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

by Ananthaswamy, Anil

  As expected, Everett’s thesis was received rather coldly in Copenhagen. An American physicist, Alexander Stern, who was in Copenhagen at the time, organized a seminar in May 1956 in which he, Niels Bohr, and others discussed Everett’s ideas. Stern wrote a letter to Wheeler a week later, in which he detailed the criticisms of the Copenhagen crowd, taking issue particularly with Everett’s idea of a universal wavefunction. Stern said that Everett’s ideas “ lack meaningful content” and said that some aspects were a “ matter of theology.”

  Wheeler wrote back almost immediately, and was even somewhat apologetic. “ I would not have imposed upon my friends the burden of analyzing Everett’s ideas, nor given so much time to past discussions of these ideas myself, if I did not feel that the concept of ‘universal wavefunction’ offers an illuminating and satisfactory way to present the content of quantum theory.” He then both praised Everett and mischaracterized his position: “. . . this very fine and able and independently thinking young man has gradually come to accept the present [Copenhagen] approach to the measurement problem as correct and self consistent, despite a few traces that remain in the present thesis, draft of a past dubious attitude [italics mine].”

  Everett did no such thing. He did rework his thesis into a version that was almost three-quarters shorter (Wheeler had asked him to make it “ javelin proof”); he took out the sharpest attacks against the Copenhagen interpretation, including his denunciation of the measurement problem, and recast his views about quantum mechanics as a way to solve the problem of reconciling general relativity with quantum mechanics into a theory of quantum gravity. But the underlying mathematical formalisms in the long and short versions of the thesis were essentially the same. His views on the Copenhagen interpretation had not changed, something that became abundantly clear in a correspondence with the theoretical physicist Bryce DeWitt.

  DeWitt had edited the issue of Reviews of Modern Physics in which Everett’s shortened thesis had appeared. DeWitt would later say about Everett’s paper: “ I was stunned, I was shocked.” DeWitt wrote to Wheeler, raising some concerns, including the issue of the splitting of observers: “ I can testify to this from personal introspection, as can you. I simply do not branch.” Wheeler forwarded the letter to Everett.

  In his reply, Everett called the Copenhagen interpretation “ hopelessly incomplete” and “ a philosophic monstrosity with a ‘reality’ concept for the macroscopic world and denial of the same for the microcosm.”

  Everett also clearly outlined what happens to the various macroscopic superpositions in the universal wavefunction: “ From the viewpoint of the theory, all elements of a superposition (all ‘branches’) are ‘actual,’ none any more ‘real’ than another. It is completely unnecessary to suppose that after an observation somehow one element of the final superposition is selected to be awarded with a mysterious quality called ‘reality’ and the others condemned to oblivion. We can be more charitable and allow the others to coexist—they won’t cause any trouble anyway because all the separate elements of the superposition (‘branches’) individually obey the wave equation with complete indifference to the presence or absence (‘actuality’ or not) of any other elements.” In other words, to answer DeWitt, one version of “you” does not interact with any other version of “you” after splitting, so you can never feel yourself splitting.

  But a more seemingly preposterous idea was waiting in the wings to be unleashed: that somehow each splitting is causing the universe itself to divide into parallel worlds. Everett would bring up the idea at a conference in October 1962 in Cincinnati, Ohio. Among the participants were many luminaries, including Nathan Rosen, Boris Podolsky, Paul Dirac, Abner Shimony, and Eugene Wigner. Everett was there too. The attendees began raising the uncomfortable question of parallel universes. At one point, Shimony said that the idea that all macroscopic superpositions continue to exist, even for a single observer, had strange consequences. “ It seems to me that if this is the case, there are two possibilities. The two possibilities involve awareness. One possibility is that ordinary human awareness is associated with one of these branches and not with the others. Then the question becomes, how does your formalism permit this solution? The other possibility is that awareness is associated with each branch.”

  Podolsky said, “ Somehow or other we have here the parallel times or parallel worlds that science fiction likes to talk about so much. Every time a decision is made, the observer proceeds along one particular time while the other possibilities still exist and have physical reality.” To which Everett replied, “ Yes, it’s a consequence of the superposition principle that each separate element of the superposition will obey the same laws independent of the presence or absence of one another. Hence, why insist on having a certain selection of one of the elements as being real and all of the others somehow mysteriously vanishing?”

  After some back-and-forth, Shimony said to Everett, “ You eliminate one of the two alternatives I had in mind. You do associate awareness with each one of these.” Everett concurred: “ Each individual branch looks like a perfectly respectable world where definite things have happened,” he said. This was about the only instance in which Everett explicitly acknowledged the notion of multiple worlds.

  It was DeWitt who eventually gave credence to the idea of many worlds. In an article for Physics Today in 1970, DeWitt explained the new interpretation, in which a universe is represented by a single wavefunction. “ This universe is constantly splitting into a stupendous number of branches, all resulting from the measurementlike interactions between its myriads of components. Moreover, every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself.”

  DeWitt would later remember his own astonishment at the realization: “ I still recall vividly the shock I experienced on first encountering this multiworld concept. The idea of 10100+ slightly imperfect copies of oneself all constantly splitting into further copies, which ultimately become unrecognizable, is not easy to reconcile with common sense. Here is schizophrenia with a vengeance.”

  Despite his shock and awe, DeWitt was a convert and he’d play a major role in proselytizing Everett’s interpretation, which goes by many names now, but we’ll refer to it as Everett’s many worlds or simply the many worlds interpretation.

  —

  The first thing that greets you as the elevator doors open on the fourth floor of the Downs-Lauritsen Laboratory of Physics at Caltech is a giant mural of Feynman diagrams—the kind of squiggly drawings that Feynman would draw on paper napkins to visualize the interaction of particles. I was there to meet theoretical physicist Sean Carroll, a proponent of the many worlds interpretation. We were midway through our discussion about quantum mechanics when Carroll decided he was going to split the world.

  His iPhone has an app called the Universe Splitter, which is a version of the watch that Vaidman wanted to patent—one that will help you make up your mind when confronted with a difficult YES or NO decision. There is no wrong decision, for—in the Everettian view—there exists a universe in which the app suggests a different decision. So why worry?

  Carroll fired up the app, with its default choices of what to do: Take a chance or Play it safe (we could have typed in something else, but we stuck with those choices). Carroll pressed a button that said, ominously, “Split Universe.” The app sent a command to a lab somewhere near Geneva, Switzerland, where a single photon was sent through a beam splitter. “If you believe in Everett, there is a world in which the photon goes left and a world in which the photon goes right,” said Carroll.

  A few seconds later, the result came back. “Ah, we are in the universe where we have to take a chance.” And the act of saying aloud the words Take a chance (and presumably the words Play it safe in another world) had split the universe irreconcilably (we’ll come to why in a moment). “Now there are just two copies of me.”

  And presumabl
y me, I thought. Was this real or surreal?

  What I had witnessed was an experimental realization of one part of the Mach-Zehnder interferometer, which becomes a strangely simple thing to behold in the many worlds interpretation.

  Consider first a configuration with just the first beam splitter, and nothing else. The Everettian view is that the wavefunction of the universe now has two components: one in which the photon is transmitted, and one in which the photon is reflected (let’s assume for now that this is the only quantum choice being exercised in the entire universe). So far, both the Copenhagen interpretation and the many worlds interpretation are in sync. The system is now in a superposition of those states and continues to evolve according to the Schrödinger equation.

  If we now put detectors at the ends of each path, the two interpretations give us wildly different views of reality.

  In the Copenhagen view of things, one of the detectors clicks. If the measurement apparatus is considered classical, then that click, so to say, is the sound of the wavefunction collapsing.

  For a while, physicists thought they had come up with a way to explain this collapse without resorting to magic. Let’s say the detector can also be treated as a quantum mechanical object. If it’s not kept completely isolated, the detector eventually starts interacting with its environment, mainly through other ambient photons and air molecules bouncing off it, and the detector becomes entangled with the environment. It’s mathematically impossible to describe this complicated interaction. So, what quantum mechanics does is to describe the combined state of the photon and the detector using something called a density matrix—basically, a mathematical formalism that ignores the environment. Before the interaction with the environment, the photon and the detectors are in a definite state of “the photon is reflected and D1 clicks” and “the photon is transmitted and D2 clicks.” After the interaction with the environment, the quantum formalism says that the system is in a state of either “the photon was reflected and D1 clicked” or “the photon was transmitted and D2 clicked,” but we don’t know which. The latter situation now represents a state that encodes our ignorance of what happened.

  “If you ignore the environment, the best you can say about your quantum system and the measuring apparatus is that they are in a mixed state, described by a density matrix,” said Carroll.

  The density matrix allows you to calculate the probability that D1 clicked or D2 clicked (0.5 each, for this experiment). In this case, the probabilities look like classical probabilities, in that they are grounded in our ignorance. The process of interaction with the environment is called decoherence, and the fact that the resultant density matrix lets you calculate the correct probabilities led physicists to think that decoherence—when it was first proposed—actually caused the collapse of the wavefunction and thus solved the measurement problem. But that excitement was short-lived. Decoherence, while it says that the combination of a quantum system and the measuring apparatus evolves to look like a system in a probabilistic mixture of classical states, doesn’t really explain why.

  In the classical world, when we use probabilities to talk about the state of a system, it’s because we are ignorant, but the system nonetheless is in some definite state, and there is nothing else it’s interacting with. In the quantum world, the probabilities calculated using the density matrix are somewhat different. It appears as if we are ignorant of the exact state, but unlike the classical state, the quantum state being described by the density matrix is not a definite state. We’d have to consider the entanglement with the outside world to describe the quantum state in its entirety, and the density matrix doesn’t do that.

  So the theory of decoherence comes tantalizingly close to making sense of collapse, but fails. The Copenhagen interpretation drops the ball at this point, whereas the many worlds interpretation picks it up and runs with it.

  According to many worlds, both D1 and D2 click, each in their own branch of the wavefunction. This clicking and the consequent interactions with their local environments lead to entanglement and decoherence. Once decoherence sets in, the two worlds begin evolving independently, but still according to the Schrödinger equation. However, the two branches of the evolving wavefunction are now impossible to recombine. “The environments attached to each decoherent branch are orthogonal to each other, which means that there will never be any interference,” said Carroll. So, from the point of view of any one branch of the wavefunction, “all the other branches are still there, they are just exponentially hard to find.”

  But let’s say that you did not put detectors D1 and D2 at the end of each path coming out of the beam splitter, thus avoiding decoherence. Then, in principle, it’s possible to recombine the two worlds by bringing the two paths together at a second beam splitter. That is exactly what happens in a Mach-Zehnder interferometer. In order to calculate the probability of finding the photon at D1 or D2, after it crosses the second beam splitter, we have to take into account that it went through both paths, a different world for each path.

  This is reminiscent of Feynman’s approach to solving the puzzle of the double-slit experiment, or quantum mechanics more generally. Feynman came up with what he called the path integral formulation of quantum mechanics. In this approach, a particle approaching a double slit can still be treated classically—in that it goes through one or the other slit, but in order to calculate the probability that it lands on a particular place on the far screen, you have to let the particle take every possible path from the two slits to the screen. These paths include all sorts of squiggly trajectories that don’t make any classical sense. Each of these paths is assigned a weight that dictates its contribution to the final probability.

  “What quantum mechanics tells us fundamentally about how to think about the universe is that in order to calculate the probability of something happening we have to add the amplitudes for all the different ways it could occur,” Aephraim Steinberg told me. When you do that, you get interference. “The insight that Feynman had was to realize that what’s really interfering are two different states of the universe. And in the simplest case, those two states might only differ by where a single particle is. Is the electron in the upper path or the lower path?”

  While Feynman’s path integral approach is a tool for calculating the probabilities of experimental outcomes in this world, the many worlds approach takes this idea of different states of the universe rather more literally. And this, according to Carroll, is what makes its take on reality very appealing, and understanding the double slit a breeze, assuming, of course, that you are not perturbed by the idea of new branches of the wavefunction and hence new worlds appearing at every quantum fork in the road. “There is a heavy psychological price to pay, and the question is, how much does that bother you?” said Carroll. “Doesn’t bother me at all.”

  He is far more bothered by the Copenhagen interpretation. Take, for instance, Bohr’s language that’s used to describe the double-slit experiment: if we don’t collect which-way information, the photon behaves like a wave; if we do, it behaves like a particle. “All that is complete nonsense,” said Carroll.

  As an Everettian, Carroll thinks simply in terms of a wavefunction that splits into two components at a beam splitter, and each continues to evolve according to the Schrödinger equation. If there’s no decoherence, then those two parts of the wavefunction can be made to interfere. “If you don’t entangle the photon as it moves through the slits, then you’ll see the interference pattern, because that’s the solution of the Schrödinger equation,” said Carroll.

  There’s no doublespeak, so to say, about the photon showing its wave nature or particle nature. It’s just the wavefunction evolving and doing its thing—and the wavefunction represents the quantum state of reality. “Many abstract thinking physicists are . . . impressed by the underlying mathematical beauty and elegance of Everett,” said Carroll. “Physicists are suckers for mathematical beauty and elegance.”

  There’s certainly a mathe
matical simplicity to the many worlds idea. There’s just the wavefunction and its evolution. No added ingredients (such as hidden variables) or ungainly nonlinear dynamics (such as stochastic collapse à la Penrose or GRW) or Copenhagen-like magic to induce collapse.

  This point was brought home vividly when I visited philosopher David Wallace, whose office is about fifteen miles away from Carroll’s, at the University of Southern California, Los Angeles. Wallace, who had previously worked with David Deutsch at the University of Oxford, had just moved to California. And like Deutsch, Wallace is a strong proponent of the many worlds interpretation. He began his academic career as a theoretical physicist but then switched to philosophy (when theoretical physics “ started to sound a little bit too practical,” he’s known to joke). And as a philosopher, he was seduced by Everett’s many worlds interpretation.

  “To me, one of the most attractive things about the Everett interpretation is that it doesn’t commit you to a revisionary project in physics,” Wallace told me. “I’m very skeptical that a revisionary project would succeed.”