by Jed Brody
3. For simplicity, I’m assuming that the hidden variable is deterministic (not random). The key feature of a hidden variable, however, is the realism: the hidden variable, even if it is truly random, determines the properties of an object regardless of whether the object is ever observed.
Chapter 2
1. This effect was first demonstrated by W. Gerlach and O. Stern (1922), “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift für Physik 9: 349–352.
2. A. Einstein, B. Podolsky, and N. Rosen (1935), “Can quantum-mechanical description of physical reality be considered complete?” Physical Review 47: 777–780.
3. J. Bell (1964), “On the Einstein Podolsky Rosen Paradox,” Physics 1: 195–200. Curiously, the date of this paper is sometimes incorrectly given as 1965, sometimes even in Bell’s own book (2004), Speakable and Unspeakable in Quantum Mechanics, 2nd ed. (Cambridge University Press).
4. This average number is called the quantum correlation.
Chapter 3
1. This process is called spontaneous parametric downconversion.
2. This splitting respects conservation of energy: each infrared photon has half the energy of the original violet photon.
3. Even if the hidden variables theory is probabilistic, such that properties are randomly assigned to photons at the moment they’re created, this theory at least conforms to local realism. Quantum theory, in contrast, leaves the properties of the photons undetermined until measurement.
4. S. J. Freedman and J. F. Clauser (1972), “Experimental test of local hidden-variable theories,” Physical Review Letters 28: 938–941.
5. J. Brody and C. Selton (2018), “Quantum entanglement with Freedman’s inequality,” American Journal of Physics 86: 412–416.
6. Philip Ball (2018), Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different (Basic Books).
Chapter 4
1. This example is based partially on V. Scarani (2006), Quantum Physics—A First Encounter: Interference, Entanglement, and Reality (Oxford University Press). The original idea is from J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt (1969), “Proposed experiment to test local hidden-variable theories,” Physical Review Letters 23: 880–884.
2. A realistic analyzer is more complicated because we don’t want to block any photons. For example, we might direct horizontally polarized photons to one detector, and vertically polarized photons to a different detector: each analyzer requires two detectors, as well as a device that separates photons according to polarization.
3. N. Gisin (2014), Quantum Chance: Nonlocality, Teleportation and Other Quantum Marvels (Springer International Publishing). I was also influenced by N. David Mermin’s papers cited later in this chapter.
4. A. Zeilinger (2010), Dance of the Photons (Farrar, Straus and Giroux), based on E. P. Wigner (1970), “On hidden variables and quantum mechanical probabilities,” American Journal of Physics 38: 1005–1009; and B. d’Espagnat (1995), Veiled Reality: An Analysis of Present-Day Quantum Mechanical Concepts (Addison-Wesley).
5. Assuming that the angle between polarizers is between 0° and 90°.
6. More precisely, we know that the other photon will pass through a polarizer set to the same angle as the first polarizer.
7. R. Penrose (2004), The Road to Reality: A Complete Guide to the Laws of the Universe (Alfred A. Knopf).
8. T. Maudlin (2002), Quantum Non-Locality and Relativity, 2nd ed. (Blackwell Publishing). My version of Maudlin’s example appeared previously as the afterword to J. Brody (2017), “Hidden Variables,” in M. Brotherton (ed.), Science Fiction by Scientists (Springer), 67–79.
9. N. D. Mermin (1994), “Quantum mysteries refined,” American Journal of Physics 62: 880–887.
10. N. D. Mermin (1990), “Quantum mysteries revisited,” American Journal of Physics 58: 731–734. I draw also from J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger (2000), “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403: 515–519.
Chapter 5
1. They’ll also disagree about the wavelength of light (Doppler effect), but this can be inferred from their disagreements about lengths and time intervals. Based on these disagreements, they’ll also disagree about the speed of something that is moving relative to both of them.
2. Earth, of course, is rotating about its axis and revolving around the sun. The sun itself is moving in a complicated way around the center of the galaxy. Compared with the accelerating bus, however, we may imagine that Earth is at rest.
3. There are alternative explanations for the twin paradox that do not explicitly depend on acceleration (https://en.wikipedia.org/wiki/Twin_paradox).
Chapter 6
1. B. Skyrms (1982), “Counterfactual definiteness and local causation,” Philosophy of Science 49: 43–50.
2. S. Hossenfelder (2014), “Testing superdeterministic conspiracy,” Journal of Physics: Conference Series 504: 012018.
3. B. S. DeWitt and N. Graham (eds.) (2015), The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press).
4. M. Schlosshauer (2005), “Decoherence, the measurement problem, and interpretations of quantum mechanics,” Reviews of Modern Physics 76: 1267.
5. The “throwing out of the equation” process is called the collapse of the wavefunction.
6. A. Aspect, J. Dalibard, and G. Roger (1982), “Experimental test of Bell’s inequalities using time-varying analyzers,” Physical Review Letters 49: 1804–1807.
7. Three groups achieved this in 2015: B. Hensen et al. (2015), “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers,” Nature 526: 682–686; M. Giustina (2015), “Significant-loophole-free test of Bell’s theorem with entangled photons,” Physical Review Letters 115: 250401; L. K. Shalm et al. (2015), “Strong loophole-free test of local realism,” Physical Review Letters 115: 250402.
8. A. S. Friedman et al. (2019), “Relaxed Bell inequalities with arbitrary measurement dependence for each observer,” Physical Review A 99: 012121.
9. J. Handsteiner et al. (2017), “Cosmic Bell test: Measurement settings from Milky Way Stars,” Physical Review Letters 118: 060401.
10. C. Abellán et al. (2018), “Challenging local realism with human choices,” Nature 557: 212–216.
11. This video game is still available: https://museum.thebigbelltest.org/quest/.
12. J. Maldacena and L. Susskind (2013), “Cool horizons for entangled black holes,” Fortschritte der Physik 61: 781–811.
13. A. Einstein and N. Rosen (1935), “The particle problem in the general theory of relativity,” Physical Review 48: 73–77.
14. N. Gisin (2014), Quantum Chance: Nonlocality, Teleportation and Other Quantum Marvels (Springer International Publishing).
15. As in E. A. Abbott (1884), Flatland (Seeley & Co.).
16. Gisin, Quantum Chance.
17. T. Maudlin (2002), Quantum Non-Locality and Relativity, 2nd ed. (Blackwell Publishing).
18. A. J. Leggett (2003), “Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem,” Foundations of Physics 33: 1469–1493.
19. J. Cartwright (2007), “Quantum physics says goodbye to reality,” Physics World, https://physicsworld.com/a/quantum-physics-says-goodbye-to-reality/.
20. O. Ulfbeck and A. Bohr (2001), “Genuine fortuitousness. Where did that click come from?” Foundations of Physics 31: 757–774.
21. C. A. Fuchs, N. D. Mermin, and R. Schack (2014), “An introduction to QBism with an application to the locality of quantum mechanics,” American Journal of Physics 82: 749–754.
Further Reading
Ball, Philip. 2018. Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different. Chicago: University of Chicago Press.
Becker, Adam. 2018. What Is Real? The Unfinished Quest for the Meaning of Quantum Physics. New York: Basic Books.
&
nbsp; Brody, Jed. 2017. “Hidden Variables.” In Science Fiction by Scientists, ed. Michael Brotherton, 67–79. Cham, Switzerland: Springer International Publishing.
Bub, Tanya, and Jeffrey Bub. 2018. Totally Random: Why Nobody Understands Quantum Mechanics. Princeton: Princeton University Press.
Capra, Fritjof. [1975] 2013. The Tao of Physics: An Exploration of the Parallels between Modern Physics and Eastern Mysticism, 5th ed. Boulder: Shambhala Publications.
Fuchs, Christopher A., N. David Mermin, and Rudiger Schack. 2014. “An introduction to QBism with an application to the locality of quantum mechanics.” American Journal of Physics 82: 749–754.
Gilder, Louisa. 2008. The Age of Entanglement: When Quantum Physics Was Reborn. New York: Alfred A. Knopf.
Gisin, Nicolas. 2014. Quantum Chance: Nonlocality, Teleportation and Other Quantum Marvels. New York: Springer International Publishing.
Greenstein, George S. 2019. Quantum Strangeness: Wrestling with Bell’s Theorem and the Ultimate Nature of Reality. Cambridge, MA: MIT Press.
Herbert, Nick. 1985. Quantum Reality: Beyond the New Physics. New York: Anchor Books.
Kaiser, David. 2011. How the Hippies Saved Physics. New York: W. W. Norton & Company.
Kwiat, Paul G., and Lucien Hardy. 2000. “The mystery of the quantum cakes.” American Journal of Physics 68: 33–36.
Maudlin, Tim. [1994] 2002. Quantum Non-Locality and Relativity, 2nd ed. Malden, MA: Blackwell Publishing.
Mermin, N. David. 1981. “Bringing home the atomic world: Quantum mysteries for anybody.” American Journal of Physics 49: 940–943.
Mermin, N. David. 1985. “Is the moon there when nobody looks? Reality and the quantum theory.” Physics Today 38: 38–47.
Mermin, N. David. 1990. “Quantum mysteries revisited.” American Journal of Physics 58: 731–734.
Mermin, N. David. 1994. “Quantum mysteries refined.” American Journal of Physics 62: 880–887.
Scarani, Valerio. 2006. Quantum Physics—A First Encounter: Interference, Entanglement, and Reality. Trans. Rachel Thew. New York: Oxford University Press.
Siegfried, Tom. Jan. 27, 2016. “Entanglement is spooky, but not action at a distance,” Science News.
Zeilinger, Anton. 2010. Dance of the Photons. New York: Farrar, Straus and Giroux.
Index
Bell, John, 24–29, 39. See also Bell inequalities
Bell inequalities, 26, 30, 39–42, 47, 67, 123–124, 126, 132, 134–135, 142
Bohm, David, 142
Bohr, Niels, xv. See also Copenhagen interpretation
Coincidence (simultaneous detection of two photons), 37–38
Copenhagen interpretation, xvii, 143
Counterfactual definiteness, 125–128
Detection loophole, 132–133
Einstein, Albert, xv, xvii–xix, 1, 22, 39, 99–102, 117, 136, 140
Fair sampling. See Detection loophole
Freedom-of-choice loophole, 134–135
Heisenberg, Werner, xvii
Hidden variables, 5–9, 12–13, 17–18, 24–26, 51, 94
Local hidden variables. See Hidden variables
Locality, 3, 14–15, 18, 22–23, 26, 39, 53–54, 66–67, 74, 77, 82–83, 123, 127, 138, 140, 142–143. See also Local realism
Locality loophole, 133–134
Local realism, 3–4, 14–18, 24–26, 29–30, 39–45, 53–54, 72–74, 85, 90–93, 96, 121–125, 133–135, 138
Many-worlds interpretation, 127–131
Maudlin, Tim, 74, 141
Measurement problem, 129, 141
Mermin, N. David, 84
Polarization (of light), 33–36
Planck, Max, xv
QBism, 144–147
Quantum decoherence, 141–142
Realism, 3, 10–13, 18, 22–23, 26, 39, 53, 67, 74, 77, 82–83, 123, 138, 140, 142–143. See also Local realism
Relativity
apparent conflict with quantum entanglement, 117–119
length contraction, 110–112
Relativity (cont.)
time dilation, 105–110
twin paradox, 108–110
Schrödinger, Erwin, xv–xvi
Special relativity. See Relativity
Spin, 19–20
Superdeterminism, 126, 134, 138
Zeilinger, Anton, 60, 91
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Jed Brody is Senior Lecturer in Physics at Emory University. He has written two science-fiction novels, The Philodendrist Heresy and The Entropy Heresy, originally published by Moon Willow Press and republished in 2019 by Stormbird Press.