by Jed Brody
Quantum Entanglement
The MIT Press Essential Knowledge Series
A complete list of the titles in this series appears at the back of this book.
Quantum Entanglement
Jed Brody
The MIT Press | Cambridge, Massachusetts | London, England
© 2020 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
This book was set in Chaparral Pro by Toppan Best-set Premedia Limited.
Library of Congress Cataloging-in-Publication Data
Names: Brody, Jed, author.
Title: Quantum entanglement / Jed Brody.
Description: Cambridge, Massachusetts : The MIT Press, [2020] | Series: The
MIT press essential knowledge series | Includes bibliographical references
and index.
Identifiers: LCCN 2019024770 | ISBN 9780262538442 (paperback) |
ISBN 9780262357616 (ebook)
Subjects: LCSH: Quantum entanglement.
Classification: LCC QC174.17.E58 B76 2020 | DDC 539.7/25--dc23
LC record available at https://lccn.loc.gov/2019024770
10 9 8 7 6 5 4 3 2 1
d_r0
Contents
Series Foreword
Preface
Introduction
1 The Negative Space of Quantum Physics
2 An Experiment to Challenge a Philosophy
3 Entangled Light
4 Rigorous Contradiction of Everyday Assumptions
5 Reconciling with Relativity
6 Direct Observation Is the Only Reality?
Glossary
Notes
Further Reading
Index
Series Foreword
The MIT Press Essential Knowledge series offers accessible, concise, beautifully produced pocket-sized books on topics of current interest. Written by leading thinkers, the books in this series deliver expert overviews of subjects that range from the cultural and the historical to the scientific and the technical.
In today’s era of instant information gratification, we have ready access to opinions, rationalizations, and superficial descriptions. Much harder to come by is the foundational knowledge that informs a principled understanding of the world. Essential Knowledge books fill that need. Synthesizing specialized subject matter for nonspecialists and engaging critical topics through fundamentals, each of these compact volumes offers readers a point of access to complex ideas.
Bruce Tidor
Professor of Biological Engineering and Computer Science
Massachusetts Institute of Technology
Preface
I read The Tao of Physics in high school, and it left me hungry to understand the mathematical rigor that inspired mystical statements about quantum physics. I was equally unsatisfied in college physics courses, which had plenty of mathematical rigor but no mystical statements whatsoever. I wrote a term paper about quantum entanglement, which is mysterious if not quite mystical. While working on the term paper, I read classic articles about entanglement, but the information sank into my mind no further than the level that handles paraphrasing.
One reason I didn’t understand quantum entanglement is that I had never done an experiment with entangled particles. Indeed, the laboratory is the place where abstract concepts crystallize into palpable significance between your hands. The laboratory is where nature answers the questions posed by theorists. It’s impractical, however, for every interested person to do every interesting experiment. Now that I’ve done experiments with entangled particles, I hope I’m able to explain the phenomenon to anyone who’s curious.
Physics lab instructors sometimes feel the need to justify their existence—our existence. We insist that laboratory education is illuminating in ways that can never be fully conveyed in the lecture hall. Gesturing wildly for emphasis, we lavish praise on instructional experiments. Lab teaches hands-on skills and proves that physics actually works. Direct experience with an experiment gets you to think about the underlying physics more than anything else does. Certainly, doing experiments with entangled particles intensified my fascination with quantum mysteries. And I never would have done the experiments without the assistance and encouragement of several organizations and individuals.
Teaching physics lab isn’t nerdy enough, so every three years physics lab instructors come together to learn from one another, and generally geek out, at a conference organized by the Advanced Laboratory Physics Association (ALPhA). In summer 2012, the lab conference happened to be in Philadelphia when I was there anyway, visiting my parents. If the conference had been anywhere else, I probably wouldn’t have gone. I guard my summer vacation as greedily as Gollum guards the ring. I decided to go to the conference only because it practically arrived at my door. It almost would have been more effort to avoid going.
I expected to feel a bit disgruntled about being at the conference. Although I genuinely enjoy physics, I enjoy vacation even more. To my amazement, the conference was as enjoyable as a vacation. The talks and workshops were illuminating and inspiring. At that conference, I learned about the entanglement experiments for instructional labs. I also learned that ALPhA sponsors three-day “immersions” to teach instructors how to set up the experiment. In summer 2015, I attended the immersion led by Professor Enrique Galvez at Colgate University. I think I learned more physics in those three days than in any other three-day interval in my life.
After completing an immersion, instructors are eligible to apply to the Jonathan F. Reichert Foundation for a grant to help purchase the lab equipment. I’m grateful for the assistance that the Reichert Foundation provided for my instructional lab. The Emory physics department, where I work, covered the rest of the cost.
The final catalyst for this book was Emory’s Interdisciplinary Exploration and Scholarship (IDEAS) program, which organizes “sidecar” courses, each of them geared to explore a topic that intersects with (and is cosponsored by) two existing courses in different departments. I wanted to teach a sidecar course about quantum entanglement. I expected it to be cosponsored by my Advanced Lab course and a philosophy course. But I couldn’t find any philosophy professors who were interested. Luckily, I found a willing collaborator in the English department: Dave Fisher, who was scheduled to teach Technical Writing. We created a sidecar course to examine the different ways people write about quantum entanglement. If I hadn’t delved into the existing literature to prepare for the sidecar course, I never would have thought to write this book.
Erin Bonning, Michael Weissman, Alissa Bans, and Tom Bing generously read and commented on a draft of this book. I’m grateful for additional helpful discussions with colleagues, especially Sergei Urazhdin, Daniel Weissman, Keith Berland, Vincent Huynh, Luiz Santos, Ajit Srivastava, and Justin Burton. I take full responsibility, however, for any errors or imprecision.
Albert Einstein memorably described quantum entanglement as “spooky action at a distance.”1 I recall another memorable Einstein quote, this one from a letter he wrote to the philosopher Erik Gutkind in 1954. There Einstein explained his view that the scientist’s “religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systemic thinking and acting of human beings is an utterly insignificant reflection.” In a book about physics, it may be irrelevant to observe that the rapturous harmony of the natural world is increasingly imperiled. And yet, I dedicate this book to the preservation and restoration of the natural world.
Introduction
Quantum physics describes the behavior (and misbehavior) of tiny things: atoms, photons, and electrons, to name a few. What electrons lack in size, they make up for in importance. Electrons are the glue in chemical bonds, so quantum physics is used to understand the chemical bonds that hold together metals, plastics, skin, and every other material. Electrons are the lifeblood of computer chips, for instance, so engineers use quantum physics to design faster, smaller devices. Wherever quantum physics is applied, it’s unerringly accurate.
The most amazing feature of quantum physics isn’t its accuracy or its usefulness, but its brazen defiance of our common sense. Quantum physics challenges our basic understanding of reality itself. And yet, quantum physics started off in a very mundane way, seeking explanations for dry, quantitative data.
The most amazing feature of quantum physics isn’t its accuracy or its usefulness, but its brazen defiance of our common sense. Quantum physics challenges our basic understanding of reality itself.
For example, hydrogen gas can emit four colors of visible light: violet, blue, aqua, and red. Physicists had carefully measured the wavelengths of these four colors: 410 nanometers, 434 nanometers, 486 nanometers, and 656 nanometers. Surely there’s a reason for these four specific numbers. But what is the reason? Physicists were scratching their heads. In 1885, a physicist even came up with an equation that fit all four wavelengths, but there was no explanation for the equation. It was a purely empirical equation, with no theory behind it.
Finally, in 1913, Niels Bohr came up with a theory that explained the four wavelengths. He claimed that the electron in the hydrogen atom is constrained to have certain amounts of energy. The electron cannot gain or lose energy smoothly; it can only make “quantum leaps” from one allowed energy level to another. Whenever an electron drops from one energy level to a lower energy level, it releases the energy in the form of light. The light emitted in a single quantum leap is called a photon. A photon is the smallest possible quantity of light with a particular wavelength. More generally, the smallest possible quantity of something is called a quantum.
These new quantum ideas had already solved two other mysteries. Max Planck explained the wavelengths of light emitted by hot objects, and Albert Einstein explained how photons knock electrons off the surface of metals. But even as quantum physics accumulated triumphs and grew in sophistication, it began to hint at deep mysteries in the fundamental nature of reality.
The fundamental quantum equation, which was established by Erwin Schrödinger and then published in 1926, dealt with probabilities: the likelihood of an electron appearing one place or another. Probability was not unfamiliar; the outcomes of coin tosses are also given as probabilities. But once a coin lands, the side that faces up is an objective fact, regardless of whether anybody knows what it is. In contrast with this common understanding of objective facts, the new quantum theory began to hint at a fundamental unknowability or uncertainty in unobserved particles. This conundrum drove Schrödinger to complain about the implications of his own equation.
Schrödinger asks us to imagine a cat trapped in an opaque box with an “infernal machine.” The machine includes a radioactive material that occasionally emits a particle that can be detected by a Geiger counter. If the Geiger counter detects a particle, it triggers the release of a poisonous gas, which kills the sacrificial cat. The radioactive emission is governed by quantum physics. Quantum theory can specify only the probability that a particle will be emitted to trigger the release of poison gas. But unlike a tossed coin, which lands heads or tails up regardless of whether anyone observes it, quantum predictions aren’t so easy to interpret. Quantum theory implies that before a measurement is performed, somehow the particle is neither emitted nor not emitted, or (equivalently?) both emitted and not emitted. In this case, the poison gas is both released and not released, and the cat is both dead and alive. This confusing condition persists until a measurement is performed. But what constitutes a measurement? The intervention of a conscious observer who looks in the box? Or simply the interaction of the emitted particle with the Geiger counter?
Making matters worse, in 1927 Werner Heisenberg showed that the more precisely an electron’s position is known, the more uncertain its speed becomes. The electron seems committed to not being pinned down. When an electron takes the witness stand, it never agrees to tell the whole truth (both its position and its speed). But does its refusal to tell the whole truth hint at a deeper truth? Are quantum measurements like breezes through a curtain, giving us shifting glimpses of a reality that is never fully revealed?
Some scientists argue that quantum physics predicts outcomes of measurements and nothing more; we shouldn’t even ask the question “What does it all mean?” At least, we shouldn’t claim to know what particles are doing when we’re not measuring them. This is a form of Bohr’s “Copenhagen interpretation,” though the Copenhagen interpretation itself has been interpreted different ways by different people.
Are quantum measurements like breezes through a curtain, giving us shifting glimpses of a reality that is never fully revealed?
People like Einstein were fed up with vagueness, uncertainty, and contradictions. If 1984 had already been written when these physicists were grappling with these qualities of quantum mechanics, Einstein would have accused his opponents of doublethink: “Doublethink means the power of holding two contradictory beliefs in one’s mind simultaneously, and accepting both of them.”1 Surely nature itself is not guilty of doublethink. Surely quantum physics can be massaged and refined, retaining its accuracy while eliminating the fuzziness and absurdity.
Einstein, uncharacteristically, was wrong.
1
The Negative Space of Quantum Physics
The quantum contradiction of common sense takes many forms. An especially rigorous form occurs in experiments with entangled particles. Two particles are entangled if the measurement of one of them, for all practical purposes, instantly affects the other particle over any distance.1 Einstein called it “spooky action at a distance.” Even spookier: the measurements of the particles do not reveal properties that the particles had all along. Prior to measurement, the particles’ properties are not merely unknown, they are undetermined; and the measurement somehow transforms them—the properties are no longer fuzzy but focused.
The purpose of this book is to empower you to deeply understand how our common-sense assumptions impose constraints—from which entangled particles burst free. In other words, this book explains what quantum physics is not. Our task is to paint the negative space of quantum physics, a space composed of seemingly plausible theories that cannot account for measured results. I’m using “negative space” the way an artist would, to indicate the space around a subject. Let’s imagine a space full of concepts. If we draw a border around quantum physics, our everyday assumptions occupy the excluded space, the negative space. Surprisingly, irritatingly, or magically—depending on your disposition—our everyday assumptions are contradicted by experiments with entangled particles.
Mathematics is a vehicle through which our assumptions become experimentally testable. We need only logic and arithmetic to understand how our everyday assumptions are contradicted by measurements of entangled particles. This is a relief, and perhaps surprising, since harder math is required to understand rocketry, semiconductor devices, heat conduction, and many other topics. Unlike these technological topics, quantum entanglement addresses the fundamental nature of reality. Perhaps nature’s apology for behaving so strangely at the deepest level is to make its negative space mathematically accessible to all of us.
Does the mathematics of quantum entanglement say something mystifying, or even mystical, about the universe? Or, rather, should we be mystified by the quantum contradiction of our everyday assumptions? To answer this question, we will dive deep into simple yet rigorous logic. We will see that our common-sense assumptions impose simple mathematical constraints on measurable quantit
ies. These constraints are violated by both quantum theory and measured data.
Measurements of entangled particles contradict at least one of the following two assumptions:
1.Realism: Objects have properties that exist regardless of whether anyone is observing them. Observation merely reveals properties that the objects had all along.
2.Locality: The measurement of one object can’t affect the measurement of another object that is arbitrarily far away.
The combination of the two is called local realism: the assumption that objects have definite properties, independent of our knowledge of them, and independent of measurements performed on other objects. Local realism is deeply embedded in our common sense. When I measure the length of my left foot, I determine the length it already had, without affecting the length of my right foot. And yet this common-sense claim would be exactly wrong if my feet were entangled particles. (Though my feet do become entangled in a different sense, whenever I attempt to dance.)
How can experiments contradict our everyday assumptions? In this book I intend to answer that question. It’s surprising that a philosophical assumption has mathematical consequences, which can be tested experimentally. But local realism isn’t the only philosophical assumption with mathematical consequences. We might characterize geocentrism as a philosophical assumption:2 “Everything must orbit our planet due to our own preeminence in the universe.” It’s not obvious that this assumption should have mathematical consequences. And yet, ancient and medieval astronomers labored mightily with the mathematical consequences. They had to explain why the other planets occasionally go into retrograde, backing up as if looking for something they dropped. The geocentric astronomers came up with hugely complex and surprisingly accurate mathematical models. Ultimately, however, the preponderance of evidence, and the preference for a simple unifying theory, forced astronomers to abandon the geocentric assumption. Similarly, as we’ll see, experimental evidence forces us to abandon the everyday assumption of local realism.