Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

by Ananthaswamy, Anil

  When contemplating this virtual ensemble, Wiseman wondered: what if this virtual ensemble is real, in that every particle exists, but in a different world? Each particle is influenced by those in its local surroundings (some regions are more dense with particles than others). Then the way each particle moves is dictated by interactions with its immediate neighbors, like starlings in a murmuration. Crucially, you don’t need a wavefunction to determine how any given particle moves. “When that idea occurred to me, it was like, wow!” Wiseman said.

  He and his colleagues Dirk-André Deckert and Michael Hall postulated a particular many-world force law for this situation, then did simulations. First, they used Bohmian mechanics—wavefunction, hidden variables, and all—to plot trajectories of particles going through a double slit. Next, they treated each particle trajectory as being the outcome of its interactions with other particles that exist in other worlds, without resorting to the mathematics of the evolution of the wavefunction. The results they obtained are eerily similar.

  “That’s just about the theory for one particle,” said Wiseman. “Of course, the universe is not one particle.”

  In a many-particle system, while each particle exists in 3-D space, the wavefunction exists in configuration space. Any given distribution of particles in 3-D space corresponds to one point in the configuration space. This one point represents a world. In Bohmian mechanics, our knowledge about the initial configuration of particles is subject to uncertainty—and this uncertainty corresponds to a probabilistic distribution of points in configuration space, or a virtual ensemble of worlds. Bohmian mechanics says there is one real world whose evolution can be described by the evolution of the wavefunction, subject to this initial uncertainty. Just as in the case of the single particle in 3-D space being influenced by other particles in other worlds, Wiseman’s argument is that you can treat this virtual ensemble of points in configuration space as a collection of real worlds. Any given world interacts with the other worlds in configuration space, and this interaction is local, with nearby worlds influencing each other more than distant worlds.

  This has enormous consequences. For example, a local interaction in configuration space can appear nonlocal in 3-D space. “So that’s where the nonlocality of quantum mechanics would come from,” said Wiseman. He’s dubbed this still-nascent idea “many interacting worlds” (to distinguish it from the Everettian many worlds idea). It’s an example of how the behavior of the quantum mechanical world emerges from the dynamics of a deeper reality. But he’s certainly not claiming that this is what’s happening in the quantum world. The exercise is to make the point that there are myriad ways of explaining quantum phenomena, some of which are on stronger mathematical footing than others, and each has its own set of problems, whether it’s the measurement problem in the Copenhagen interpretation, or the problem of potential conflicts with special relativity in Bohmian mechanics (not to mention the distaste for hidden variables in the eyes of some), or the ad hoc nature of stochastic collapse in collapse theories, or the problem of explaining probability in Everett’s many worlds.

  And depending on which axis you choose for analyzing the quantum world, the theories and interpretations fall into different bins, making for strange bedfellows.

  Take determinism. The de Broglie-Bohm theory, the Everettian many worlds interpretation, and Wiseman’s many interacting worlds are deterministic; Copenhagen and collapse theories are not. QBism doesn’t say anything about whether or not the real world is deterministic.

  What about realism? Well, de Broglie-Bohm, collapse, many worlds, and many interacting worlds are all realist. Copenhagen is not. QBism is realist, with the caveat that the wavefunction is not about this reality.

  What about claims that there is nothing but the wavefunction? Many worlds and collapse theories say yes. De Broglie-Bohm says no (because the theory has hidden variables besides). There is no wavefunction in many interacting worlds. In Copenhagen, the wavefunction represents the quantum world, but there is the classical world to contend with. In QBism, the status of the wavefunction is entirely subjective (it’s personal to one observer).

  Then there’s the whole issue of locality versus nonlocality. From the point of view of our 3-D world, the theories of de Broglie-Bohm, collapse, and many interacting worlds are all nonlocal. There’s some dispute about the status of the Everettian many worlds interpretation in this regard, but opinions tend toward it being local. Copenhagen is obscure: if you take the wavefunction to be representative of something out there, then it’s nonlocal, else you can dismiss concerns of nonlocality by saying that all one does is make measurements, compare them to results of other experiments, find correlations, and that’s that (there’s no attempt to explain the cause of the correlations). QBism, as we saw earlier, dismisses nonlocality.

  There are finer distinctions to be made, but the message is clear: there’s no way to classify these theories in a consistent manner. It’s a strong clue that our understanding of the quantum world is still up for grabs. And it’s very likely that further attempts at clarification will involve the double-slit experiment in some form or the other.

  And nowhere does this become more apparent than in experiments being done to verify one of the key assumptions of quantum mechanics: the Born rule. As one prominent theorist has said, “ If Born’s rule fails, everything goes to hell.” All of the various mathematical formalisms for explaining the quantum world, ultimately, are designed to answer why, when we do experiments like the double slit, we get the outcomes we do. A photon goes through the double slit, its wavefunction splits, evolves, recombines, and so on. Eventually, the wavefunction can be written down as a linear combination of different wavefunctions (one for each path the photon takes), each evolving according to the rules of the Schrödinger equation. The photon is said to be in a superposition of taking all possible paths. The Born rule says that the probability of finding the photon at any given location is given by the modulus-squared of the value of the wavefunction at that location. But “the Born Rule is conjecture,” said Urbasi Sinha, formerly of the Institute for Quantum Computing at Waterloo, Canada, and now of the Raman Research Institute in Bengaluru, India. “There is no formal proof of the Born Rule.”

  Of course, there are many quantum mechanical phenomena that agree with theoretical predictions to astonishing precision, but these predictions all assume the validity of the Born rule. Now, Sinha and her colleagues are trying to directly test the Born rule—using, what else, the double-slit (or sometimes the triple-slit experiment, which makes some measurements sharper but is conceptually identical to doing the experiment with two slits). Take a photon going through the double slit. According to Feynman’s path integral approach, to calculate the probability of finding the photon at, say, the center of the screen, you have to consider the classical paths (which go through one slit or the other) and nonclassical paths, such as one that starts off going through one slit, then instantly turns toward the other slit, and then goes toward the screen.

  Sinha’s team calculated the expected intensity of light at the center of the screen, given the most dominant classical and nonclassical paths the photon can take through the apparatus. The next step was to figure out the expected change in intensity if the nonclassical path is blocked (which can be done by placing a baffle through one slit—this prevents the photon from taking its unusual slit-hugging route. The baffle is thin, so there is still room on either side of it for a photon taking the classical path to go through the slit). The measured intensity is sensitive to the exact formulation of the Born rule. Is the probability equal to the square of the amplitude of the wavefunction? Or is it equal to the amplitude raised to some number 2+δ, where δ represents a tiny deviation? Many teams besides Sinha’s are asking such questions. “Even a small deviation will change many things,” Sinha told me.

  While the Born rule has held up so far to a certain level of precision, the experimentalists are tightening the screws. If they can show that the Born ru
le needs tweaking, it will create an opening, giving theorists essential clues on how to proceed toward the correct quantum mechanical view of nature. The experiments also highlight that the double slit, a simple contraption if ever there was one, continues to conceal some central principle that animates reality.

  As Feynman put it in his Cornell lecture: “ Any . . . situation in quantum mechanics, it turns out, can always be explained afterwards by saying ‘You remember the case of the experiment with the two holes?’”

  Physics has yet to complete its passage through the double-slit experiment. The case remains unsolved.

  NOTES

  “Allow me to express now” : Carl C. Gaither and Alma E. Cavazos-Gaither, eds., Gaither’s Dictionary of Scientific Quotations (New York: Springer, 2008), 502.

  “There is nothing more surreal” : Siri Hustvedt, “The Drama of Perception: Looking at Morandi,” Yale Review 97, no. 4 (Oct 2009): 20–30.

  But in November 1964 : http://www.cornell.edu/video/playlist/richard-feynman-messenger-lectures .

  “It’s odd, but in the infrequent occasions” : Feynman Messenger Lectures, Lecture 1, “Law of Gravitation,” http://www.cornell.edu/video/richard-feynman-messenger-lecture-1-law-of-gravitation .

  “Then we see unexpected things” : Feynman Messenger Lectures, Lecture 6, “Probability and Uncertainty: The Quantum Mechanical View of Nature,” http://www.cornell.edu/video/richard-feynman-messenger-lecture-6-probability-uncertainty-quantum-mechanical-view-nature .

  “They behave in their own inimitable way” : Ibid.

  “That is, they’re both screwy” : Ibid.

  “But the difficulty” : Ibid.

  “one experiment which has been designed” : Ibid.

  let’s orient the device : The British physicist Jim Al-Khalili has used the same idea to demonstrate the double-slit experiment done with particles, https://youtu.be/A9tKncAdlHQ?t=125 .

  “The Last Man Who Knew Everything” : Andrew Robinson, The Last Man Who Knew Everything (London: OneWorld, 2007).

  “doctor of physic, surgery, and midwifery” : Ibid., 51.

  “The experiments I am about to relate” : Thomas Young, “The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics,” Philosophical Transactions of the Royal Society of London 94 (1804): 1–16.

  “I made a small hole in a window-shutter” : Ibid.

  “I brought into the sunbeam” : Ibid.

  Young saw such optical interference fringes : Ibid.

  Henry Brougham : https://www.britannica.com/biography/Henry-Peter-Brougham-1st-Baron-Brougham-and-Vaux .

  “destitute of every species” : Whipple Museum of the History of Science, http://www.sites.hps.cam.ac.uk/whipple/explore/models/wavemachines/thomasyoung/#ref_2 .

  “The idea of an objective real world” : Werner Heisenberg, Physics and Philosophy (London: Penguin Books, 2000), 83.

  He elucidated his laws : https://www.aps.org/publications/apsnews/200007/history.cfm .

  “When Light reaches us from the sun” : Louis de Broglie, Matter and Light: The New Physics, trans . W. H. Johnston (New York: W. W. Norton & Co., 1939), 27.

  He presented these ideas on December 8, 1864 : J. Clerk Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Philosophical Transactions of the Royal Society of London 155 (1865): 459–512.

  In 1879, the Prussian Academy of Sciences : D. Baird, R. I. Hughes, and A. Nordmann, eds., Heinrich Hertz: Classical Physicist, Modern Philosopher (Dordrecht, NL: Springer Science, 1998), 49.

  “But in spite of having abandoned” : Ibid.

  “It is of no use whatsoever” : Andrew Norton, ed., Dynamic Fields and Waves (Bristol: CRC Press, 2000), 83.

  “To be sure, it is a discovery” : Joseph F. Mulligan, “Heinrich Hertz and Philipp Lenard: Two Distinguished Physicists, Two Disparate Men,” Physics in Perspective 1, no. 4 (Dec 1999): 345–66.

  “A chronic, and painful, disease” : “Heinrich Hertz,” editorial in Nature 49, no. 1264 (Jan 18, 1894): 265.

  “Heinrich Hertz seemed to be predestined” : Mulligan, “Heinrich Hertz and Philipp Lenard.”

  was a scientific curiosity : https://history.aip.org/history/exhibits/electron/jjrays.htm .

  “At first there were very few” : http://history.aip.org/exhibits/electron/jjelectr.htm .

  His experiments clearly showed that : Mulligan, “Heinrich Hertz and Philipp Lenard.”

  While Einstein did not fully embrace Planck’s ideas : Abraham Pais, “Einstein and the Quantum Theory,” Reviews of Modern Physics 51, no. 4 (Oct 1979): 863–914.

  “Entrance is forbidden to Jews” : Mulligan, “Heinrich Hertz and Philipp Lenard.”

  “Einstein was the embodiment” : Philip Ball, “How 2 Pro-Nazi Nobelists Attacked Einstein’s ‘Jewish Science’” excerpt, February 13, 2015, https://www.scientificamerican.com/article/how-2-pro-nazi-nobelists-attacked-einstein-s-jewish-science-excerpt1/ .

  Thomson argued that there should be blurry fringes : George K. Batchelor, The Life and Legacy of G. I. Taylor (Cambridge: Cambridge University Press, 1996), 40.

  “I chose that project for reasons” : Ibid.

  To create a single slit : Ibid., 41.

  “I had, I think rather skillfully, arranged” : Ibid.

  Taylor reportedly went away sailing : Sidney Perkowitz, Slow Light: Invisibility, Teleportation, and Other Mysteries of Light (London: Imperial College Press, 2011), 68.

  After that three-month-long exposure : George K. Batchelor, The Life and Legacy of G. I. Taylor , 41.

  it’d take him a decade or so more : Gösta Ekspong, “The Dual Nature of Light as Reflected in the Nobel Archives,” https://www.nobelprize.org/nobel_prizes/themes/physics/ekspong/ .

  “That he might sometimes have overshot” : Walter Isaacson, Einstein: His Life and Universe (New York: Simon & Schuster, 2007), 100.

  The moment, captured in a now-iconic photograph : Participants of the Fifth Solvay Congress, https://home.cern/images/2014/01/participants-5th-solvay-congress .

  Bohr first met Heisenberg : Jagdish Mehra, Einstein, Physics and Reality (Singapore: World Scientific, 1999), 94.

  He also invited Heisenberg to Copenhagen : Gino Segré, Faust in Copenhagen: A Struggle for the Soul of Physics (New York: Viking Penguin, 2007), 116.

  “perhaps it would be possible one day” : Jagdish Mehra, Golden Age of Theoretical Physics , vol. 2 (Singapore: World Scientific, 2001), 648.

  There, between long walks and contemplating : Ibid., 650.

  “It was almost three o’clock in the morning” : Ibid., 651.

  “I thought the whole day” : Ibid., 652.

  “discouraged, if not repelled” : Ibid., 840.

  “A few days ago I read” : Walter Moore, Schrödinger: Life and Thought (Cambridge: Cambridge University Press, 2015), 192.

  “A few days before Christmas” : Dick Teresi, “The Lone Ranger of Quantum Mechanics,” review of Walter Moore’s Schrödinger: Life and Thought, January 7, 1990, http://www.nytimes.com/1990/01/07/books/the-lone-ranger-of-quantum-mechanics.html .

  “The motion of particles follows probability” : Abraham Pais, “Max Born’s Statistical Interpretation of Quantum Mechanics,” Science 218 (Dec 17, 1982), 1193–98.

  He wrote to Pauli, complaining : Moore, Schrödinger, 221.

  Züricher Lokalaberglauben : Ibid.

  “Don’t take it as a personal unfriendliness” : Ibid.

  “The discussion between Bohr and Schrödinger” : Ibid., 226.

  “Schrödinger was a ‘visualizer’” : Ibid., 228.

  “trust in the newly developed” : Stefan Rozental, ed., Niels Bohr: His Life and Work as Seen by His Friends and Colleagues (Amsterdam: North-Holland Publishing, 1967), 104.

  “Like a chemist who tries to concentrate” : Jørgen Kalckar, ed., Niels Bohr Collected Works, vol. 6 (Amsterdam: North-Holland, 1985), 15.

  “I went for a walk” : Rozental, Niels Bohr, 105.

  “Dear Mr. Bohr” : Léon Rose
nfeld and J. Rud Nielsen, eds., Niels Bohr Collected Works, vol. 3 (Amsterdam: North-Holland, 1976), 22.

  “To meet you” : Ibid.

  “However, with all the participants” : Manjit Kumar, Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality (New York: Norton, 2011), 273.

  physicists since then have reimagined : The illustration of the recoiling double slit is inspired by a drawing in P. Bertet et al., “A Complementarity Experiment with an Interferometer at the Quantum-Classical Boundary,” Nature 411 (May 10, 2001): 166–70.

  “But the electron must be somewhere” : Jorrit de Boer, Erik Dal, and Ole Ulfbeck, eds., The Lesson of Quantum Theory (Amsterdam: North-Holland, 1986), 17.

  “The electron, as it leaves the atom” : Arthur Eddington, The Nature of the Physical World (New York: Macmillan Company, 1929), 199.

  “It is fair to state that we are not” : Stefan Hell, Nobel Banquet Speech, December 10, 2014, https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2014/hell-speech_en.html .