A Brief Guide to the Great Equations (43 page)
2
Jammer,
The Conceptual Development
, p. 170.
3
Ibid., p. 178.
4
‘It appears to me that hydrogen’, Balmer wrote prophetically in his paper, ‘more than any other substance is destined to open new paths to the knowledge of the structure of matter and its properties.’ Quoted in Jammer,
The Conceptual Development
, p. 65.
5
A. Einstein to C. Habicht, May 1905, in
Collected Works
, vol. 5, p. 20.
6
A. Einstein, ‘On the Quantum Theory on Radiation’, in
Collected Works
, vol. 6, pp. 220–33.
7
Ibid.
8
Physical Review
21 (1923), 483–502.
9
Jammer,
The Conceptual Development
, p. 171.
10
N. Bohr, H. Kramers, and J. Slater, ‘The Quantum Theory of Radiation’,
Philosophical Magazine
47 (1924), p. 785.
11
Jammer,
The Conceptual Development
, p. 196.
12
The remarkable route to the wave equation has been extensively analysed by several historians of science, including Martin Klein, ‘Einstein and the Wave-Particle Duality’,
The Natural Philosopher
3 (1964), pp. 3–49; L. Wessels, ‘Schrödinger’s Route to Wave Mechanics’,
Stud Hist Phil sci
10 (1979), pp. 311–40; M. Jammer,
The Conceptual Development of Quantum Mechanics
, 1966, ch. 5, sec. 3.
13
Walter Moore,
A Life of Erwin Schrödinger
(Cambridge: Cambridge University Press, 1994), pp. 195–96.
14
Quoted in Mara Beller,
The Genesis of Interpretations of Quantum Mechanics 1925–1927
, PhD Dissertation, University of Maryland, 1983, p. 124.
15
Moore,
A Life
, pp. 195–96.
16
Quoted in ibid.
17
Jammer,
The Conceptual Development,
p. 267.
18
E. Schrödinger,
Collected Papers on Wave Mechanics
(Providence, RI: AMS/Chelsea Publishing, 1982), p. 59.
19
Ibid., p. 20.
20
Ibid., p. 9.
21
Jammer,
The Conceptual Development
, p. 284.
22
Born, ‘Physical Aspects of Quantum Mechanics’,
Nature
119 (1926), pp. 354–57.
23
Quoted in Jammer,
The Conceptual Development
, p. 285.
24
Quoted in Beller,
Genesis
, p. 144.
25
Beller,
Genesis
, p. 105.
: The Double Consciousness of Scientists
1
Quoted in Mara Beller,
The Genesis of Interpretations of Quantum Mechanics 1925–1927
, PhD Dissertation, University of Maryland, 1983, p. 86.
2
Ibid., p. 91.
1
Anne Bogart and Kristin Linklater, ‘Balancing Acts’,
American Theatre
, January 2001.
2
David Cassidy,
Uncertainty: The Life and Science of Werner Heisenberg
(New York: Freeman, 1992).
3
Interview, Werner Heisenberg, February 27, 1963,
Archives for the History of Quantum Physics
[hereafter
AHQP
] (College Park, MD: American Institute of Physics), p. 22. This is not what Heisenberg would have said at the time. At that time, he was trying to get rid of classical notions altogether.
4
W. Heisenberg, ‘Erinnerungen an der Zeit die Entwicklung der Quantenmechanik’, in
Theoretical Physics in the Twentieth Century
, ed. M. Fierz and V. F. Weisskopf (New York: Interscience, 1960).
5
Isn’t it possible, indeed, that the human perceptual and imaginative capacities have evolved to handle environments of a scale about that of the human body, rather than for the microworld, a billion orders of magnitude smaller?
6
Mara Beller,
Quantum Dialogue: The Making of a Revolution
(Chicago: University of Chicago Press, 1999), p. 22.
7
Patrick A. Heelan,
Quantum Mechanics and Objectivity
(The Hague: Nijhoff, 1965), p. 23.
8
Max Born,
My Life and My Views
(New York: Scribner’s, 1968), p. 216.
9
W. Heisenberg,
Physics and Beyond: Encounters and Conversations
(New York: Harper and Row, 1971), p. 60.
10
Ibid., p. 61.
11
W. Heisenberg, ‘On the Quantum-Mechanical Reinterpretation of Kinematic and Mechanical Relations’,
Zeitschrift für Physik
(
ZfP
) 33 (1925), 879–93; in B. L. van der Waerden,
Sources of Quantum Mechanics
(Amsterdam: North-Holland, 1967), p. 261.
12
W. Heisenberg,
AHQP
Interview, February 15, 1963.
13
‘Über quantentheoretische Umdeutung kinematischer und mechanisher Beziehungen’, in
ZfP
53 (1925), p. 893.
14
Quoted in Beller,
Quantum Dialogue
, p. 43.
15
M. Born, ‘Remarks at Le Banquet Nobel’, in
Les Prix Nobel en 1954
(Stockholm: Royale P. A. Norstedt & Stoner, 1955).
16
Max Born,
Physics in My Generation
(New York: Pergamon Press, 1969), p. 100.
17
Nancy Greenspan,
The End of the Certain World: The Life and Science of Max Born
(New York: Basic Books, 2005), p. 127.
18
Before it was published, they received a shock, in the form of a paper
by a Cambridge student named Paul Dirac, who had been given a copy of Heisenberg’s paper in Cambridge, studied it, and had come to the same conclusions as Born and Jordan, using slightly different language. Meanwhile, Dirac heard Heisenberg’s talk, applied new notation, and came up with a distinction between
q
numbers and
p
numbers. The variables were not classical variables, or those satisfying the commutative law (what Dirac would soon call c-numbers), but symbols referring to quantum mechanical variables (q-numbers).
19
Quoted in Abraham Pais,
Inward Bound
(New York: Oxford University Press, 1986), p. 258.
20
One irony, pointed out by Jammer (
The Conceptual Development
p. 215), is that the mathematics of this attempt to rid atomic physics of a solar-system-like picture was based on so-called secular equations that derived from methods of astronomers to compute planetary orbits.
21
Quoted in Beller,
Genesis
, p. 81.
22
E. Schrödinger, ‘The Continuous Transition from Micro- to Macro-Mechanics’,
Die Naturwissenschaften
28 (1926), pp. 664–66, in Schrödinger,
Collected Papers
, pp. 41–44.
23
Jammer,
The Conceptual Development
, p. 271.
24
Quoted in Beller,
Genesis
, pp. 85, 89.
25
M. Born to E. Schrödinger, November 6, 1926, in
AHQP
.
26
Schrödinger,
Collected Papers
, pp. 45–61.
27
Beller,
Genesis
, p. 93.
28
Cassidy,
Uncertainty
, p. 215.
29
Schrödinger,
Collected Papers
, p. 46.
30
Ibid., p. 59.
31
E. Schrödinger to W. Wien, June 1926, cited in Cassidy,
Uncertainty
, p. 214.
32
Beller,
Genesis
, p. 207.
33
Beller,
Quantum Dialogue
, p. 410.
34
W. Heisenberg,
Physics and Beyond
, p. 73.
35
Pauli put this interpretation in a footnote to one of his papers: ‘Über Gasentartung und Paramagnetismus’,
ZfP
41, 1927.
36
Quoted in Beller,
Genesis
, p. 137.
37
W. Pauli to W. Heisenberg, October 19, 1926, in A. Hermann, K. Meyenn, and V. Weisskopf,
Wolfgang Pauli: Wissentschaftlicher Brief-wechsel mit Bohr, Einstein, Heisenberg, u.a.
(New York: Springer, 1979), p. 347.
38
W. Heisenberg to W. Pauli, November 15, 1926, ibid., p. 355.
39
W. Heisenberg to W. Pauli, November 23, 1926, ibid., p. 359.
40
In effect, Jordan’s article implicitly expresses what many people are tempted to think when they first encounter the uncertainty principle – that electrons and other tiny bits of matter
really do
have positions and momenta, but that we cannot track them down because of some defect – maybe even an essential and ineradicable defect – in our measuring instruments.
41
John H. Marburger, III, ‘A Historical Derivation of Heisenberg’s Uncertainty Relation Is Flawed’,
American Journal of Physics
76 (2008), pp. 585–87.
42
Beller,
Genesis
, p. 217.
43
Quoted in ibid., p. 318.
44
W. Heisenberg,
AHQP
Interview, February 25, 1963.
45
Beller,
Genesis
, p. 245ff.
46
N. Bohr,
Atomic Theory and the Description of Nature
(Cambridge: Cambridge University Press, 1934), p. 54.
47
Quoted in ‘The Philosophy of Niels Bohr’, by Aage Peterson, in
Bulletin of the Atomic Scientists
19, no. 7 (1963).
48
Quoted in Beller,
Genesis
, p. 248.
: The Yogi and the Quantum
1
P. W. Bridgman, ‘The New Vision of Science’,
Harper’s
, March 1929, pp. 443–51.
2
I am greatly indebted to John H. Marburger, III, for pointing this out to me. ‘It’s a clear, logical, and consistent way of framing the complementarity issue’, Marburger says. ‘It clarifies how quantum phenomena are represented in alternative classical ‘pictures’, and it fits in
beautifully
with the rest of physics. The clarity of this scheme removes much of the mysticism surrounding complementarity. What happened was like a Gestalt-switch, from a struggle to view microscopic nature from a classical point of view to an acceptance of the Hilbert space picture, from which classical concepts emerged naturally. Bohr brokered that transition.’
: Bringing the Strange Home
1
Peter Galison,
Image and Logic: A Material Culture of Microphysics
(Chicago: University of Chicago Press, 1997), p. 801.
2
Leon Lederman, ‘The Pleasure of Learning’,
Nature
430:5 (August 2004), p. 617.
This book, like my previous book,
The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science
, grew out of a column I wrote for
Physics World
. Once again I am grateful to its editors, especially Matin Durrani, for allowing me to write a column for that magazine, as well as to the hundreds of people who responded to my column about great equations. That column made it possible for me to try out many ideas in this book, and bits and pieces of my columns show up throughout. I am indebted to my literary agent, John Michel, for steering me again and again in the right direction; to Margaret Maloney, for helping me through the manuscript process; to production manager Julia Druskin; and to my editor, Maria Guarnaschelli, for her thoughtful reading and guidance. Like all columnists, I rely heavily on colleagues and correspondents for inspiration, ideas, and information, and those who provided helpful suggestions, comments, and other kinds of assistance include: Edward S. Casey, David Cassidy, Carlo Cercignani, Allegra de Laurentiis, John de Pillis, David Dilworth, B. Jeffrey Edwards, Elizabeth Garber, Patrick Grim, Richard Harrison, George W. Hart, Richard Howard, Don Ihde, Eric Jones, Ed Leibowitz, Gerald M. Lucas, Bob Lloyd, Peter Manchester, Eduardo Mendieta, Hal Metcalf, Lee Miller, Eli Maor, Anthony Phillips, Xi Ping, Mary Rawlinson, Robert C. Scharff, David Socher, Marshall Spector, Clifford Swartz, Dick Teresi, Beth Young. Without the capable help of Alissa Betz, Ann-Marie Monaghan, and Nathan Leoce-Schappin in the Department of Philosophy office this manuscript would have been much delayed. John H. Marburger, III, helped me to avoid numerous errors of fact and interpretation in the chapters on quantum mechanics, though I’m sure I still managed to commit some. Alfred S. Goldhaber provided me with thoughtful advice on the quantum mechanics and relativity chapters, and I benefited from many discussions that I had with him while co-teaching a course on
the influence of quantum mechanics outside physics. My wife, Stephanie, not only read the manuscript but put up with my difficult – some would say impossible – work routines, which are trying to anyone within range, but nevertheless managed to provide me throughout with the sounds of surprise. My son, Alexander, likewise had to endure my work habits and periodic unavailability, and drew several of the diagrams. My daughter, India, always made sure I was in the right dimension. My dog, Kendall, was always willing to go for a walk with me when the rest of them got fed up. And again I want to thank Charles C. Mann, the finest science writer of this generation, for his generosity, inspiration, and example.
Page numbers in
italics
refer to illustrations.
Abbott, Edwin A.,
211
absolute rest,
166
absolute space,
60–61
,
62–63
,
159
,
161
,
164
,
199