Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics

by David Kaiser

Overview

Winner of the 2007 Pfizer Prize from the History of Science Society.
 
Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process.

Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calculational skills, David Kaiser frames his story around the crafting and stabilizing of the basic tools in the physicist's kit—thus offering the first book to follow the diagrams once they left Feynman's hands and entered the physics vernacular.

Product Details

ISBN-13:	9780226422671
Publisher:	University of Chicago Press
Publication date:	06/15/2005
Edition description:	1
Pages:	376
Product dimensions:	6.00(w) x 9.00(h) x 1.30(d)

About the Author

David Kaiser is the Germeshausen Professor of the History of Science and professor of physics at the Massachusetts Institute of Technology. He is the author of several books, including How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival, and is coeditor of Groovy Science: Knowledge, Innovation, and American Counterculture, also published by the University of Chicago Press.

Read an Excerpt

Drawing Theories Apart
The Dispersion of Feynman Diagrams in Postwar Physics

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By DAVID KAISER
The University of Chicago Press
Copyright © 2005 The University of Chicago
All right reserved.
ISBN: 978-0-226-42267-1

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Chapter One
Introduction: Pedagogy and the Institutions of Theory

I would wish, therefore, that the man who claims to be scientific first tell me the method he employs for his scientific demonstrations and then show me how he has been trained in it. GALEN, CA. AD 150

RICHARD FEYNMAN AND HIS DIAGRAMS

Few scientists, living or dead, surpass Richard Feynman (1918-88) as a widely recognized scientific icon. His star rose early. Following undergraduate work at the Massachusetts Institute of Technology and graduate study at Princeton, Feynman served as the youngest subgroup leader in wartime Los Alamos-he was only twenty-five-leading a band of fellow physicists in the sprawling effort to build atomic bombs. As the war ground closer to a conclusion, physics departments throughout the United States jockeyed to hire Feynman, as word of his creativity and sheer calculating power began to spread. His boss at Los Alamos, Hans Bethe, managed to lure Feynman to Cornell, where he taught for five years before the California Institute of Technology enticed him away from Ithaca's winters to the golden groves of Southern California. At Caltech, Feynman's renown as an animated teacher grew to match that of his physics prowess. An invitation to teach Caltech's large introductory physics class during the late 1950s led to the famous Feynman Lectures on Physics-a three-volume set still known simply as "the red books" by admiring physicists the world over. In later years, Feynman made a habit of giving informal lectures on physics at neighboring industries and of teaching his "Physics X" class, a freewheeling class open to anyone with questions about science. All the while hemadelasting contributions to physicists' understanding of electrodynamics, nuclear forces, solid-state physics, and gravitation, many of which still bear his name.

The Nobel Prize that Feynman shared with two fellow physicists in 1965 piqued thewider public's interest; by the mid-1980s, he had became a folk hero well beyond the world's clique of theoretical physicists. A visible role in the 1986 investigation of the explosion of the space shuttle Challenger-dunking a piece of O-ring rubber in a glass of ice water in the midst of a televised press conference-capped a decades-long process of becoming a household name. One year after his death, the American Physical Society, American Association of Physics Teachers, and American Association for the Advancement of Science jointly organized a daylong memorial. Since then, four biographical portraits and at least five collections of friends' and colleagues' reminiscences have been published, supplementing the two best-selling compilations of his own anecdotes and aphorisms that were published near the end of his life. A book of his artwork and a compact disk of his celebrated bongo drumming were each on sale during the 1990s. Television specials have supplemented his popular accounts of modern physics and of his own life story. During the late 1990s, the Apple Computer Company selected various portraits of Feynman, along with portraits of other iconic figures such as Albert Einstein, Pablo Picasso, and Charlie Chaplin, for their "Think different" advertising campaign. (See fig. 1.1.) More recently, no less an actor than Alan Alda depicted Feynman in a solo performance at the Vivian Beaumont Theater in New York City's Lincoln Center. The show sold out so quickly upon its opening in November 2001 that the producers brought it back for an even longer run the following spring. As Alda explained, with more than a little Feynmanesque hyperbole, "Feynman's personality is so strong that if he was played by a three-foot-high dwarf of the opposite sex, you would still think it was Feynman up there." Few academics answer to such depictions.

When the journal Physics Today dedicated a special memorial issue to Feynman in February 1989, the editor faced the difficult task of summing up Feynman's many contributions. She selected a simple graphic theme to unify the volume. "The diagram you see scattered throughout this issue is a reminder of the legacy Richard Feynman left us," the editor explained. A simple line drawing, known to physicists as a "Feynman diagram," appeared atop each article in the issue, its white lines set against a dark field of mourning. (See fig. 1.2.) It was a fitting gesture. For all of Feynman's many contributions to modern physics, his diagrams have had the widest and longest-lasting influence. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Feynman first introduced his diagrams in the late 1940s as a bookkeeping device for simplifying lengthy calculations in one area of physics-quantum electrodynamics, physicists' quantum-mechanical description of electromagnetic forces. Soon the diagrams gained adherents throughout the fields of nuclear and particle physics. Not long thereafter, other theorists adopted-and subtly adapted-Feynman diagrams for many body applications in solid-state theory. By the end of the 1960s, some physicists even wielded the line drawings for calculations in gravitational physics. With the diagrams' aid, entire new calculational vistas opened for physicists; theorists learned to calculate things that many had barely dreamed possible before World War II. With the list of diagrammatic applications growing ever longer, Feynman diagrams helped to transform the way physicists saw the world, and their place within it.

Today physicists all over the world scribble down the diagrams when studying everything from the mundane to the bizarre. Whether calculating the properties of materials that will form electronic computer chips, the levitation of magnets above superconductors, the behavior of particles near black holes, or the origin of matter itself just fractions of a second after the big bang, physicists begin by drawing Feynman diagrams. Everything about using the diagrams has become routine. Particle physicists can now download computer programs that will both draw the standardized diagrams and evaluate the associated mathematical terms: the diagrams' lines and their mathematical content have become both algorithmic and automatic. As one physicist wrote in a recent preprint detailing the new automated diagram tools, "Explaining the necessity of [diagrammatic] one-loop calculations in the light of modern-day colliders is like carrying owls to Athens"-the centrality of Feynman diagrams to everyday practice, and the need to evaluate large numbers of them quickly, simply goes without saying. The latest programs can generate and evaluate one thousand simple diagrams in about five minutes on an ordinary desktop computer.

Yet it hasn't always been this way. A generation of theoretical physicists earned doctorates for performing far less grandiose tasks just a few short decades ago. Evaluating a few Feynman diagrams by hand was a publishable feat in the early 1950s, and the stuff of which scores of dissertations were made. More important, both aspects of the diagrams' use and interpretation-how to draw them and how to calculate with them, that is, what they meant-became contested and shifting during the two decades after their introduction in the late 1940s. Today's automated computational utopia hides a rich history of competing appropriations and theoretical foundations for these bare line drawings. During the 1950s and 1960s, Feynman diagrams did not compel, by themselves, a unique meaning or interpretation. They were drawn differently and mustered in different fashions to varying calculational, and ultimately ontological, ends. Despite the diagrams' centrality today, and despite all the attention lavished on Feynman himself-his quirky genius, his lasting contributions to physics, his now-famous eccentricities-no attention has been paid to how his simple-looking diagrams actually came to be embraced by so many physicists for so many distinct applications. Indeed, more has been written about the hunt for Feynman's celebrated passenger van, bedecked in larger-than-life Feynman diagrams, than about how scores of physicists-and soon hundreds and thousands-came to traffic in the diagrams in the first place.

Several physicists and historians have scrutinized various roots within Feynman's thinking for what became Feynman diagrams. My project concerns instead what happened to the diagrams once they made the leap out of Feynman's head. How did the diagrams spread so quickly? What kinds of applications did physicists forge for the line drawings? Why did the diagrams remain central to physicists' work even as related methods of calculation came and went? Feynman's protracted and largely private struggles to work out a consistent calculational scheme for quantum electrodynamics paled in comparison with the efforts required to equip other physicists with the new diagrammatic tool. Long after Feynman himself had grown accustomed to thinking and working with his diagrams, they remained neither obvious nor automatic for others. In fact, Feynman's particular ideas about the diagrams provided only one-and by no means the most important one-of several contrasting factors in determining how other physicists would treat them.

Rather than dwell on the isolated thoughts of a few Nobel laureates, therefore, I focus in this book on the pedagogical work involved in training large numbers of researchers to approach physical questions in similar ways. Unlike previous historical treatments of modern physics, this study follows neither the grand march of particular theories nor the lumbering progress of ever-growing experiments. Instead, I follow Feynman diagrams around, focusing on how physicists fashioned-and constantly refashioned-the diagrams into a calculational tool, a theoretical practice. My goal is to unpack the history of postwar theoretical physics from the ground up, as a story ultimately about crafting, deploying, and stabilizing the tools that undergird everyday calculations. Research tools such as Feynman diagrams never apply themselves; physicists have to be trained to use them, and to interpret and evaluate the results in certain ways. Stabilizing the new tool went hand in hand with training a new generation of theoretical physicists after World War II. The story of Feynman diagrams' spread thus illuminates larger transformations in what "theoretical physics" would be and how young physicists would become "theorists" after the war.

By following how physicists learned about and used Feynman diagrams from the late 1940s through the late 1960s, we bring broader changes in the infrastructure and intellectual development of postwar physics into focus. Everything about physicists' patterns of work came in for reevaluation after the war, from the methods of training young theorists, to the means of communicating new results and techniques, to decisions about what topics merited study and by what means. The diagrams likewise reveal the fissures and politics of becoming a young theorist after the war-from the international politics of the cold war, which shaped how physicists could communicate with colleagues in other countries; to the cold war's domestic doppelgänger, McCarthyism, and its effects on physicists' civil liberties and patterns of thought; to the generational politics between mentors and students, and the microsocial politics between competing research groups. In all these ways, following Feynman diagrams around helps us make sense of theoretical physicists' changing world.

This account of the dispersion of Feynman diagrams draws on several general themes, which I discuss in this introductory chapter and elaborate upon in the chapters that follow. Before turning to these issues in more detail, I should pause and discuss the book's title, Drawing Theories Apart. Two senses of the phrase are likely to be recognizable already: first, an emphasis upon drawing and similar pencil-and-paper work within theoretical physics; and second, the need to rethink the roles of theories versus tools in our accounts of modern physics. A third reference might not be as obvious for all readers: an inverted analogy with Bruno Latour's 1986 article "Drawing Things Together." As scholars in science studies will no doubt recognize in the chapters that follow, this book draws on several quintessentially Latourian themes: the building of networks, the importance of inscriptions, the work of translation and enrollment, and so on. Indeed, the very idea of following a nonhuman scientific object around as an organizing principle bears a certain Latourian signature. Yet I follow a different line when it comes to the question of "immutable mobiles," a notion that Latour introduced in his 1986 article. Whereas Latour emphasizes "optical consistency" (even "immutability") as an essential feature of why diagrams and other scientific inscriptions carry so much force among scientists, I focus instead on unfolding variations within their work-on the production and magnification of local differences, and the work required to transcend these differences when comparing results from different places. Hence the "apart" of my title, in place of Latour's "together."

PAPER TOOLS AND THE PRACTICE OF THEORY

Despite their centrality, the crafting and use of theoretical tools such as Feynman diagrams has not found an easy place within historians' and philosophers' traditional accounts of modern physics. Most studies have followed in the spirit of a joke that the wisecracking theorist George Gamow was fond of making. Gamow used to explain to his students what he liked most about being a theoretical physicist: he could lie down on a couch, close his eyes, and no one would be able to tell whether or not he was working. For too long, historians and philosophers have adopted Gamow's central (not to say sleepy) metaphor: research in theory, we have been told, concerns abstract thought, wholly separated from anything like labor, activity, or skill. Theories, worldviews, or paradigms seemed to be the appropriate units of analysis, and the challenge became charting the birth and conceptual development of particular ideas. In these traditional accounts, the skilled manipulation of tools played little role: theorists were assumed to write papers whose content other theorists could understand, at least in principle, anywhere in the world. Ideas, embodied in texts, traveled easily from theorist to theorist in these accounts, shorn of the material constraints that might make bubble chambers or electron microscopes (along with the skills required for their use) difficult to carry from place to place. The age-old trope of minds versus hands has been at play: a purely cognitive realm of ideas has been pitted against a manual realm of action. In short, more "night thoughts" than desk work, more Weltbild than Fingerspitzengefühl.

During the past decade, a rival vision of how to analyze work in theoretical sciences has begun to take shape. Building upon these studies, this book begins with a simple premise: since at least the middle of the twentieth century-and, arguably, during earlier periods as well-most theorists have not spent their days (or, indeed, their nights) in some philosopher's dream world, weighing one cluster of disembodied concepts against another, picking and choosing among so many theories or paradigms. Rather, their main task has been to calculate. Theorists have tinkered with models and estimated effects, always trying to reduce the inchoate confusion of "out there"-an "out there" increasingly percolated through factory-sized apparatus and computer-triggered detectors-into tractable representations. They have accomplished these translations by fashioning theoretical tools and performing calculations. Theorists have used calculational tools, in other words, to mediate between various kinds of representations of the natural world. These tools have provided the currency of everyday work.

Focusing on theorists' tools cuts orthogonally across conceptual histories of theoretical physics, since physicists often improvise with calculational techniques across a wide range of distinct topics or fields of inquiry. Feynman himself explained near the end of his life that he chose various topics to work on-from the scattering of electrons to the superfluid behavior of liquid helium, from vortex rings and polarization waves in crystals to superconductivity, from the scattering of constituents inside protons to the scattering of gravity waves off of planets-because such problems all fell "in the range of my tools." Concentrating on the separate theory domains with which such problems are usually associated-electrodynamics, solid-state physics, nuclear and particle physics, or gravitation-obscures deeper continuities in daily practice and calculational approach. Historians Andrew Warwick and Ursula Klein have given useful names to such calculational techniques, each drawing on an analogy to instruments: Warwick introduced the term "theoretical technology," and Klein the phrase "paper tools." Since the late 1940s, generations of physicists have turned more and more often to Feynman diagrams as their paper tool of choice.

(Continues...)

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Excerpted from Drawing Theories Apart by DAVID KAISER Copyright © 2005 by The University of Chicago. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Preface and Acknowledgments

Abbreviations

Chapter 1. Introduction: Pedagogy and the Institutions of Theory

Richard Feynman and His Diagrams

Paper Tools and the Practice of Theory

Pedagogy and Postwar Physics

Overview: The Two Meanings of "Dispersion"

PART I. DISPERSING THE DIAGRAMS, 1948-54

Chapter 2. An Introduction in the Poconos

Quantum Electrodynamics and the Problem of Infinities

Initial Reception and Lingering Confusion

Evidence of Dispersion

Chapter 3. Freeman Dyson and the Postdoc Cascade

The Rise of Postdoctoral Training

Dyson as Diagrammatic Ambassador

Life and Physics at the Institute for Advanced Study

The Postdoc Cascade

A Pedagogical Field Theory

Chapter 4. International Dispersion

The Diagrams' Diaspora

Feynman Diagrams in Great Britain

Feynman Diagrams in Japan

Feynman Diagrams in the Soviet Union

Tacit and Explicit Knowledges

PART II. DISPERSION IN FORM, USE, AND MEANING

Chapter 5. Seeds of Dispersion

The Feynman-Dyson Split

Perturbative Methods Fail, Feynman Diagrams Flourish

Chapter 6. Family Resemblances

Kroll's Perturbative Bookkeepers

Marshak's Meson Markers

Climbing Bethe's Ladder: Feynman Diagrams and the Many-Body Problem

Training Theorists for House and Field

PART III. FEYNMAN DIAGRAMS IN AND OUT OF FIELD THEORY, 1955-70

Chapter 7. Teaching the Diagrams in an Age of Textbooks

The Postwar Age of Textbooks

The New Diagrammatic Textbooks

Pedagogy and the Pictures' Place

Chapter 8. Doodling toward a New "Theory"

Dispersion Relations

Crossing to a New Representation

From Bookkeepers to Pole Finders: Polology and the Landau Rules

Chew the Program Builder: Nuclear Democracy and the Bootstrap

Diagrammatic Bootstrapping and the Emergence of New Theories

Chapter 9. "Democratic" Diagrams in Berkeley and Princeton

Geoffrey Chew: A Scientist's Politics of Democracy in 1950s America

Pedagogical Reforms: "Secret Seminars" and "Wild Merrymaking"

The View from Princeton

Conditions of Diagrammatic Possibilities

Chapter 10. Paper Tools and the Theorists' Way of Life

Why Did the Diagrams Stick? Inculcation and Reification

In Search of the Vanishing Scientific Theory

Appendix A. Feynman Diagrams in the Physical Review, 1949-54

Appendix B. Feynman Diagrams in Proceedings of the Royal Society, 1950-54

Appendix C. Feynman Diagrams in Progress of Theoretical Physics, 1949-54

Appendix D. Feynman Diagrams in Soryushi-ron Kenkyu, 1949-52

Appendix E. Feynman Diagrams in Zhurnal eksperimental'noi i teoreticheskoi fiziki, 1952-59

Appendix F. Feynman Diagrams in Other Journals, 1950-54

Interviews

Bibliography

Index

Editorial Reviews

2006 book prize

Forum for the History of Science in America

"A rich, original and most recommendable contribution to the history of modern science. It skilfully integrates social history with conceptual history, a technical mastery of Feynman diagrams with a broad and novel perspective of the historicity of the diagrams. . . . Drawing Theories Apart will surely be studied by historians, sociologists and philosophers of physics. . . . It has much to offer also to readers with no background in physics."

British Journal of the History of Science

"Kaiserer's masterly written book provides a readable account of the role of Feynman's intuitive tools for today's physics."

Zentralblatt Math - Gert Roepstorff

"A stimulating and readable book that is also accessible to a wider audience. . . . The book is a valuable contribution to the history and philosophy of physics."

Studies in History and Philosophy of Modern Physics - Adrian Wuethrich

"This is a rich and original contribution to the expanding historical scholarship on the development of scientific tools and practices. Kaiser is one of the few historians to deal with the conceptual equipment of science as a kind of malleable paper tool, showing how Feynman diagrams were refracted through local environments and ultimately transformed. In all, a dazzling piece of work."-Daniel J. Kevles, Yale University

Daniel J. Kevles

"This is surely the definitive study of one of the great ubiquitous tools of modern quantum field theory."

Contemporary Physics - A. I. Solomon

"This is a fascinating book., if you are interested in the history, sociology and people of physics. It should be in every physics library."

Australian Physics - Bruce H.J. McKellar

Only a few people have the talent to write the history of theoretical physics. Only one or two can conceptualize and explain the elaboration of theory as a practical activity, which, like fine art, has its own competing traditions and conventions of representation.  David Kaiser accomplishes all this and backs it up with a level of detailed scholarship that makes it totally convincing.

Harry Collins

"Kaiser is prodigiously talented in telling the adventure of modern theoretical physics: the richness of the book may impress even the most demanding historians and physicists. Physicists will probably be surprised to learn of so many varieties of Feynman diagrams. Historians will be delighted with the originality of the approach. . . . Everybody will be enchanted by the style of the book: even when (very) difficult physics is presented, it is never boring; it is always luminous and exciting."

International Studies in the Philsophy of Science - Anouk Barberousse

Intellectual tools can have profound impacts. Feynman diagrams have greatly improved how theoretical physicists think and, consequently, our understanding of nature. Drawing Theories Apart provides an informative description of how their influence came about.”

Science - Gordon Kane

This book is a double delight. It is the best example so far of a new way of doing the history of science, not as an account of evolving theories, experiments, and instruments, but of diagrams. It is a story of how a generation of physicists came to think for themselves and to talk to others in a new way. It takes you inside their minds and their seminars. It is also a wonderful way to learn how Feynman diagrams work and what they mean—in effect, a super do-it-yourself manual.

Ian Hacking

"A colorful and readable account of the earliest applications of the diagrammatic technique."

Physics Today - Eugen Merzbacher

A stimulating and readable book that is also accessible to a wider audience. . . . The book is a valuable contribution to the history and philosophy of physics.

— Adrian Wuethrich

Studies in History and Philosophy of Modern Physics

A colorful and readable account of the earliest applications of the diagrammatic technique. . . . The book comes equipped with a formidable ancillary apparatus of footnotes and appendices and a massive bibliography that alone is worth the price.

— Eugen Merzbacher

Physics

Kaiser is prodigiously talented in telling the adventure of modern theoretical physics: the richness of the book may impress even the most demanding historians and physicists. Physicists will probably be surprised to learn of so many varieties of Feynman diagrams. Historians will be delighted with the originality of the approach. . . . Everybody will be enchanted by the style of the book: even when (very) difficult physics is presented, it is never boring; it is always luminous and exciting.

— Anouk Barberousse

International Studies in the Philosophy of Science

This is a fascinating book., if you are interested in the history, sociology and people of physics. It should be in every physics library.

— Bruce H.J. McKellar

Australian Physics

Intellectual tools can have profound impacts. Feynman diagrams have greatly improved how theoretical physicists think and, consequently, our understanding of nature. Drawing Theories Apart provides an informative description of how their influence came about.”

— Gordon Kane

Science

This is surely the definitive study of one of the great ubiquitous tools of modern quantum field theory.

— A. I. Solomon

Contemporary Physics

A colorful and readable account of the earliest applications of the diagrammatic technique.

— Eugen Merzbacher

Physics Today

"Kaiser is prodigiously talented in telling the adventure of modern theoretical physics: the richness of the book may impress even the most demanding historians and physicists. Physicists will probably be surprised to learn of so many varieties of Feynman diagrams. Historians will be delighted with the originality of the approach. . . . Everybody will be enchanted by the style of the book: even when (very) difficult physics is presented, it is never boring; it is always luminous and exciting."—Anouk Barberousse, International Studies in the Philsophy of Science

— Anouk Barberousse

International Studies in the Philsophy of Science