Appendix 2: Further Reading
If you find your interest piqued by this little book, you may want to explore the subject further. Here I list some good readings. All include a discussion of Bell’s Theorem, although in some cases only tangentially.
Non- Technical Works
The following are specifically aimed at a general audience. I can testify from personal experience that are all very well written and a pleasure to read
Becker, Adam. What Is Real? The Unfinished Quest for the Meaning of Quantum Physics.
New York: Basic Books, 2018.
As the title makes clear, this book is primarily concerned with attempts to understand what quantum theory is telling us about the world. It contains many personal anecdotes, and also much about the three “alternative” approaches that I mentioned in chapter 2
Bernstein, Jeremy. “John Stewart Bell: Quantum engineer,” in Jeremy Bernstein, Quantum Profiles. Princeton: Princeton University Press, 1991, pp. 3– 91.
Far broader in scope than most of the other readings I have listed here, Bernstein surveys the entire field of quantum theory and its many mysteries.
Gilder, Louisa. The Age of Entanglement: When Quantum Physics was Reborn. New York: Alfred A. Knopf, 2008.
With a novelist’s skill, Gilder humanizes and dramatizes the story of the discovery of entanglement. Much of the material in my chapter 11 is taken from this book.
Herbert, Nick. Quantum Reality: Beyond the New Physics. New York: Anchor Press /
Doubleday, 1985.
A broad survey of quantum theory’s mysteries.
126
Appendix 2
Kaiser, David. How the Hippies Saved Physics: Science, Counterculture and the Quantum Revival. New York: W. W. Norton, 2011.
Kaiser is a physicist and a historian of science: the title of his book tells it all.
Much of the material in my chapters 4 and 12 is taken from this book.
Kaiser, David. “Quantum theory by starlight.” New Yorker (online), February 7, 2017,
available at https://www.newyorker.com/tech/elements/quantumtheorybystarlight
Kaiser describes here the experiment that closed the freedom of choice loophole (in which he participated).
Kaiser, David. “Free will, video games, and the most profound quantum mystery.”
New Yorker (online), May 9, 2018, available at https://www.newyorker.com/science
/elements/freewillvideogamesandthemostprofoundquantummystery
Kaiser describes here the experiment that used a video game to elicit random choices from people worldwide to be used in Bell test experiments.
Zeilinger, Anton. Dance of the Photons: From Einstein to Quantum Teleportation. New York: Farrar, Straus and Giroux, 2010.
Zeilinger, a physicist at the forefront of contemporary experimental research on entanglement and Bell’s Theorem, provides an insider’s view of the field. Much of the material in my chapter 15 is taken from this book.
Semitechnical Books
You probably would need a certain amount of technical background to
fully engage with the following books, but they are not solely for experts.
Freire, Olival. Quantum Dissidents: Rebuilding the Foundations of Quantum Mechanics.
Berlin: Springer, 2015.
Friere is a historian of science. This book is particularly revealing on the “stigma”
attached to thinking about the foundations of quantum mechanics.
Lewis, Peter J. Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics.
Oxford: Oxford University Press, 2016.
Lewis is a philosopher: the title tells it all.
Whitaker, Andrew. John Stewart Bell and Twentieth- Century Physics. Oxford: Oxford University Press, 2016.
A detailed look at Bell’s life and work, written by a physicist.
Further Reading 127
Other Forms of Bell’s Theorem
As I commented in appendix 1 on the GHZ theorem, since Bell’s discovery
other forms of his theorem have been found. And as I commented in chapter 10, Bell’s Theorem is not really about physics at all. It is pure logic: a matter of analyzing all the ways a random variable can be distributed.
And in particular, it is not even solely about spin. Two different works
have described a form of Bell’s Theorem using a “spin free” approach.
d’Espagnat, Bernard. “The quantum theory and reality.” Scientific American (November 1, 1979), pp. 158– 181.
The above article is written for a general audience. On the other hand, you may find yourself positively scared when you first pick up the following
book, since it is intended for an audience of physics students. But do not give up! The specific section listed here requires no special training at all: once again, it is all a matter of pure logic.
Greenstein, George, and Arthur G. Zajonc. The Quantum Challenge: Modern Research on Quantum Mechanics. 2nd edition. Burlington, MA: Jones and Bartlett, 2006, pp.
142– 148. This describes a method developed by N. David Mermin.
In general, I would guess that if you found yourself comfortable with
chapter 9’s treatment of a hidden variable theory, or the appendix’s treatment of the GHZ Theorem, you will find yourself equally comfortable with either of the above two references.
But I cannot help but point you toward the article in which Mermin
first introduced his new proof. I mentioned this article in chapter 9: it was immensely helpful to me in my efforts to understand Bell’s Theorem. Even
though it is written for an audience of physicists, a great part of it consists of an utterly delightful history of the early arguments among the founders of quantum theory: you really should take a look at it!
Mermin, N. David. “Is the Moon there when nobody looks?” Physics Today 38 (April 1985): 38– 47.
Notes
Foreword
1. Erwin Schrödinger, “Discussion of probability relations between separated systems,” Mathematical Proceedings of the Cambridge Philosophical Society 31 (1935): 555–
563, on 555.
2. Schrödinger, 555; Albert Einstein, Boris Podolsky, and Nathan Rosen, “Can quantum
mechanical description of physical reality be considered complete?,”
Physical Review 47 (1935): 777– 780.
3. Einstein, Podolsky, and Rosen, “Can quantum mechanical description of physical reality be considered complete?,” 777.
4. Niels Bohr, “Can quantum mechanical description of physical reality be considered complete?,” Physical Review 48 (1935): 696– 702. Abraham Pais recounts the story of Einstein asking him about the moon in Pais, “Subtle Is the Lord …”: The Science and the Life of Albert Einstein (New York: Oxford University Press, 1982), pp. 5– 6.
On the Einstein– Bohr debate, see especially Don Howard, “Einstein on locality and separability,” Studies in History and Philosophy of Science 16 (1985): 171– 201; Don Howard, “‘Nicht sein kann was nicht sein darf,’ or the prehistory of EPR, 1909– 1935: Einstein’s early worries about the quantum mechanics of composite systems,” in Sixty- Two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics, ed. Arthur I. Miller (New York: Plenum, 1990), pp. 61– 112; Arthur Fine, The Shaky Game: Einstein, Realism, and the Quantum Theory (Chicago: University of Chicago Press, 1986); and Mara Beller, Quantum Dialogue: The Making of a Revolution (Chicago: University of Chicago Press, 1999).
5. See esp. Jeremy Bernstein, “John Stewart Bell: Quantum engineer,” in Bernstein, Quantum Profiles (Princeton: Princeton University Press, 1991), 3– 91; Louisa Gilder, The Age of Entanglement: When Quantum Physics was Reborn (New York: Knopf, 2008); David Kaiser, How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival (New York: W. W. Norton, 2011); Olival Freire, Jr., The Quantum Dissidents: Rebuilding the Foundations of Quantum M
echanics, 1950– 1990 (New York: Springer,
130 Notes
2014); and Andrew Whitaker, John Stewart Bell and Twentieth- Century Physics (New York: Oxford University Press, 2016).
6. John S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1 (1964): 195– 200.
7. See esp. John Clauser, Michael Horne, Abner Shimony, and Richard Holt, “Proposed experiment to test local hidden variable theories,” Physical Review Letters 23
(1969): 880– 884; Stuart Freedman and John Clauser, “Experimental test of local hidden variable theories,” Physical Review Letters 28 (1972): 938– 941. On the early experimental efforts to test Bell’s inequality, see also Gilder, Age of Entanglement, chapters 30– 31; Kaiser, How the Hippies Saved Physics, chapters 3 and 8; and Freire, Quantum Dissidents, chapters 7– 8.
8. John Trimmer, “The present situation in quantum mechanics: A translation of Schrödinger’s ‘Cat Paradox’ paper,” Proceedings of the American Philosophical Society 124 (1980): 323– 338. Schrödinger’s paper was originally published in three installments as “Die gegenwärtige Situation in der Quantenmechanik,” Naturwissenschaften 23 (1935): 807– 812, 823– 828, and 844– 849. For recent discussion of loopholes in experimental tests of Bell’s inequality, see J. A. Larsson, “Loopholes in Bell inequality tests of local realism,” Journal of Physics A 47 (2014): 424003; and N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of Modern Physics 86 (2014): 419– 478.
9. The first loophole to be addressed experimentally concerns “locality,” that is, whether information from one side of the apparatus could have affected the other side during the conduct of a given experiment. See Alain Aspect, Jean Dalibard, and Gérard Roger, “Experimental test of Bell’s inequalities using time varying analyzers,” Physical Review Letters 49 (1982): 1804– 1807; Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, and Anton Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Physical Review Letters 81
(1998): 5039– 5043.
10. B. Hensen et al., “Loophole free Bell inequality violation using electron spins separated by 1.3 kilometers,” Nature 526 (2015): 682– 686; M. Giustina et al., “Significant
loophole free test of Bell’s theorem with entangled photons,” Physical Review Letters 115 (2015): 250401; L. K. Shalm et al., “Strong loophole free test of local realism,” Physical Review Letters 115 (2015): 250402; W. Rosenfeld et al., “Event ready Bell test using entangled atoms simultaneously closing detection and locality loopholes,” Physical Review Letters 119 (2017): 010402; and M. H. Li et al., “Test of local realism into the past without detection and locality loopholes,” Physical Review Letters 121 (2018): 080404.
11. Jason Gallicchio, Andrew Friedman, and David Kaiser, “Testing Bell’s inequality with cosmic photons: Closing the setting independence loophole,” Physical Review Letters 112 (2014): 110405; Johannes Handsteiner et al., “Cosmic Bell test: Measurement settings from Milky Way stars,” Physical Review Letters 118 (2017): 060401; Dominik Rauch et al., “Cosmic Bell test using random measurement settings from high redshift
Notes 131
quasars,” Physical Review Letters 121 (2018): 080403. See also C. Abellán et al. (The Big Bell Test collaboration), “Challenging local realism with human choices,” Nature 557
(2018): 212– 216.
12. Jason Palmer, “Subatomic opportunities: Quantum leaps,” Economist (March 9, 2017).
13. Kurt Jacobs and Howard Wiseman, “An entangled web of crime: Bell’s Theorem as a short story,” American Journal of Physics 73 (2005): 932– 937; Paul Kwiat and Lucien Hardy, “The mystery of the quantum cakes,” American Journal of Physics 68
(2000): 33– 36; Seth Lloyd, Programming the Universe: A Quantum Computer Scientist takes on the Cosmos (New York: Knopf, 2006), 120– 121; see also Kaiser, How the Hippies Saved Physics, pp. 37– 38.
Chapter 4
1. From a taped discussion with R. Jost on December 2, 1961; quoted in Abraham Pais, Niels Bohr’s Times (New York: Oxford University Press, 1991), p. 318.
2. L. Rosenfeld in Proceedings of the 14th Solvay Conference (New York: Interscience, 1968), p. 232.
3. Letter from Einstein to Schrodinger May 31, 1928, reprinted in “Letters on Wave Mechanics” ed. M. Klein (New York: Philosophical Library, 1967).
4. Letter to Paul Ehrenfest, quoted in Abraham Pais, Subtle Is the Lord (New York: Oxford University Press, 1982), pp. 416– 417.
5. David Kaiser, How the Hippies Saved Physics (New York: W. W. Norton, 2011), p. 164.
6. Kaiser, p. 143.
7. John Clauser, “Early history of Bell’s Theorem,” in Quantum [Un]speakables: From Bell to Quantum Information, ed. R. A. Bertlmann and A. Zeilinger (Berlin: Springer
Verlag, 2002), p. 72.
Chapter 7
1. Einstein, Podolsky, and Rosen, “Can quantum mechanical description of physical reality be considered complete?,” p. 777.
2. Leon Rosenfeld, in S. Rozental, ed., Niels Bohr, His Life and Work as Seen by His Friends and Colleagues, (Amsterdam: North Holland, 1967), pp. 128– 129.
3. Andrew Whitaker in Bertlmann and Zeilinger, Quantum [Un]speakables, p. 15.
4. In Graham Farmelo, “Random acts of science,” New York Times Sunday Book Review, June 11, 2010.
132 Notes
5. In Douglas Huff and Omer Prewett, eds., The Nature of the Physical Universe: 1976
Nobel Conference (New York: John Wiley & Sons, 1979), p. 29.
Chapter 10
1. Reinhold A. Bertlmann in Quantum [Un]speakables, ed. R. A. Bertlmann and A.
Zeilinger (Berlin: Springer Verlag, 2002), p. 29.
2. Abner Shimony in Bertlmann and Zeilinger, Quantum [Un]speakables, p. 55.
3. M. Bell, K. Gottfried, and M. Veltman, eds., John S. Bell on the Foundations of Quantum Mechanics (World Scientific, 2001), p. 216.
4. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987), p. 28.
5. Bell, p. 2.
6. Bertlmann and Zeilinger, Quantum [Un]speakables, p. 295.
7. George Greenstein and Arthur G. Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics, 2nd ed. (Burlington, MA: Jones and Bartlett, 2006), pp. 142– 148.
Chapter 11
1. David Kaiser, “How the hippies saved physics” (New York: W. W. Norton, 2011), p. xiv.
Chapter 12
1. Louisa Gilder, The Age of Entanglement (New York: Alfred A. Knopf, 2008), p. 253.
2. Interview of John Clauser by Joan Bromberg on May 20, 2002, Niels Bohr Library
& Archives, American Institute of Physics, College Park, MD, www.aip.org/ history
programs/nielsbohrlibrary/oralhistories/25096 (hereafter “AIP Interview”).
3. AIP Interview.
4. AIP Interview.
5. Gilder, The Age of Entanglement, p. 261.
6. AIP Interview.
7. AIP Interview.
8. Clauser, “Early history of Bell’s Theorem,” p. 80.
Notes 133
9. AIP Interview.
10. AIP Interview.
11. Gilder, The Age of Entanglement, pp. 267– 268.
12. Gilder, p. 267.
13. AIP Interview.
14. AIP Interview.
15. Clauser, “Early history of Bell’s Theorem,” p. 62.
16. Clauser, p. 72.
17. David Kaiser “Quantum theory by starlight,” New Yorker (online), February 7, 2017.
Chapter 13
1. AIP Interview.
2. E. T. Jaynes, “Quantum Beats,” in Foundations of Radiation Theory and Quantum Electrodynamics, ed. A. O. Barut (New York: Plenum Press, 1980).
Chapter 16
1. Reinhold A. Bertlmann, “Magic Moments with John Bell,” Physics Today 68, no.
7 (July 2015): 40.
2. Richard
Feynman, “Simulating physics with computers, International Journal of Theoretical Physics 21, nos. 6/7 (1982): 467– 488.
Epigraph
1. Richard Feynman, The Character of Physical Law (Cambridge, MA: MIT Press, 1965), p. 129.
Index
Numbers in italics indicate images.
Abellan, Carlos, 85, 85, 85–90
locality assumption in, 94–96
Abstract thinking, 34, 35
nature violating, 93
Aspect, Alain, 79–82, 80, 85, 93
nonlocality and, 97–100
Atomic bomb, 66, 104
other forms of, 127
“Aunt Martha’s Coffin,” 105
randomness and, 85–90
scientists’ desire to close loopholes in,
Bank transfers, 102–106
90–91
Bell, John, 2–7, 58, 101, 117
Bennett, Charles, 104–105, 106
background of, 57–58
Bohm, David, 98
combination of mathematical quanti
Bohr, Niels, 22–26, 25, 37, 40, 66, 101,
ties by, 61–62
121
GHZ theorem and, 121–122
Brassard, Gilles, 104–105, 106
Greenstein’s meeting with, 59–60
indifference over work of, 65–66
Can QuantumMechanical Description
passion and commitment of, 60–61
of Physical Reality Be Considered
pioneering work of, 61
Complete?,” 37
work of, 55–62
Clauser, John, 71–79, 72
Bell, Mary, 58
desire to discredit quantum theory, 93
Bell’s Theorem, 2–3, 26, 81
CNN, 98
Alain Aspect and, 79–82, 85
Cold War, the, 66–67, 101
Anton Zeilinger and, 82–85
Computers, quantum, 109–111
experiments based on, 63–64
George Greenstein’s early understand
Defense Intelligence Agency, 110
ing of, 45–46, 113–117
as hidden variable theory, 46–53
Einstein, Albert, 6, 17–19, 18, 25, 30, 35,
hidden variable theory and
Quantum Strangeness Page 14