero, same thing over here, and what we have is if we ignore this is exactly the same system [50:34] from an information theoretical point of view as a coin with a sensor, we have two classical [50:39] particles that are perfectly correlated with each other in a classical sense. I should [50:47] remind you of the experiment that we did at the beginning of the talk where everybody [50:54] agreed that that's something was green. And we can get that from quantum mechanics, we [50:59] get these two systems that are in classical correlation. But we did that not by actual--not [51:04] by having an objective physical reality that we reflect but actually by ignoring the thing [51:08] that we're measuring, or that we think we're measuring. As it turns out that this extends [51:14] to any macroscopic ecosystem. If you add an arbitrary number of particles the entropy [51:18] diagram ends up looking exactly the same. So, this is now the mathematical description [51:23] of a quantum measurement. You have the system that you're measuring. It's particle Q. It [51:29] interacts and gets entangled with A particle, which is in the parlance of the theory called [51:35] an ancilla which is why they label it A, and that ancilla then gets entangled with a macroscopic [51:42] measurement apparatus in system of 10 to the 23 particles, and the entropy diagram ends [51:46] up looking exactly the same where this entire system has the same quantum information, theoretical [51:54] information content, as the third particle in a three-particle entangled system. So, [52:04] that is now a description of what measurement looks like purely in terms of quantum mechanics. [52:07] And the interesting thing about that is it describes all of the microscopic phenomenon [52:12] that we see that we naively observe about classical measurements but it's purely in [52:17] terms of quantum mechanics, which means that it's reversible. So, their--so, somehow, we [52:24] ought to be able to undo an actual physical classical measurement but in practice we can't [52:34] seem to. And the reason for that is because in order to do that--in theory, it's possible, [52:37] but in practice we would have to undo all of the entanglements in this macroscopic system. [52:43] So, for me, to now go back in--back in time, you know, we aren't really going back in time, [52:47] but for me to erase all of your memories of having seen this green thing on the screen [52:53] and agreed that it was green at the beginning of the screen, I would have to undo this enormous [52:59] web of entanglement that has since proliferated at the speed of light. I have to bring all [53:04] those particles back together and recombine them. And in principle, that's possible and [53:09] in practice, obviously, it's not, which is why classical measurement seems to be irreversible [53:17] despite the fact that the physics of the universe say that everything is reversible. So, this [53:23] has some philosophical implications. I call it the zero universe interpretation of quantum [53:29] mechanics. If you really--if you buy this as a description of what the physics of the [53:34] universe is really like, then it tells you unambiguously that it is not the case; that [53:39] the reason that measurements are consistent across space and time is because there's a [53:45] real underlying metaphysical reality out there. It tells you in fact, the exact opposite, [53:52] that what we really are is, as David Mermin puts it, "correlations without correlata." [54:00] We are not made of atoms we are actually made of bits. We are our thoughts and these thoughts [54:07] actually reside, if you will forgive stretching a metaphor to the breaking point, we are a [54:13] simulation running on a quantum computer. I'm going to skip that. So, the take-home [54:22] message is, going back to this Einstein quote that, "The most incomprehensible thing about [54:27] the universe is that it's comprehensible." Here's an explanation in terms of physical [54:30] theory of why the universe is comprehensible. Quantum mechanics actually predicts a comprehensible [54:36] universe but at the cost of forcing you to believe that what you perceive as physical [54:42] reality is not actually real it's actually an illusion. And the motto here is that "spooky [54:52] action at a distance" is no more and no less mysterious than the "spooky action across [54:56] time" that lets us perceive the universe as consistent from one moment to the next. They're [55:03] both produced by the exact, same physical phenomenon, namely entanglement. And I'll [55:09] leave you with this quote from an ancient Japanese Zen master and open the floor for [55:18] questions. Uh-oh, the physicists are walking out. Yeah? [55:31] >> So you have the three particles when you remove from the shell what the main two look [55:45] like and they were building to the point in the sensor. Why not leave the--what happens [55:50] when you leave a third particle away? And if you're taking that as another thought experiments [55:53] and say, "Well, this is equivalent too." >> GARRET: Yeah. Well, this is--so these are [55:56] all just math, right? >> Right. [55:57] >> GARRET: So, these are all mathematical manipulations, the results of which we interpret [56:04] in order to tell stories about what our world is like. And if you leave it in, then what [56:10] you have is a description of the unadulterated underlying physical reality, which is quantum. [56:16] And the reason that's hard to wrap your brain around is because your brain is classical, [56:21] everything that you are is classical. You're made of classical bits that ones--or you're [56:26] a Turing machine, you're not a quantum computer, but you're made out of a quantum computer. [56:31] And that's why there's this fundamental disconnect that will always take a toll in our intuitions [56:37] that will never go away because they're really fundamentally different. The difference between [56:41] real numbers and complex numbers, the underlying reality is complex, but the thing that is [56:47] processing the information that lets you think about these things is real. It's made of real [56:51] numbers. That's really the underlying--the pithiest way I know of summarizing this so [56:57] it just depends on what point of view you want to take. [57:00] >> I'd like to make a short pitch for the multiple universes and hear your response. [57:13] The multiple universes, one way to look at it is the natural equation, it allows for--because [57:19] it's linear, you can have things occurring that live in the same equation and sometimes, [57:28] say, with the dead and a live cat, you can see that you can actually sort of separate [57:33] them, each goes its own way, they don't interact much, so a very good approximation is to consider [57:41] them one at a time. However, when real quantum effects go then you cannot do it this way. [57:49] So, there are--there are some things that you can separate and some not. So, now, you're [57:56] saying that you have an interpretation of a one universe so... [58:00] >> GARRET: No, not one. Zero. >> Zero, all right. [58:01] >> GARRET: Very important distinction. One universe, one classical universe really is [58:05] untenable. >> Well... [58:06] >> GARRET: You can--you can--that's Copenhagen. >> Yeah. [58:10] >> GARRET: You can--you can--yes, the--so the question was, what do I think about multiple [58:15] universes? Multiple universes are just as tenable, according the math, as zero universes. [58:23] The only thing that's not tenable is one classical universe, that's--that's the only thing that [58:26] the math tells you unambiguously does not exist. And it's a matter of taste. You know, [58:33] I personally--one of the things that the--that the math tells you if you think about it in [58:38] terms of multiple universes, is that once you get beyond a certain level of separation [58:44] these universes are forever inaccessible to us, even, you know, to any reasonable degree [58:53] of approximation. And then there's this philosophical question of is the thing actually real and [59:00] the analogy that--the best analogy that I've heard is imagine a photon that leaves the [59:07] back of the sun and goes away from us and so it's forever outside our light cone, is [59:14] that photon real? And my reply to that is there's a difference between the photon that [59:22] leaves the back of the sun and travels away from us because there's always the possibility [59:27] that somewhere out there's a mirror that's going to reflect that photon back to us and [59:32] we won't know that until that mirror actually reflects it and it comes back and we can see. [59:37] But in the case of multiple universes, we know unambiguously the math tells us so that [59:43] once another universe splits off, it's never coming back. There's no way to bring it back. [59:48] >> After a concurrent time, it will. >> GARRET: Excuse me? [59:52] >> After a concurrent time, it will. >> GARRET: Okay, in any amount of time that [59:57] we have any practical reason to care about. So, yes, if you're thinking cosmologically, [60:07] multiple universes is a--is a tenable interpretation. If you're thinking in terms--if--if you want [60:15] a story that you can help you to understand how the universe works in terms of your everyday [60:20] life and what your fundamental nature is, I personally find that I gravitate more towards [60:27] the information theoretic point of view and believing that--that I'm--I--the universe [60:33] that I exist in is a very good high-quality simulation. But that's a matter of taste. [60:39] >> So do multiple universes conserve mass energy? [60:43] >> GARRET: That I don't know. I have to defer that to the physicists. That's a very good [60:50] question. I don't--I actually don't know the answer to that. [60:53] >> Could you amplify a bit more for what does a zero universe mean? [61:00] >> GARRET: This--oh, by the way, the question back here was do multiple universes conserve [61:03] mass energy. It's a very--a very good question because--and I don't know the answer. I should--I [61:08] should ask--I need to ask a physicist who... >> I've asked this question of "many worlds" [61:10] proponent and the answer I got is, yes, that you're not actually doubling the amount of [61:24] mass, you're dividing the amount of mass into two effectively but... [61:25] >> GARRET: Oh, okay. So somebody in the audience is saying that when universes split, the total [61:29] amount of mass in the universe gets evenly divided between the two universes and I'm [61:33] guessing that math works out in such a way that if you reduce the amount of mass in a [61:38] classical universe uniformly by one half, that everything ends up working out the same [61:44] as it did before. But I'm going to have to think about that. [61:46] >> So this is just even one universe does not conserve mass energy with anything. Universes [61:47] as whole... >> GARRET: Okay. [61:48] >> And yet, in one--in the universe we're in, we don't seem to see this mass dwindling [61:56] away. >> But it's, you know, because we're doing [61:58] the same... >> GARRET: Yeah. So in that, we are now beyond [62:02] the limits of my knowledge of this stuff. Yeah? [62:04] >> For those of us who are intrigued and teased, where can we learn more? [62:08] >> GARRET: So, I have paper about this. It's on the web. I highly recommend David Mermin's [62:14] book, Boojums: All the Way Through, where he doesn't actually talk about this but he [62:21] talks about the Bell inequality in a very accessible way, which is also--I didn't have [62:26] time to talk about that but it's very worthwhile knowing about. Or send--send me an email. [62:34] I can actually put you in touch with the guys whose research this talk is based on. They're [62:38] down at Caltech, I think. Yeah? >> So is this an entirely local theory that [62:39] all interactions are interacting locally propagating at the speed of light, or is it? [62:53] >> GARRET: Well, so this get--so, the question was is this a local, purely local theory. [62:57] It's quantum mechanics. And whether quantum mechanics is purely local is the subject of [63:04] debate. And it depends--it depends on what you mean by purely local. Classically, it's [63:14] not, and quantum mechanically, it is. You know, I--this sheds no extra light on that [63:21] question. Okay, I guess, that's it.