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Sandu Popescu and Yakir Aharonov at Perimeter

Yakir Aharanov has followed his intuition to some remarkable places: discovering the surpassingly strange Aharonov-Bohm effect, and founding the entire field of weak value measurement, for starters. “Here is an interesting answer,” he’s been known to tell his students. “Go find me a question.”

At 83, he seems to be have been purified by time into sinew and paradigm. “You could say my life’s work is finding the correct story to tell about quantum mechanics,” he says. Ask him now if he thinks he has found that story, and he answers simply: “Yes.”

Aharonov, who is a Perimeter Distinguished Visiting Research Chair and Professor at Chapman University, works mostly with young people, and often leaves the publishing to them. Not all of his best ideas make it into the scientific record. This summer, Perimeter’s Lucien Hardy set out to fix that, convening a month-long program on quantum foundations. For the first three weeks, Aharonov gave long lectures every morning – without notes – to researchers from Perimeter and further afield. At the week-long conference that followed, “Concepts and Paradoxes in a Quantum Universe,” he continued with a series of lectures entitled “Finally making sense of quantum mechanics.” No question mark included. (All of the talks are available here.)

It was not a topic that sat well with everyone. Bill Unruh – a University of British Columbia professor and Perimeter Distinguished Visiting Research Chair who, like Aharonov, is a giant in the field of quantum foundations – is a case in point. Ask him if we are finally making sense of quantum mechanics, and he pushes back at the premise of the question. “I have always found the claim that we do not understand quantum mechanics weird,” he says. “It is not only highly successful, but physicists have no trouble applying it to new situations, and even brand new theories (except gravity) with very little trouble.”

Unruh is not alone. Quantum mechanics is arguably the most successful theory in science – the most broadly applicable, the most precise, the most thoroughly tested. In the face of that, what does it mean to say that we don’t understand it? For most of a century, the mantra “shut up and calculate” has been the majority opinion.

But there’s a subtle shift in the wind. Aephraim Steinberg, of the University of Toronto, has done landmark experiments testing some of Aharonov’s ideas. Ask him if we’re finally making sense of quantum mechanics and you will still find your question questioned – but in a very different way. “‘Are we finally’ is a funny question,” he says. “If that means we’ve been struggling for a century and now we’re approaching the end? No, I don’t believe that at all.”

Yakir Aharonov course
Yakir Aharonov shares his ideas with peers and colleagues at Perimeter Institute.

What he thinks instead is that the questions of how we make sense of quantum mechanics are becoming mainstream. There has always been a small group dedicated to this field of quantum foundations, but for decades it was marginal – to choose quantum foundations was seen as a good way to commit career suicide.

But things are changing. We can build and control large quantum systems now. We can use quantum metrology to measure unbelievably small shifts, such as those created by passing gravitational waves. Practical quantum computers and quantum sensors seem within reach. As we reach further and further into the quantum world, questions which once seemed abstract become increasingly pressing – and increasingly possible to answer. It’s as if the scholastics who once asked how many angels could fit on the head of a pin suddenly had experimental access to the spirit realm.

At this conference, at least, “shut up and calculate” has given way to “sit down and listen,” and “stand up and talk.” So, what, exactly are they talking about? What does it mean to make sense of quantum mechanics?

The value of events

For almost 100 years, those studying quantum mechanics have struggled with disconnection between the quantum world – generally the world of the small – and the macroscopic world, the world of clocks and tables and cups of coffee. At the conference, wide-ranging discussion of this disconnection lit again and again on a single word: events.

Philip Pearle, professor emeritus at Hamilton College, is an expert in “quantum collapse”: the transition in a quantum system from a state that exhibits superposition to a state that doesn’t – that is, from the alive/dead cat in Schrödinger’s unopened box to the cat after you check. He boils it down: “Something is missing from quantum mechanics: events. Events occur. Things actually happen in nature. And quantum mechanics does not describe that.”

Quantum mechanics provides us with a wave function, which we can use to make predictions. It’s fundamentally probabilistic. Where classical mechanics might tell you that an apple falling from a tree will definitely fall on your head, with such-and-such an energy, quantum mechanics can only tell you that an electron fired from a cathode ray tube has such-and-such a probability of hitting your head, with such-and-such a range of energies. Sometimes the probability is pretty high, and sometimes the range is pretty narrow – sometimes things are nearly known. But never, ever, are they exactly known.

This by itself can be a bit disturbing, philosophically. Quantum mechanics describes the universe with statistics and uncertainty; it rolls the dice. The door is still open – or at least ajar – to the possibility that quantum uncertainty is a limit on what we can know about nature, rather than a description of nature’s own indeterminateness. But whether you think quantum uncertainty is in the nature of the particle or the eye of the beholder, you still have a deeper and more fundamental problem.

How do we move from the universe where the electron has a 95 percent chance of hitting you in the eye, to the universe where it definitely just did hit you in the eye? Those systems would be described by two different wave functions. Quantum mechanics can describe the one before, and the one after, but never the moment you go blind.

“This is what’s called the measurement problem,” says Pearle. “Once you see something happening –” he claps his hands together with a snap – “the wave function has to change. And quantum mechanics just doesn’t do that.”

Andrew Briggs is a professor of nanomaterials at Oxford; he studies new materials that might be of use in quantum technologies. “If you have a closed quantum system you can never talk about an event having happened,” he says. “But our lives consist of events. We get up in the morning. Babies are born. Couples marry. Parents die. Events happen, and we know what we mean by events.

“There’s no place for that in the quantum theory. So somehow, we’ve got to do something that will relate the fantastic, experimentally verified mathematical precision of the quantum theory of the very small, to the everyday experience of reality that you and I have in our lives.”

But how? The experts attending the conference were only a small handful from a large and growing field, but the conference showcased a number of theories and approaches. Some of them are in direct opposition to others: they cannot all be true. There was debate aplenty, and very little certainty.

But Yakir Aharonov is certain. Or, at least, he’s certain that he’s discovered what uncertainty is for. To hear Aharonov tell it, the trouble began when quantum mechanics first dropped researchers into a universe run by statistics, where one radioactive atom might decay, and yet another, exactly the same, might remain whole. “We can know everything about a system at a given time, yet we still can’t predict what it will do in the future,” he says. “That’s crazy. That’s a terrible thing. The whole idea of science is that we can give a reason for everything. And yet, suddenly, for no reason at all, these atoms behave differently.

“This made Einstein so unhappy that he coined the phrase ‘God doesn’t play dice.’ In my research I was guided all the time by the anguish of Einstein’s statement, and I always set for myself the goal to find out, why does God play dice? There might be some reason for nature to behave in that way. My whole approach to quantum mechanics is to find out that reason.”

To resolve the anguish of Einstein takes something radical. Aharonov’s proposal is that information about the future comes back and affects the present. “If two quantum particles from the same situation behave differently in the future, perhaps nature is trying to tell us there was a difference between them − but that this difference is not in the past, but in the future.” Or to put it more baldly: the future affects the present.

Ideas worth listening to

The physicists gathered at the conference are skeptical, but listening. After all, it’s Yakir Aharonov. “I know how it sounds,” says Avshalom Elitzur, a former student and collaborator of Aharonov’s who is now a quantum foundations leader in his own right. “It would shake the Earth under us. But it would not be Yakir’s first earthquake.”

“I am not convinced,” says Pearle. “I am not qualified to assess Aharonov, but I would never dismiss him.”

“I’ve been hearing Yakir say very similar things for a long time,” says Steinberg. “The task of absorbing his brilliant insights is a difficult one. It’s impossible for most of us to judge to what extent his new insights have really resolved these deep problems or not, but I’m certainly ready to say that he’s invented a number of new perspectives that I firmly believe will help us understand things better.”

Aharonov’s bald statement – that the future affects the present – is new, but it builds on decades of work and enchanting hints.

“Quantum mechanics tell us that the universe is much richer than we thought,” says Elitzur. He’s one of the namesakes of the Elitzur-Vaidman bomb paradox, and discoverer of the quantum liar paradox. Both demonstrate that sometimes the mere possibility that particles might interact during an experiment is enough to affect the final state of the experiment – even if they did not interact. “That things that could have happened, but didn’t, have a say in our universe,” he says. “Even shadowy possibilities are important.” It is a poet’s universe.

More directly related is work on weak measurements. Almost 30 years ago, Aharonov and colleagues proposed a unique way of measuring quantum systems. Weak measurements were meant to resolve what’s long been a quantum conundrum: we can’t say what a particle is doing when we’re not looking at it, but when we do look at it, we change its behaviour.

Concepts and Paradoxes conference attendees
Attendees of the “Concepts and Paradoxes in a Quantum Universe” conference at Perimeter Institute.

Weak measurements are a work-around for that dilemma, a technique for glimpsing what a particle is doing when we’re not looking at it – or at least not looking at it very much. The scheme uses a measurement so weak, so noisy, that it gives very little information, but also creates very little disturbance in the particle: there is a good chance that it will keep on doing its quantum thing. The weak measurement scheme also screens out unwanted cases by preparing particles in some initial state, and throwing away data related to particles that end up in some unwanted final state: a schema of pre-selection and post-selection.

In 2011, Steinberg and colleagues used weak measurements to track the average paths of single photons passing through a double slit. The resulting plot showed a beautiful wave form, as quantum as could ever be imagined. Weak measurements are still controversial, and still mysterious, but looking at the Steinberg plot, one may reasonably feel that they have seen what particles do when we aren’t looking at them. That they have looked at the particle and seen the wave.

Why does this work? This is the piece that’s new. After years of research, Aharonov has developed a new description of quantum mechanics known as the two-state vector formalism. In it, any quantum system would be described not with one wave equation but with two: the familiar one evolving forward from the past, and a new one evolving backward from the future. In the case of the well-known double-slit experiment, for example, the familiar vector describes what happens when a photon (or other quantum particle) leaves its source, while the new vector evolves backwards from the final location of the photon on the detection screen. A combination of the two vectors is needed to predict what occurs when the photon passes the slits.

Steinberg helps turn this into a story anyone can follow: “If I leave here at 8:00 and I tell you I’m hoping to get home at 10:00, that gives you more information about where my car is at the intervening times.” He’s quick to add: “That’s not the standard way we approach quantum mechanics. In the normal approach to quantum mechanics, you don’t get any more information by looking at where something lands, than you had about just watching where it was emitted.” But in Aharonov’s new formulation, information about where something lands – information from the future − is exactly what’s needed.

In reformulating quantum mechanics in this way, Aharonov thinks he has resolved the anguish of Einstein. “Why does God play dice?” he says. “Because it opens the possibilities for nature to behave in a new way.”

Time is central

Uncertainty, in his view, is a blessing in disguise, because it spares us from something worse: paradox.“It’s like in the movies, like Back to the Future. Our intuition is that if something comes back from the future, like in a time machine, it immediately leads to terrible paradoxes – to stories about people who kill their grandfathers. It’s all paradoxes, paradoxes, paradoxes.”

But in Aharonov’s new formalism, uncertainty is the price we pay for ensuring that information coming back from the future to the present cannot create a paradox. “It turns out,” says Aharonov, “that the only consistent way for something to come back from the future without paradoxes is to have uncertainty.”

You can see the importance of uncertainty play out in the weak measurement experiments, or, in Aharonov’s own words: “If you have uncertainty, then in the present your measurement has lots of noise. So you do the experiment in the present, you recognize that there are lots of possibilities for error, so you repeat the same experiment many times. You record the results many times.

“And then you come to the future and you make some experiments in the future. You take the results of these experiments and come back to your recording of the ‘present.’ And you find something remarkable. Out of this error, suddenly a new order comes about, that you could not understand before.”

Aharonov’s two-state vector formalism does not make quantum mechanics predictive, but rather explains why it cannot be. In other words, it shows that God does play dice – which is not a new insight – and tells us why – which is. The formalism would explain why weak measurement seems to offer such impossible glimpses. And, perhaps most centrally, it smooths out the fundamental problem of events by introducing a new approach to time, in which the state of the present – the event – is described by the interaction of a wave function coming from the past, and a different wave function coming from the future.

“Time was always the most mysterious thing in nature,” says Aharonov. “We experience time as a becoming – the present becomes another present becomes another present. There was no way for the old physics to explain this behaviour of time. We need a new approach to time. To begin this new approach I reformulated quantum mechanics.”

Time is not merely mysterious; it is central. As human beings, we are fundamentally storytellers: there is not a culture in the world that does not put stories at its centre. In stories, one thing happens after another, after another. In stories, the past is different from the future. In stories, we can use the word become, and we can use the word because. This is how we make sense of the world. Giving that up is hard. But Aharonov is a storyteller.

“Let me say the following,” says Elitzur, his former student. “As crazy as quantum mechanics is, it still obeys basic principles of conservation. It occurs within spacetime, which surely has some quantum properties, but still must have the classical properties which enable classical physics and relativity to succeed. So it tells a story. Somewhere, sometime, one thing has led to another. As Chekov says, if you see a pistol in act one, there will be a shooting. Yakir is seeing many pistols, and he manages to follow them to the shooting. Or, sometimes the opposite: he hears a shot, and his methods are powerful enough to go back and reveal the gun or even the smoking gun.”

“If you like,” says Aharonov, “my lifetime work is trying to find the correct story to tell about quantum mechanics, and from this, to be able to predict features in the theory, new phenomena. In finding new ways of thinking I’ve been able to uncover many very interesting and beautiful new phenomena.”

And now, he says, he’s done that. “There are still open questions about how to combine quantum mechanics with general relativity, but the main problem with how to make sense of quantum mechanics – this is the story. This is the right story.”


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