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

by Ananthaswamy, Anil

  To make his case, Wallace tore a page off his yellow, lined writing pad, and sketched a 2-D coordinate system, with the X-axis representing “Change the physics?” and the Y-axis representing “Change the philosophy?”. The positive part of each axis represented YES and the negative part represented NO.

  The physics here refers to the evolution of a physical system according to the standard Schrödinger equation. The philosophy refers to the way we do science: standard scientific realism, the idea that our theories are an objective, observer-independent description of the reality that is out there.

  He crosshatched the quadrant that involved YES for both. “Nobody would want to do both of them, so cross out that box,” he said.

  Copenhagen and Quantum Bayesianism (QBism) went into the NO, YES quadrant: they don’t change the physics, but they change the philosophy, because the interpretations are not observer-independent (however you define an observer). Copenhagen does involve a collapse, which is non-Schrödinger evolution, but since it does claim a law for how that happens, one can argue that it does not modify the physics.

  Bohmian mechanics, GRW, and Penrose’s collapse theory all modify the physics, either by adding hidden variables or by adding new dynamics that interrupt the Schrödinger evolution of a system, causing it to collapse. But they leave the philosophy alone.

  Everett modifies neither the physics nor the philosophy. “This sounds weird for something as crazy as the Everett interpretation, but the attraction for me is that it’s extremely conservative,” said Wallace.

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  If the many worlds interpretation is such a thing of beauty and elegance, then how come not everyone is sold on the idea? For starters, there’s the obvious discomfort with the thought of, well, many worlds. This was voiced early in the life of the Everett interpretation, most notably by Abner Shimony at the October 1962 meeting in Cincinnati, Ohio. Shimony said, “ I think one should invoke Occam’s razor: Occam said that entities ought not to be multiplied beyond necessity. And my feeling is that among the entities which aren’t to be multiplied unnecessarily are histories of the universe. One history is quite enough.” Change the word histories to worlds , and the objection gets even more trenchant.

  Of course, the proponents think that the naysayers have applied Occam’s razor to the wrong issue. The physicist Paul Davies once asked David Deutsch, “ So the parallel universes are cheap on assumptions but expensive on universes?” Deutsch said, “Exactly right. In physics we always try to make things cheap on assumptions.”

  Wallace is of the same opinion. Yes, the Everettian interpretation argues for the existence of many histories, worlds, universes (however you want to think of what’s happening). “But the crucial thing is that you didn’t add that material to the underlying equation. You just interpreted the equations that way,” said Wallace. “I don’t think there is a particularly defensible scientific principle that says that fewer things are better. There is a very defensible scientific principle that says simpler things are better. The many worlds interpretation mathematically is uncontentiously simpler than any of [the other] modifications.”

  And from a cosmological point of view, the idea that the many worlds interpretation requires too much stuff is also batted away by Carroll and Wallace. Carroll, who is a cosmologist, likes thinking in terms of a wavefunction for the entire universe and its evolution independent of observers—it allows him to deal with the physics of the big bang and black holes, for example. Also, cosmologists think that our unobserved universe is in any case far, far larger than what we can see through our telescopes. “We are already, in physics, committed to incredibly large amounts of stuff,” said Wallace. What’s some more of the same?

  There are other arguments in defense of many worlds. In the mathematical formalism of quantum mechanics, a quantum state can be represented by a vector in a coordinate system called the Hilbert space. A vector in 2-D space is a directed arrow that begins at the origin (0,0) and goes to a point (X,Y). Similarly, a vector in 3-D space begins at the origin and ends at some point (X,Y,Z). A vector in Hilbert space is conceptually the same, except it’s dimensionality can be enormous. And in the Everettian way (or indeed when you contemplate the state of the entire universe in any interpretation), the wavefunction of the universe is a vector in the Hilbert space for the entire universe, and the dimensionality of this abstract mathematical space is mind-bogglingly large. “It could be infinite, but even in the most pessimistic readings, it is something like e to the power of 10120 , which is just an enormously crazy number,” said Carroll (where e equals 2.72, approximately). “There’s plenty of room for many, many branchings. We are nowhere near done.”

  Schrödinger evolution merely tells you how the quantum state of the universe, represented by one vector in this Hilbert space, changes to another vector. So if a wavefunction denoted by one vector splits into two vectors, does each vector represent a physical universe? “People fret about that, but I think it’s fine. I have no trouble thinking of them as universes,” said Carroll. “They are not located in our physical space, they are separate copies of our physical space, located in Hilbert space.”

  Similar arguments are also used against those who say that the many worlds interpretation flouts laws of conservation of energy. Where does the energy for the new physical branches come from? Well, all these worlds/universes exist in Hilbert space—not in physical space—so the question is a bit ill posed. Nobel laureate Frank Wilczek has argued, for instance, that “ if the other universes are inaccessible, they cannot be sources or sinks of energy.”

  To Carroll, worrying about the number of worlds is fruitless. “Let’s grow up and move beyond that,” he said.

  That’s because there are other seemingly more pressing and legitimate concerns about the Everettian view. One is about trying to figure out what exactly happens when a universe splits. Say we send a photon through a beam splitter and let each path decohere, resulting in two separate worlds. Does the entire universe split into two everywhere at the same instant (and what does that mean, given that Einstein’s relativity abolished the notion of a universal “now”) or does it start splitting at the point where the decoherence happens near the beam splitter, and move outward at the speed of light? Opinions differ, and there’s no consensus, even among those who are not troubled by the idea of many worlds.

  Perhaps the most well known concern about the Everettian view has to do with the meaning of probability, which is contested in physics and science in general. But it comes to the fore in the many worlds interpretation. “It just brings into the open the inherently mysterious nature of probability,” said Wallace.

  Let’s say you set up a Mach-Zehnder interferometer with path lengths such that if you sent photons one by one into the interferometer, 75 percent of them will end up at detector D1 and 25 percent at detector D2 (recall that the difference in path lengths can be tuned to get this result). The wavefunction of the photon after it has crossed the two beam splitters can be written as a linear combination of two wavefunctions (ψ = a.ψD1 + b.ψD2 , where a and b are amplitudes, and |a|2 equals 0.75 and |b|2 equals 0.25, and these numbers are to be taken as the probabilities of detecting the photon at D1 and D2, respectively, the so-called Born rule). “The question is why do amplitudes-squared get interpreted as probabilities of anything?” said Carroll.

  In the Copenhagen interpretation, that’s just by decree: randomness is inherent in reality and the Born rule gives us the probabilities of measurement outcomes. In Bohmian mechanics, even though the entire evolution of the quantum system is deterministic, the probabilities arise because we are uncertain of the initial conditions. In collapse theories, there is irreducible randomness in the dynamics of a quantum system and there is really something stochastic happening at the microscale, regardless of measurement.

  In the many worlds interpretation, the waters get muddied somewhat. In Everett’s original view, each time you send the photon into our 75-25-tuned interferometer, the universe
splits into two: one in which D1 clicks and D2 doesn’t, and another in which D2 clicks and D1 doesn’t. So in one world D1 clicks with a probability of 1, and in the other world D2 clicks with a probability of 1. Significantly, both worlds are real. Then what’s one to make of the probabilities of 0.75 and 0.25 assigned to these outcomes by quantum mechanics? One tack is to imagine that the experiment continues in each new branch of the universe, and splitting continues too, creating more branches. After a large, potentially infinite number of observations, one can look at the frequency of clicks of D1 and D2 in each branch and ask: do the frequencies come close to the ideal of 75 percent for D1 and 25 percent for D2? Not quite. “It doesn’t work if you just count up the worlds,” says the Australian physicist Howard Wiseman, whose work we encountered in the context of weak measurements and Bohmian trajectories. “In the vast majority of worlds, the relative frequencies are nothing like the quantum probabilities.” Everett used a sleight of hand to argue that some of these worlds should be disregarded—an argument that relies on the Born rule. In the remaining worlds, given an extremely large number of observations, probabilities can be thought of as frequency of outcomes. “But then what happened to the idea that all worlds are equally real?” says Wiseman. “How come you are now effectively throwing away almost all of them, as if they are not as good as the others?”

  He’s not the only one troubled by this way of linking frequency of outcomes to probability in the many worlds scenario. Carroll and Wallace are too.

  Carroll suggests one way out: think of probability as something subjective. Carroll and philosopher Charles “Chip” Sebens have argued that |a|2 and |b|2 should be interpreted as numbers that represent our uncertainty about the outcome of a measurement. So, as in classical physics, probabilities here are due to our ignorance, except in this case the ignorance is about something quite dramatic: we don’t know which branch of the wavefunction we are on. Let’s say you did one run of the experiment, sending one photon through the interferometer. D1 clicks in one branch and D2 clicks in the other branch of the wavefunction, decoherence ensues, and you’ll soon enough find yourself in a branch of the universe in which either D1 clicked or D2 clicked. “The branching happens first, because decoherence is very, very fast, on microscopic time scales, [of] 10-20 seconds or less. There is always a period of time in which the branching has occurred and there are two copies of you, but those two copies are exactly the same, because they don’t know what branch they are on yet,” said Carroll. Thus, even though there are two copies of you, for a very tiny time period, those two copies are ignorant about the branching, and it’s this ignorance that explains the outcomes of experiments in terms of probabilities. Carroll and Sebens have shown that in that brief moment, post-decoherence, if you were to assign probabilities to D1 clicking or D2 clicking, under certain simple assumptions, you’d end up with |a|2 and |b|2 , respectively: which is the Born rule. “There’s a real world,” but we are uncertain about where we are in that real world, said Carroll.

  There’s yet another way to think of probabilities in many worlds. Wallace uses decision theory, an approach pioneered by David Deutsch, which is the study of the reasons behind the choices one makes or the bets one places. If you were doing the above experiment and had to bet on the outcome of the measurement, then, according to Wallace, the rational thing for you to do before the experiment is to treat |a|2 and |b|2 as probabilities to place your bets on which branch of the wavefunction you’ll find yourself in, once the experiment is complete. That’s what a rational agent would do: trust the Born rule. Wallace has tried to derive the Born rule using decision theory, by making certain seemingly simple and acceptable assumptions. For example, if the wavefunction of the universe were to change only by a small amount, your betting strategy should only change by a small amount.

  Not everyone is convinced of this approach. The above assumption “would be reasonable with normal physical quantities. [But] is that reasonable when we talk of the wavefunction of the universe? It’s such a bizarre thing. How can we get our heads around what this thing really is?” said Wiseman. “It’s certainly not just a thing that we are experiencing in the world. It’s actually describing us and simultaneously all our possible futures. I’m just not convinced that that problem [of probability] has been solved, despite the work that has been done on it. That’s really in my mind the biggest problem with the many worlds interpretation, which has been the problem with it all along. Everett was certainly aware of this problem.”

  If nothing else, the many worlds interpretation undeniably questions our understanding of the meaning of probabilities in quantum mechanics.

  The adherents of many worlds are not the only ones fussing about the meaning of probability. Our final interpretation—at first called Quantum Bayesianism, but now known as QBism—initially got its name from the Bayes rule of probability (named after an eighteenth-century statistician and theologian, Thomas Bayes). Not only is the issue of probability front and center in QBism, but it brings the observer back into the mix, claims that probabilities are subjective (personal to each observer), and throws up questions about what quantum states (the vectors in Hilbert space) say about objective reality. QBism, “ rather than relinquishing the idea of reality . . . [says] that reality is more than any third-person perspective can capture.”

  —

  When Christopher Fuchs was a researcher at the Perimeter Institute in Waterloo, Canada, he and his wife, Kiki, bought an enormous house and refurbished it. The previous owner had been a woman who died in her nineties. The house had a small room where she had watched television and drank and smoked heavily, evidenced by the burn marks on the wooden floor next to the couch. Chris Fuchs thought the room would be perfect for a library with floor-to-ceiling bookshelves, so Kiki Fuchs designed one. She removed by hand the nicotine-soaked burlap wallpaper, common in houses built in the late nineteenth century, and had the room cleaned up. Then they got a carpenter to build the bookshelves (made of quartersawn oak, because both Chris Fuchs and the carpenter felt that the 1886 house deserved nothing less) and stocked it with Fuchs’s favorite books on philosophy, mostly on American pragmatism (by the likes of William James and John Dewey). But there was one section of the library dedicated to the modern American philosopher Daniel Dennett. It wasn’t that Fuchs admired Dennett’s philosophy—quite the opposite. “The reason Dennett was there was not because I’m a supporter or interested in him in any way, but rather I see him as the enemy,” Fuchs told me. “You should know your enemy.”

  Dennett is a well-known materialist who has long argued that the perceived immateriality of consciousness is an illusion. Fuchs wants to take our conscious experience seriously—a stance he attributes to William James’s philosophy. Fuchs has also been heavily influenced by John Wheeler (with whom he studied at the University of Texas at Austin). Wheeler was a staunch advocate of Bohr’s vision of quantum mechanics and the Copenhagen interpretation, the strong version of which argues the observer cannot be separated from that which is observed. For Bohr, the observer was some macroscopic experimental setup. Wheeler sometimes went further in his speculations, wondering whether the entirety of existence came down to individual quantum phenomena, each of which was linked to an observer, so that we end up with a universe “ built on billions upon billions of elementary quantum phenomena, those elementary acts of observer-participancy.”

  The alternatives to the Copenhagen interpretation we have seen so far—Bohmian mechanics, collapse theories, many worlds—all remove the observer from the mix (a move that Dennett would likely applaud). Fuchs, however, hitched his wagon to Bohr and Wheeler. He wants to bring the observer back into reckoning. His reading of Wheeler’s works in particular led him to thinking about what it means for something to be intrinsically random (which the quantum world is, according to the Copenhagen interpretation, making the probabilities we assign to the outcomes of measurements an objective part of reality). “That led me to think about probability theory,” Fu
chs told me as we sat at the University of Massachusetts Boston, his new academic home after he moved there from Waterloo (ironically, Boston is just a few miles away from Dennett’s home turf at Tufts University in Medford).

  Fuchs’s tussle with the meaning of probability in quantum mechanics began in earnest when he was doing his PhD with Carlton Caves at the University of New Mexico in Albuquerque. At the time, Fuchs was a “frequentist”—someone who thinks probabilities are objective measures of the tendencies of things to happen, tendencies that become apparent if you do those things a very large, possibly infinite, number of times. Caves, however, was a Bayesian. In this way of thinking, probability is not an objective property of things. Rather, it’s a statement about the person assessing the likelihood of something happening and assigning it a probability: the probability incorporates the idea that the person is uncertain for whatever reason, yet must still make the best decisions possible in light of that uncertainty. Quantum Bayesianism was officially born in 2002, with the first paper by Caves, Fuchs, and Rüdiger Schack. The name proved a mouthful (and besides, the term Bayesianism caused controversy, given the many divisions within Bayesian probability theory about the meaning of the term), so Fuchs eventually shortened it to QBism, leaving the B to stand for itself. It proved a marketing masterstroke. QBism has a ring to it.

  QBism challenged notions about the meaning of the wavefunction. The debate over the status of the wavefunction has been at the heart of all the interpretations we have seen thus far. It can be broadly thought of in two ways: either that the wavefunction represents our knowledge of the quantum system, so it is epistemic, and theories that take this stance are called psi-epistemic; or that the wavefunction is part of reality itself, and theories of this persuasion are called psi-ontic (for ontology).

  The Copenhagen interpretation, which doesn’t accord any reality to the quantum world beyond what is manifest during observation, is psi-epistemic. The wavefunction contains enough knowledge for us to make probabilistic predictions about the outcomes of experiments. Also, no hidden variables are needed to complete the theory.