When referencing the primary scientific literature I’ve tried as far as possible to provide the original published article and the relevant preprint, posted on the online preprint archive managed by Cornell University. The preprints can be accessed free of charge from the arXiv home page—http://arxiv.org/—by typing the article identifier in the search window. Where they are given, direct quotes are typically derived from the preprint.
Preamble
2. Albert Einstein, quoted in Maurice Solovine,
Albert Einstein: Lettres à Maurice Solovine, Gauthier-Villars, Paris, 1956. This quote is reproduced in Arthur Fine,
The Shaky Game: Einstein, Realism and the Quantum Theory, 2nd edition (University of Chicago Press, Chicago, 1986), p. 110.
Prologue
1. N. David Mermin, ‘A Bolt from the Blue: The E-P-R Paradox’, in A. P. French and P. J. Kennedy (eds),
Niels Bohr: A Centenary Volume (Harvard University Press, Cambridge, MA, 1985), pp. 141–7.
2. In
The Character of Physical Law (MIT Press, Cambridge, MA, 1967) on p. 129 Richard Feynman famously wrote: ‘I think I can safely say that nobody understands quantum mechanics.’
Chapter 1: The Complete Guide to Quantum Mechanics (Abridged)
1. Quoted in
Abraham Pais, Subtle is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, Oxford, 1982), p. 382.
3. Einstein wrote: ‘Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that
He does not play dice.’ Letter to Max Born, 4 December 1926. Quoted in ibid., p. 443.
4. ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’ was the title of Eugene Wigner’s Richard Courant lecture in mathematical sciences delivered at New York University on 11 May 1959. It was published in
Communications on Pure and Applied Mathematics,
13 (1960), 1–14.
5. Erwin Schrödinger, quoted by Werner Heisenberg in
Physics and Beyond: Memories of a Life in Science (George Allen & Unwin, London, 1971), p. 75.
Chapter 2: Just What is This Thing Called ‘Reality’, Anyway?
1. Steven Weinberg,
Dreams of a Final Theory: The Search for the Fundamental Laws of Nature (Vintage, London, 1993), p. 133.
5. Larry and Andy Wachowski,
The Matrix: The Shooting Script (Newmarket Press, New York, 2001), p. 38.
6. Richard E. Cytowic and David M. Eagleman,
Wednesday is Indigo Blue: Discovering the Brain of Synesthesia (MIT Press, Cambridge, MA, 2009).
7. Thanks to Michela Massimi for spelling this out for me in a personal communication dated 20 March 2019.
8. Philip K. Dick, from the 1978 essay ‘How to Build a Universe that Doesn’t Fall Apart Two Days Later’, included in the anthology
I Hope I Shall Arrive Soon, edited by Mark Hurst and Paul Williams (Grafton Books, London, 1988). This quote appears on p. 10.
9. Bernard d’Espagnat,
Reality and the Physicist: Knowledge, Duration and the Quantum World (Cambridge University Press, Cambridge, UK, 1989), p. 115.
10. Karl Popper, quoted in John Horgan,
The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age (Abacus, London, 1998), p. 35.
11. Werner Heisenberg,
Physics and Philosophy: The Revolution in Modern Science (Penguin, London, 1989; first published 1958), p. 46.
12. Albert Einstein, quoted in Maurice Solovine,
Albert Einstein: Lettres à Maurice Solovine (Gauthier-Villars, Paris, 1956). This quote is reproduced in Arthur Fine,
The Shaky Game: Einstein, Realism and the Quantum Theory, 2nd edition (University of Chicago Press, Chicago, 1986), p. 110.
13. Ian Hacking,
Representing and Intervening: Introductory Topics in the Philosophy of Natural Science (Cambridge University Press, Cambridge, UK, 1983), p. 23.
14. And I have to confess that I first heard about logical positivism from the infamous Australian ‘Bruces’ sketch, which appeared in an episode of
Monty Python’s Flying Circus first broadcast in November 1970 (I was 13). This is set in the Philosophy Department of the University of Woolamaloo, in which all the faculty members are called Bruce. ‘Now, Bruce teaches classical philosophy, Bruce
teaches Hegelian philosophy, and Bruce here teaches logical positivism and is also in charge of the sheep dip.’ From
Monty Python’s Flying Circus: Just the Words, volume 1 (Mandarin Paperbacks, London, 1990), p. 295.
15. Einstein was forever indebted to Mach for his approach to physics, but not his aggressively empiricist approach to philosophy. Einstein once commented that ‘Mach was as good at mechanics as he was wretched at philosophy.’ Quoted in Abraham Pais,
Subtle is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, Oxford, 1982). This quote appears on p. 283.
16. For a much more detailed discussion of this aspect of the use of mathematics in physics, I strongly recommend Giovanni Vignale,
The Beautiful Invisible: Creativity, Imagination, and Theoretical Physics (Oxford University Press, Oxford, 2011).
17. For an example of a scientist arguing for the acceptance of absolute spacetime see Brian Greene,
The Fabric of the Cosmos: Space, Time and the Texture of Reality (Allen Lane, London, 2004), p. 75 (where he writes: ‘spacetime is a something’).
18. Thomas Huxley, ‘Biogenesis and Abiogenesis’, Presidential Address to the British Association for the Advancement of Science, 1870,
Collected Essays: Discourses Biological and Geological, volume 8, p. 229. See:
https://mathcs.clarku.edu/huxley/CE8/B-Ab.html. ‘Harsh’, ‘brutal’, and ‘ugly’—I’m clearly not the first to think that Empirical Reality is a pretty mean-spirited place.
19. Pierre Duhem,
The Aim and Structure of Physical Theory, English translation of the second French edition of 1914 by Philip P. Wiener (Princeton University Press, Princeton, NJ, 1954), p. 145.
Chapter 3: Sailing on the Sea of Representation
2. Bertrand Russell,
The Problems of Philosophy (Oxford University Press, Oxford, 1912), p. 35.
3. For an overview of the philosophical programme of naturalized metaphysics, see James Ladyman and Don Ross, with David Spurrett and John Collier,
Every Thing Must Go: Metaphysics Naturalized (Oxford University Press, Oxford, 2007).
4. Michela Massimi, personal communication, 25 March 2019.
5. Karl Popper,
Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge & Kegan Paul, London, 1963), p. 49.
6. Lee Smolin,
Time Reborn: From the Crisis in Physics to the Future of the Universe (Penguin Books, London, 2013), p. 38.
7. Albert Einstein, letter to Paul Ehrenfest, 17 January 1916, quoted in Robert E. Kennedy,
A Student’s Guide to Einstein’s Major Papers (Oxford University Press, Oxford, 2012). The quote appears on p. 214.
8. Paul Feyerabend,
Against Method, 3rd edition (Verso, London, 1993), pp. 52–3.
9. Larry Laudan, ‘The Demise of the Demarcation Problem’, in R. S. Cohen and L. Laudan (eds),
Physics, Philosophy and Psychoanalysis (D. Riedel, Dordrecht, 1983), p. 125.
10. Massimo Pigliucci, in Massimo Pigliucci and Maarten Boudry (eds),
The Philosophy of Pseudoscience: Reconsidering the Demarcation Problem (University of Chicago Press, Chicago, 2013), p. 26.
11. Popper,
Conjectures and Refutations, p. 346. The italics are mine.
12. Albert Einstein, ‘On the Generalised Theory of Gravitation’,
Scientific American, April 1950, p. 13.
13. Don Ross, James Ladyman, and David Spurrett, ‘In Defence of Scientism’, in Ladyman and Ross,
Every Thing Must Go, pp. 33–8.
14. See, for example, Lee Smolin,
The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next (Penguin Books, London, 2008), and Jim Baggott,
Farewell to Reality: How Fairy-tale Physics Betrays the Search for Scientific Truth (Constable, London, 2013).
15. Gottfried Wilhelm Leibniz, from his correspondence with Samuel Clarke (1715–16),
Collected Writings, edited by G. H. R. Parkinson (J. M. Dent & Sons, London, 1973), p. 226.
16. Isaac Newton,
Mathematical Principles of Natural Philosophy, first American edition, translated by Andrew Motte (Daniel Adee, New York, 1845), p. 73.
17. Ernst Mach,
The Science of Mechanics: A Critical and Historical Account of Its Development, 4th edition, translated by Thomas J. McCormack (Open Court Publishing, Chicago, 1919), p. 194.
18. Albert Einstein, ‘Does the Inertia of a Body Depend on its Energy Content?’,
Annalen der Physik,
18 (1905), 639–41. This paper is translated and reproduced in John Stachel (ed.),
Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics, centenary edition (Princeton University Press, Princeton, NJ, 2005). The quote appears on p. 164.
19. See my book
Mass: The Quest to Understand Matter from Greek Atoms to Quantum Fields (Oxford University Press, Oxford, 2017).
20. See, for example, Richard Boyd, ‘On the Current Status of Scientific Realism’,
Erkenntnis 19 (1983), 45–90. Reproduced in Richard Boyd, Philip Gaspar, and J. D. Trout (eds),
The Philosophy of Science (MIT Press, Cambridge, MA, 1991), see especially p. 195.
21. Hilary Putnam,
Mathematics, Matter and Method (Cambridge University Press, Cambridge, UK, 1975), p. 73. Quoted in James Ladyman, ‘Structural Realism’,
Stanford Encyclopedia of Philosophy, Winter 2016, p. 6.
22. Ian Hacking,
Representing and Intervening: Introductory Topics in the Philosophy of Natural Science (Cambridge University Press, Cambridge, UK, 1983), p. 31. The italics are mine.
Chapter 4: When Einstein Came Down to Breakfast
1. Niels Bohr, quoted by Aage Petersen, ‘The Philosophy of Niels Bohr’,
Bulletin of the Atomic Scientists,
19 (1963), 12.
2. A careful analysis of Bohr’s philosophical influences and writings suggests that he was closer to the tradition known as
pragmatism than to positivism. Pragmatism, founded by Charles Sanders Pierce, has many of the characteristics of positivism in that they both roundly reject metaphysics. There are differences, however. We can think of the positivist doctrine as one of ‘seeing is believing’: what we can know is limited by what we can observe empirically. The pragmatist doctrine admits a more practical (or, indeed, pragmatic) approach: what we can know is limited not by what we
can see, but by what we can
do. See, for example, Dugald Murdoch,
Niels Bohr’s Philosophy of Physics (Cambridge University Press, Cambridge, UK, 1987).
3. Werner Heisenberg,
The Physical Principles of the Quantum Theory (University of Chicago Press, Chicago, 1930). Republished in 1949 by Dover Publications, New York. This quote appears in the preface.
4. Max Born and Werner Heisenberg, ‘Quantum Mechanics’,
Proceedings of the Fifth Solvay Congress, 1928. English translation from Guido Bacciagaluppi and Antony Valentini,
Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference (Cambridge University Press, Cambridge, UK, 2009), p. 437.
5. Albert Einstein ‘General Discussion’,
Proceedings of the Fifth Solvay Congress, 1928. English translation from Bacciagaluppi and Valentini,
Quantum Theory at the Crossroads, p. 488.
6. Otto Stern, interview with Res Jost, 2 December 1961. Quoted in Abraham Pais,
Subtle is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, Oxford, 1982), p. 445.
7. Niels Bohr, in Paul Arthur Schilpp (ed.), ‘Discussion with Einstein on Epistemological Problems in Atomic Physics’, in
Albert Einstein. Philosopher-scientist, The Library of Living Philosophers, Volume 1 (Harper & Row, New York, 1959; first published 1949), p. 224.
8. Albert Einstein, quoted by Hendrik Casimir in a letter to Abraham Pais, 31 December 1977. Quoted in Pais,
Subtle is the Lord, p. 449.
9. Albert Einstein, Boris Podolsky, and Nathan Rosen, ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’,
Physical Review,
47 (1935), 777–80. This paper is reproduced in John Archibald Wheeler and Wojciech Hubert Zurek (eds),
Quantum Theory and Measurement (Princeton University Press, Princeton, NJ, 1983), pp. 138–41. This quote appears on p. 138.
10. Einstein, Podolsky, and Rosen, ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’ Also Wheeler and Zurek (eds),
Quantum Theory and Measurement, p. 141.
11. Léon Rosenfeld, in Stefan Rozenthal (ed.),
Niels Bohr: His Life and Work as Seen by his Friends and Colleagues (North-Holland, Amsterdam, 1967), pp. 114–36. Extract reproduced in Wheeler and Zurek (eds),
Quantum Theory and Measurement, pp. 137 and 142–3. This quote appears on p. 142.
12. Paul Dirac, interview with Niels Bohr, 17 November 1962,
Archive for the History of Quantum Physics. Quoted in Mara Beller,
Quantum Dialogue (University of Chicago Press, Chicago, 1999), p. 145.
13. Einstein, Podolsky, and Rosen, ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’. Also in Wheeler and Zurek, (eds),
Quantum Theory and Measurement, p. 141.
14. Albert Einstein, letter to Erwin Schrödinger, 8 August 1935. Quoted in
Arthur Fine, The Shaky Game: Einstein, Realism and the Quantum Theory, 2nd edition (University of Chicago Press, Chicago, 1996), p. 78.
15. Erwin Schrödinger, letter to Albert Einstein, 19 August 1935. Quoted ibid., pp. 82–3.
16. Wolfgang Pauli, [review of Dirac,
The Principles of Quantum Mechanics],
Die Naturwissenschaften,
19 (1931), 188–9, quoted in Helge Kragh,
Dirac: A Scientific Biography (Cambridge University Press, Cambridge, UK, 1990), p. 79.
Chapter 5: Quantum Mechanics is Complete So Just Shut Up and Calculate
1. Erwin Schrödinger, letter to Albert Einstein, 7 June 1935. Quoted in
Arthur Fine, The Shaky Game: Einstein, Realism and the Quantum Theory, 2nd edition (University of Chicago Press, Chicago, 1996), pp. 66–7.
2. Albert Einstein, letter to Erwin Schrödinger, 19 June 1935. Ibid., p. 69.
3. Karl R. Popper,
Quantum Theory and the Schism in Physics (Unwin Hyman, London, 1982), pp. 99–100.
4. John Bell, quoted by Andrew Whitaker,
John Stewart Bell and Twentieth-Century Physics: Vision and Integrity (Oxford University Press, Oxford, 2016), p. 57.
5. Lee Smolin, personal communication, 21 June 2017. Quoted in Jim Baggott,
Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe (Oxford University Press, Oxford, 2018), p. 245. The italics are mine.
6. Carlo Rovelli, ‘Relational Quantum Mechanics’,
International Journal of Theoretical Physics,
35 (1996), 1637;
arXiv: quant-ph/9609002v2, 24 February 1997, p. 1.
8. Matteo Smerlak and Carlo Rovelli, ‘Relational EPR’,
Foundations of Physics,
37 (2007), 427–45; arXiv:quant-ph/0604064v3, 4 March 2007, p. 3.
9. Carlo Rovelli, personal communication, 14 October 2018.
10. Smerlak and Rovelli, ‘Relational EPR’, arXiv:quant-ph/0604064v3, p. 5.
11. Rovelli, ‘Relational Quantum Mechanics’, arXiv: quant-ph/9609002v2, p. 4.
12. Anton Zeilinger, ‘A Foundational Principle for Quantum Mechanics’,
Foundations of Physics,
29 (1999), 633.
13. See Jeffrey Bub, ‘Quantum Mechanics Is about Quantum Information’,
Foundations of Physics,
35 (2005), 541–60. See also arXiv:quant-ph/0408020v2, 12 August 2004.
14. Smerlak and Rovelli, ‘Relational EPR’, arXiv:quant-ph/0604064v3, p. 5.
16. Niels Bohr, quoted by Aage Petersen, ‘The Philosophy of Niels Bohr’,
Bulletin of the Atomic Scientists,
19 (1963), 12. The italics are mine.
17. A. J. Ayer, in A. J. Ayer (ed.),
Logical Positivism, Library of Philosophical Movements (Free Press of Glencoe, 1959), p. 11. The italics are mine.
18. Ludwig Wittgenstein,
Tractatus Logico-Philosophicus, translated by C. K. Ogden (Kegan Paul, Trench, Trubner, London, 1922), p. 90.
19. N. David Mermin, ‘Could Feynman Have Said This?’,
Physics Today, May 2004, pp. 10–11.
Chapter 6: Quantum Mechanics Is Complete But We Need to Reinterpret What it Says
1. Lucien Hardy, ‘Quantum Theory from Five Reasonable Axioms’, arXiv:quant-ph/0101012v4, 25 September 2001.
2. Giulio Chiribella, quoted by Philip Ball in ‘Quantum Theory Rebuilt from Simple Physical Principles’,
Quanta, 30 August 2017.
3. Karl R. Popper,
Quantum Theory and the Schism in Physics (Unwin Hyman, London, 1982), p. 72.
4. Robert Griffiths, personal communication, 5 November 2018.
5. Robert B. Griffiths,
Consistent Quantum Theory (Cambridge University Press, Cambridge, UK, 2002), p. 214.
6. Robert B. Griffiths, ‘The Consistent Histories Approach to Quantum Mechanics’,
Stanford Encyclopedia of Philosophy, Spring 2017, p. 3.
7. Fay Dowker and Adrian Kent, ‘On the Consistent Histories Approach to Quantum Mechanics’,
Journal of Statistical Physics,
82 (1996), 1575–1646. See also arXiv:gr-qc/9412067v2, 25 January 1996.
8. Griffiths, ‘The Consistent Histories Approach to Quantum Mechanics’, p. 46.
9. Werner Heisenberg,
Physics and Philosophy: The Revolution in Modern Science (Penguin, London, 1989; first published 1958), p. 46. The italics are mine.
10. Carlton M. Caves, Christopher A. Fuchs, and Rüdiger Schack, ‘Quantum Probabilities as Bayesian Probabilities’,
Physical Review A,
65 (2002), 022305. See also arXiv:quant-ph/0106133v2, 14 November 2001.
11. Richard Healey, ‘Quantum-Bayesian and Pragmatist Views of Quantum Theory’,
Stanford Encylopedia of Philosophy, Spring 2017, p. 9.
12. N. David Mermin, ‘Annotated Interview with a QBist in the Making’, arXiv:quant-ph/1301.6551.v1, 28 January 2013. However, Mermin interprets ‘QBism’ a little differently, preferring to acknowledge Bruno de Finetti, a pioneer of subjective probability, rather than Bayes. The ‘B’ then stands for ‘Bruno’.
13. Schack has argued that Hardy’s ‘five reasonable axioms’ can be reduced to four, by reinterpreting the first in terms of Bayesian probabilities and by modifying part of the proof. See Rüdiger Schack, ‘Quantum Theory from Four of Hardy’s Axioms’,
Foundations of Physics,
33 (2003), 1461–8. See also arXiv:quant-ph/0210017v1, 2 October 2002.
14. Christopher A. Fuchs, N. David Mermin, and Rüdiger Schack, ‘An Introduction to QBism with an Application to the Locality of Quantum Mechanics’,
American Journal of Physics,
82 (2014), 749–54. See also arXiv:quant-ph/1311.5253v1, 20 November 2013.
15. Mermin talks about CBism, the classical analogue of QBism. See N. David Mermin, ‘Making Better Sense of Quantum Mechanics’, arXiv:quant-ph/1809.01639v1, 5 September 2018.
16. Chrisopher A. Fuchs, ‘On Participatory Realism’, arXiv:quant-ph/1601.04360v3, 28 June 2016, p. 11.
Chapter 7: Quantum Mechanics is Incomplete So We Need to Add Some Things
1. John Bell,
Journal de Physique Colloque C2, Supplement 3,
42 (1981), 41–61. Reproduced in J. S. Bell,
Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, UK, 1987), pp. 139–58. This quote appears on p. 142.
2. Darrin W. Belousek, ‘Einstein’s 1927 Unpublished Hidden-Variable Theory: Its Background, Context and Significance’,
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics,
27 (1996), 437–61. Peter Holland takes a closer look at Einstein’s reasons for rejecting this approach in ‘What’s Wrong with Einstein’s 1927 Hidden-Variable Interpretation of Quantum Mechanics’,
Foundations of Physics,
35 (2005), 177–96; arXiv:quant-ph/0401017v1, 5 January 2004.
3. ‘It should be noted that we need not go any further into the mechanism of the “hidden parameters”, since we now know that the established results of quantum mechanics can never be re-derived with their help.’ John von Neumann,
Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955), p. 324.
4. According to Basil Hiley, one of Bohm’s long-term collaborators, Bohm said of his meeting with Einstein: ‘After I finished [
Quantum Theory] I felt strongly that there was something seriously wrong. Quantum theory had no place in it for an adequate notion of an individual actuality. My discussions with Einstein clarified and reinforced my opinion and encouraged me to look again.’ Quoted by Basil Hiley, personal communication to the author, 1 June 2009.
5. David Bohm,
Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951), p. 623.
6. D. Bohm and Y. Aharonov, ‘Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky’,
Physical Review,
108 (1957), 1070.
7. John Bell, in P. C. W. Davies and J. R. Brown (eds),
The Ghost in the Atom (Cambridge University Press, Cambridge, UK, 1986), p. 57.
8. John Bell, ‘Bertlmann’s Socks and the Nature of Reality’,
Journal de Physique Colloque C2, Supplement 3,
42 (1981), 41–61. Reproduced in
Bell,
Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge University Press, Cambridge, UK, 1987), pp. 139–58. This quote appears on p. 139.
9. This pictorial representation is based on Bernard d’Espagnat, ‘The Quantum Theory and Reality’,
Scientific American,
241 (1979), 158–81. See p.
162.
10. John Bell, ‘Locality in Quantum Mechanics: Reply to Critics’,
Epistemological Letters, November 1975, pp. 2–6. This paper is reproduced in Bell,
Speakable and Unspeakable in Quantum Mechanics, pp. 63–6. This quote appears on p. 65.
11. Simon Kochen and E. P. Specker, ‘The Problem of Hidden Variables in Quantum Mechanics’,
Journal of Mathematics and Mechanics,
17 (1967), 59–87.
12. John S. Bell, ‘On the Problem of Hidden Variables in Quantum Theory’,
Reviews of Modern Physics,
38 (1966), 447–52. This paper is reproduced in Bell,
Speakable and Unspeakable in Quantum Mechanics, pp. 1–13.
13. Calcite is a naturally birefringent form of calcium carbonate. It has a crystal structure which has different refractive indices along two distinct crystal planes. One offers an axis of maximum transmission for vertically polarized light and the other offers an axis of maximum transmission for horizontally polarized light. The vertical and horizontal components of either left- or right-circularly polarized light are therefore physically separated by passage through the crystal, and their intensities can be measured separately. With careful machining, a calcite crystal can transmit virtually all of the light incident on it.
14. Alain Aspect, Philippe Grangier, and Gérard Roger, ‘Experimental Tests of Realistic Local Theories via Bell’s Theorem’,
Physical Review Letters,
47 (1981), 460–3. Alain Aspect, Philippe Grangier, and Gérard Roger, ‘Experimental Realization of Einstein–Podolsky–Rosen–Bohm
Gedankenexperiment: A New Violation of Bell’s Inequalities’,
Physical Review Letters, 49 (1982), 91–4.
15. Alain Aspect, Jean Dalibard, and Gérard Roger, ‘Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers’,
Physical Review Letters, 49 (1982), 1804–7.
16. W. Tittel, J. Brendel, N. Gisin, and H. Zbinden, ‘Long-Distance Bell-Type Tests Using Energy-Time Entangled Photons’,
Physical Review A,
59 (1999), 4150–63.
17. Thomas Scheidl, Rupert Ursin, Johannes Kofler, Sven Ramelow, Xiao-Song Ma, Thomas Herbst, Lothar Ratschbacher, Alessandro Fedrizzi, Nathan K. Langford, Thomas Jennewein, and Anton Zeilinger, ‘Violation of Local Realism with Freedom of Choice’,
Proceedings of the National Academy of Sciences,
107 (2010), 19708–13.
18. Dominik Rauch, Johannes Handsteiner, Armin Hochrainer, Jason Gallicchio, Andrew S. Friedman, Calvin Leung, Bo Liu, Lukas Bulla, Sebastian Ecker, Fabian Steinlechner, Rupert Ursin, Beili Hu, David Leon, Chris Benn, Adriano Ghedina, Massimo Cecconi, Alan H. Guth, David I. Kaiser, Thomas Scheidl, and Anton Zeilinger, ‘Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars’,
Physical Review Letters,
121 (2018), 080403.
19. Jian-Wei Pan, Dik Bouwmeester, Matthew Daniell, Harald Weinfurter, and Anton Zeilinger, ‘Experimental Test of Quantum Nonlocality in Three-Photon Greenburger-Horne-Zeilinger Entanglement’,
Nature,
403 (2000), 515–19.
20. A. J. Leggett, ‘Nonlocal Hidden-Variable Theories and Quantum Mechanics: An Incompatibility Theorem’,
Foundations of Physics,
33 (2003), 1469–93. This quote appears on pp. 1474–5.
21. Simon Gröblacher, Tomasz Paterek, Rainer Kaltenbaek, Caslav Brukner, Marek Zukowski, Markus Aspelmeyer, and Anton Zeilinger, ‘An Experimental Test of Non-local Realism’,
Nature,
446 (2007), 871–5. In case you were wondering, Bell’s inequality is violated in these experiments, too.
22. Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph, ‘On the Reality of the Quantum State’,
Nature Physics,
8 (2012), 475–8.
23. For an excellent overview, see Matthew Saul Leifer, ‘Is the Quantum State Real? An Extended Overview of
ψ–ontology Theorems’,
Quanta,
3 (2014), 67–155.
Chapter 8: Quantum Mechanics is Incomplete So We Need to Add Some Other THINGS
1. See, for example, Guiseppe Pucci, Daniel M. Harris, Luiz M. Faria, and John W. M. Bush, ‘Walking Droplets Interacting with Single and Double Slits’,
Journal of Fluid Mechanics,
835 (2018), 1136–56.
3. Peter R. Holland, The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics (Cambridge University Press, Cambridge, UK, 1993), p. 475.
5. Albert Einstein, letter to Max Born, 12 May 1952. Quoted in John S. Bell,
Proceedings of the Symposium on Frontier Problems in High Energy Physics, Pisa, June 1976, pp. 33–45. This paper is reproduced in J. S. Bell,
Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge University Press, Cambridge, UK, 1987), pp. 81–92. The quote appears on p. 91.
6. See James T. Cushing,
Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony (University of Chicago Press, Chicago, 1994).
7. J. S. Bell, ‘On the Impossible Pilot Wave’,
Foundations of Physics,
12 (1982), 989–99. This paper is reproduced in Bell,
Speakable and Unspeakable in Quantum Mechanics, pp. 159–68.
8. J. S. Bell, ‘Against Measurement’,
Physics World,
3 (1990), 33.
9. These estimates are taken from Roland Omnès,
The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1994). The original calculations were reported in E. Joos and H. D. Zeh,
Zeitschrift für Physik,
B59 (1985), 223–43.
10. For some examples, see Serge Haroche, ‘Entanglement, Decoherence and the Quantum/Classical Boundary’,
Physics Today, July 1998, 36–42.
11. Frédéric Bouchard, Jérémie Harris, Harjaspreet Mand, Nicolas Bent, Enrico Santamato, Robert W. Boyd, and Ebrahim Karimi, ‘Observation of Quantum Recoherence of Photons by Spatial Propagation’,
Nature Scientific Reports (2015), 5:15330.
12. Markus Arndt, Olaf Nairz, Julian Voss-Andreae, Claudia Keller, Gerbrand van der Zouw, and Anton Zeilinger, ‘Wave-particle Duality of C
60 molecules’,
Nature,
401 (1999), 680–2; Markus Arndt, Olaf Nairz, J. Petschinka, and Anton Zeilinger, ‘High Contrast Interference with C
60 and C
70’,
Comptes Rendus de l’Académie des Sciences—Series IV—Physics,
2 (2001), 581–5; and Stefan Gerlich, Sandra Eibenberger, Mathias Tomandl, Stefan Nimmrichter, Klaus Hornberger, Paul J. Fagan, Jens Tüxen, Marcel Mayor, and Markus Arndt, ‘Quantum Interference of Large Organic Molecules’,
Nature Communications (2011), 2:263. The analogies and puns are endless. The ratio of the diameter of a C
60 molecule and the spacing of the silicon nitride grating used to observe the diffraction pattern is comparable to the ratio of the diameter of a conventional soccer ball and the width of a goal (according to FIFA standards), giving a potentially whole new meaning to the term ‘bend it like Beckham’.
13. See, for example, Jonathan R. Friedman, Vijay Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, ‘Quantum Superposition of Distinct Macroscopic States’,
Nature,
406 (2000), 43–6, and Caspar H. van der Wal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, Seth Lloyd, and J. E. Moonij, ‘Quantum Superposition of Macroscopic-Persistent States’,
Science,
290 (2000), 773–7.
14.Bell, ‘Against Measurement’, 33.
15. Roger Penrose,
The Large, the Small and the Human Mind, Canto edition (Cambridge University Press, Cambridge, UK, 2000), p. 82. Note that the collapse of the wavefunction is sometimes referred to as the ‘reduction’ of the wavefunction.
16. For example, in the second edition of David J. Griffiths’ popular textbook
Introduction to Quantum Mechanics, published by Cambridge University Press in 2017, decoherence is mentioned just once, in a footnote.
17. See G. C. Ghirardi, A. Rimini, and T. Weber, ‘Unified Dynamics for Microscopic and Macroscopic Systems’,
Physical Review D,
34 (1986), 470–91; and P. Pearle, ‘Combining Stochastic Dynamical State-Vector Reduction with Spontaneous Localization’,
Physical Review A,
39 (1989), 2277–89. Although they’re not entirely equivalent, the ‘state vector’ referred to in the title of this paper can be taken to be similar to the wavefunction.
18. J. S. Bell, ‘Are There Quantum Jumps?’, in C. W. Kilmister (ed.),
Schrödinger: Centenary Celebration of a Polymath (Cambridge University Press, Cambridge,UK, 1987), pp. 41–52. This article is reproduced in
Bell,
Speakable and Unspeakable in Quantum Mechanics, pp. 201–12. This quote appears on p. 204.
19. Giancarlo Ghirardi, ‘Collapse Theories’,
Stanford Encylopedia of Philosophy, Substantive Revision, February 2016, p. 51.
20. John Wheeler, with Kenneth Ford,
Geons, Black Holes and Quantum Foam: A Life in Physics (W.W. Norton, New York, 1998), p. 235.
21. L. Diósi, ‘A Universal Master Equation for the Gravitational Violation of Quantum Mechanics’,
Physical Letters A,
120 (1987), 377–81; L. Diósi, ‘Models for Universal Reduction of Macroscopic Quantum Fluctuations’,
Physical Review A,
40 (1989), 1165–74; and Roger Penrose, ‘On Gravity’s Role in Quantum State Reduction’,
General Relativity and Gravitation,
28 (1996), 581–600.
22. Roger Penrose,
The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics (Vintage, London, 1990), p. 475.
23. See Jim Baggott,
Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe (Oxford University Press, Oxford, 2018), pp. 259–62.
24. Roger Penrose,
Fashion, Faith and Fantasy in the New Physics of the Universe (Princeton University Press, Princeton, NJ, 2016), p. 215.
25. Rainer Kaltenbaek, Gerald Hechenblaikner, Nikolai Kiesel, Oriol Romero-Isart, Keith C. Schwab, Ulrich Johann, and Markus Aspelmeyer, ‘Macroscopic Quantum Resonators (MAQRO)’,
Experimental Astronomy,
34 (2012), 123–64, see also arXiv:quant-ph/1201.4756v2, 19 March 2012.
26. Rainer Kaltenbaek, et al., ‘Macroscopic Quantum Resonators (MAQRO): 2015 Update’,
EPJ Quantum Technology,
3 (2016), 5.
Chapter 9: Quantum Mechanics is Incomplete Because We Need to Include My Mind (Or Should That Be Your Mind?)
1. John von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955), p. 420.
3. L. Szilard, ‘On Entropy Reduction in a Thermodynamic System by Interference by Intelligent Beings’,
Zeitschrift fur Physik,
53 (1929), 840–56. NASA Technical Translation F-16723.
4. Max Jammer,
The Philosophy of Quantum Mechanics (Wiley, New York, 1974), p. 480. The italics are mine.
5. Eugene Wigner was another Hungarian compatriot. Together with Szilard and Edward Teller, Wigner was part of the ‘Hungarian conspiracy’ that influenced Einstein to write a letter to US President Franklin D. Roosevelt on 2 August 1939 warning of ‘extremely powerful bombs of a new type’. See Jim Baggott,
Atomic: The First War of Physics and the Secret History of the Atom Bomb 1939–49 (Icon Books, London, 2009), pp. 18–19.
6. Eugene Wigner, ‘Remarks on the Mind-Body Question’, in I. J. Good (ed.),
The Scientist Speculates: An Anthology of Partly-Baked Ideas (Heinemann, London, 1961), pp. 284–302. This is reproduced in John Archibald Wheeler and Wojciech Hubert Zurek (eds),
Quantum Theory and Measurement (Princeton University Press, Princeton, NJ, 1983), pp. 168–81. These quotes appear on pp. 176–8.
7. John Archibald Wheeler, ‘Law without Law’, in Wheeler and Zurek (eds), Quantum Theory and Measurement, pp. 182–213. This quote appears on p. 184.
9. John Archibald Wheeler, ‘Genesis and Observership’, in Robert E. Butts and Jaakko Hintikka (eds),
Foundational Problems in the Special Sciences (D. Reidel, Dordrecht, Holland, 1977), p. 28. Wheeler was referring to Robert Dicke, who highlighted the ‘fine tuning’ in physical laws and constants that seems to be necessary in order for life to be possible in the Universe, and Brandon Carter, who developed the anthropic principle in 1974 as a direct challenge to the Copernican principle.
10. John Wheeler, with Kenneth Ford,
Geons, Black Holes and Quantum Foam: A Life in Physics (W.W. Norton, New York, 1998), p. 338.
11. John D. Barrow and Frank Tipler,
The Anthropic Cosmological Principle (Oxford University Press, Oxford, 1986), p. 22. Italics in the original.
12. David J. Chalmers, ‘Facing up to the problem of consciousness’,
Journal of Consciousness Studies,
2 (1995), 200–19.
13. Neuroscientists Stephen Macknik and Susana Martinez-Conde explore the neuroscience of magic in their entertaining book
Sleights of Mind, published by Profile Books, London, 2011.
14. Gilbert Ryle,
The Concept of Mind (Hutchinson, London, 1949).
15. Daniel Dennett,
Consciousness Explained (Penguin, London, 1991).
16. Not all neuroscientists agree. For a lucid and witty rebuttal of the reductionist approach, I recommend Raymond Tallis,
Aping Mankind: Neuromania, Darwinitis, and the Misrepresentation of Humanity (Routledge Classics, London, 2016). For alternative ‘top-down’ arguments, see George Ellis,
How Can Physics Underlie the Mind: Top-Down Causation in the Human Context (Springer-Verlag, Berlin, 2016).
17. Cambridge Declaration on Consciousness, 7 July 2012.
18. Roger Penrose, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics (Vintage, London, 1990), p. 540.
20. Recent computer simulations of the molecular dynamics of a guanosine diphosphate (GDP) bound tubulin made use of a structure consisting of 13,432 atoms, not counting the 150,510 water molecules which surrounds and ‘solvates’ it. See Yeshitila Gebremichael, Jhih-Wei Chu, and Gregory A. Voth, ‘Intrinsic Bending and Structural Rearrangement of Tubulin Dimer: Molecular Dynamics Simulations and Coarse-Grained Analysis’,
Biophysical Journal,
95 (2008), 2487–99.
21. Max Tegmark, ‘The Importance of Quantum Decoherence in Brain Processes’,
Physical Review E,
61 (2000), 4194–206. See also arXiv:quant-ph/9907009v2, 10 November 1999.
22. Satyajit Sahu, Subrata Ghosh, Kazuto Hirata, Daisuke Fujita, and Anirban Bandyopadhyay, ‘Multi-level Memory-Switching Properties of a Single Brain Microtubule’,
Applied Physics Letters,
102 (2013), 123701.
23. Stuart Hameroff and Roger Penrose, ‘Consciousness in the Universe: A Review of the “Orch-OR” Theory’,
Physics of Life Reviews,
11 (2014), 70.
24. Chalmers, ‘Facing up to the problem of consciousness’, pp. 200–19. The italics are mine.
Chapter 10: Quantum Mechanics is Incomplete Because…. Okay, I Give Up
1. Albert Einstein, ‘Approximative Integration of the Field Equations of Gravitation’,
Preussische Akademie der Wissenschaften (Berlin) Sitzungsberichte, 1916, 688–96. Quoted in Gennady E. Gorelik and
Viktor Ya. Frenkel,
Matvei Petrovich Bronstein and Soviet Theoretical Physics in the Thirties (Birkhäuser Verlag, Basel, 1994). The quote appears on p. 86.
2. Hugh Everett III, ‘ “Relative State” Formulation of Quantum Mechanics’,
Reviews of Modern Physics,
29 (1957), 454–62. This is reproduced in John Archibald Wheeler and Wojciech Hubert Zurek (eds),
Quantum Theory and Measurement (Princeton University Press, Princeton, NJ), 1983, pp. 315–23. This quote appears on p. 316. Italics in the original. I should point out that Everett left academia and joined the Pentagon’s Weapons System Evaluation Group in June 1956, and although this paper doesn’t carry Wheeler’s name it represents a compromise that Everett was never entirely happy with.
3. Hugh Everett III, ‘The Theory of the Universal Wave Function’, Princeton University PhD Thesis. This is reproduced in B. S. DeWitt and N. Graham (eds),
The Many Worlds Interpretation of Quantum Mechanics (Pergamon Press, Oxford, 1975). The italics are mine.
4. Everett, ‘The Theory of the Universal Wave Function’, footnote on p. 68. Italics in the original.
5. Stefano Osnaghi, Fábio Freitas, and Olival Freire Jr, ‘The Origin of the Everettian Heresy’,
Studies in the History and Philosophy of Modern Physics,
40 (2009), 111.
6. Everett, ‘The Theory of the Universal Wave Function’, p. 9.
8. Bryce S. DeWitt, ‘Quantum Mechanics and Reality’,
Physics Today,
23 (1970), 30. This is reproduced in DeWitt and Graham (eds),
The Many Worlds Interpretation of Quantum Mechanics.
9. John Wheeler, in P. C. W. Davies and J. R. Brown (eds),
The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics (Cambridge University Press, Cambridge, UK, 1986), p. 60.
10. J. A. Wheeler, letter to Paul Benioff, 7 July 1977. Quoted by Shikhovtsev, ‘Biographical Sketch of Hugh Everett, III’.
11. DeWitt, ‘Quantum Mechanics and Reality’, p. 33.
12. This is an observation frequently attributed to John Wheeler, but I picked it up from the interview with David Deutsch which appears in Davies and Brown,
The Ghost in the Atom, p. 84.
13. H. D. Zeh, ‘The Problem of Conscious Observation in Quantum Mechanical Description’,
Foundations of Physics Letters,
13 (2000), 221–33. See also arXiv:quant-ph/9908084v3, 5 June 2000. Zeh explains that this paper is an update of a paper that was first informally circulated through the
Epistemological Letters of the Ferdinand-Gonseth Association in Biel, Switzerland, in 1981.
14. Michael Lockwood,
Mind, Brain and the Quantum. The Compound ‘I’ (Blackwell, Oxford, 1990).
15. David Z. Albert,
Quantum Mechanics and Experience (Harvard University Press, Cambridge, MA, 1992).
16. J. S. Bell, ‘Quantum Mechanics for Cosmologists’, in C. Isham, R. Penrose, and D. Sciama (eds),
Quantum Gravity 2 (Clarendon Press, Oxford, 1981). This paper is reproduced in J. S. Bell,
Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, UK, 1987), pp. 117–38. This quote appears on p. 118.
17. Murray Gell-Mann,
The Quark and the Jaguar: Adventures in the Simple and the Complex (Little, Brown, London, 1994), p. 138.
18. Adrian Kent, ‘One World versus Many: The Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation’, in Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace (eds),
Many Worlds? Everett, Quantum Theory, & Reality (Oxford University Press, Oxford, 2010), p. 310.
19. David Deutsch, The Fabric of Reality (Allen Lane, London, 1997), p. 45.
22. Max Tegmark, ‘The Interpretation of Quantum Mechanics: Many Worlds or Many Words?’,
Fortschritte der Physik,
46 (1998), 855–62. See also arXiv:quant-ph/9709032v1, 15 September 1997. This quote appears on p. 5.
23. David Wallace, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation (Oxford University Press, Oxford, 2012), p. 158.
25. Lev Vaidman, ‘Review: David Wallace,
The Emergent Multiverse’,
British Journal for the Philosophy of Science,
66 (2014), 465–8. See also Lev
Vaidman, ‘Many-Worlds Interpretation of Quantum Mechanics’,
Stanford Encyclopedia of Philosophy, substantive revision 17 January 2014.
26. David Wallace, ‘Decoherence and Ontology (or: How I Learned to Stop Worrying and Love FAPP)’, in Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace (eds),
Many Worlds? Everett, Quantum Theory, & Reality (Oxford University Press, Oxford, 2010), p. 62.
27. R. Raussendorf and H. J. Briegel, ‘A One-Way Quantum Computer’,
Physics Review Letters,
86 (2001), 5188–91.
28. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, ‘Experimental One-Way Quantum Computing’,
Nature,
434 (2005), 169–76. See also arXiv:quant-ph/0503126, 14 March 2005.
29. Michael Cuffaro, ‘Many Worlds, the Cluster State Quantum Computer, and the Problem of the Preferred Basis’,
Studies in History and Philosophy of Modern Physics,
43 (2012), 35–42. See also arXiv:physics.hist-ph/1110.2514v2, 10 January 2012. This quote appears on p. 17.
30. Michael Cuffaro, personal communication, 19 June 2019.
31. David Wallace, personal communication, 25 June 2019.
32. David Wallace, personal communication, 27 June 2019.
35. Max Tegmark,
Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (Penguin Books, London, 2015); see particularly
Chapter 8.
36. See for example Jim Baggott,
Farewell to Reality: How Fairy-tale Physics Betrays the Search for Scientific Truth (Constable, London, 2013), especially
Chapter 9; and Sabine Hossenfelder,
Lost in Math: How Beauty Leads Physics Astray (Basic Books, New York, 2018).
37. See Christopher A. Fuchs, ‘Copenhagen Interpretation Delenda Est?’, arXiv:quant-ph/1809.05147v2, 11 November 2018.
38. Adam Becker,
What is Real? The Unfinished Quest for the Meaning of Quantum Physics (John Murray, London, 2018), p. 264.
39. Lee Smolin,
Einstein’s Unfinished Revolution: The Search for What Lies beyond the Quantum (Allen Lane, London, 2019), p. xxiii.
40. Helge Kragh,
Higher Speculations: Grand Theories and Failed Revolutions in Physics and Cosmology (Oxford University Press, Oxford, 2011), p. 285. The italics are mine.
41. Albert Einstein, ‘On the Generalized Theory of Gravitation’,
Scientific American,
182 (April 1950), p. 13. Einstein continues: ‘I believe that every true theorist is a kind of tamed metaphysicist, no matter how pure a “positivist” he may fancy himself. The metaphysicist believes that the logically simple is also the real. The tamed metaphysicist believes that not all that is logically simple is embodied in experienced reality, but that the totality of all sensory experience can be “comprehended” on the basis of a conceptual system built on premises of great simplicity.’
42. George Ellis and Joe Silk,
Nature, 516 (2014), 321–3.
43. James Ladyman, personal communication, 29 March 2019.
Epilogue: I’ve Got a Very Bad Feeling About This
1. Lee Smolin, Einstein’s Unfinished Revolution: The Search for What Lies beyond the Quantum (Allen Lane, London, 2019), p. 180.
3. Maximilian Schlosshauer, Johannes Koer, and Anton Zeilinger, ‘A Snapshot of Foundational Attitudes toward Quantum Mechanics’, arXiv:quant-ph/1301.1069v1, 6 January 2013. Before you ask, no, I did not attend. But I was extremely gratified to be invited to talk at a follow-up conference on the same subject, held in Traunkirchen in November 2013, following publication of my book
Farewell to Reality.