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February 6, 2023

Dissolving Quantum Paradoxes
The impossibility of building a perfect clock could help explain away microscale weirdness.
by Kate Becker
FQXi Awardees: Lídia del Rio, Renato Renner
August 31, 2018
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Renato Renner
ETH Zurich
"All the world’s a stage, and all the men and women merely players."

Shakespeare’s familiar line is 400 years old; it came decades before Newton, and centuries before relativity and quantum mechanics. But, the way theoretical physicists Lídia del Rio and Renato Renner, both of ETH Zurich, see it, Shakespeare may have been on to something.

Physicists traditionally like to describe the world as if they were observing it from the outside: audience members at the theater of the universe, watching the story unfold without participating in the action on stage. Call it "the God view," says Renner. It’s a formulation that works just fine in Newton’s classical mechanics. The problem? It may not actually exist.

One of the foundational insights of quantum theory is that, just by observing a system, you change it. The problem of Schrödinger’s poor, overworked cat turns on the peculiar power of the observer. As the paradox goes, a cat is trapped in a box with a vial of poison that will be released if a radioactive particle decays. But according to quantum mechanics, until the moment it is observed, the particle is in a weird state in which it has both decayed and not decayed, which means that the cat is suspended in a limbo state in which it is both alive and dead at the same time. Some thinkers say that the cat is in a "superposition" of states: that is, the cat is both alive and dead simultaneously. Others argue that the cat is in a "mixture" of states: there are equal, 50/50 odds that the cat is alive or dead. Either way, when an observer finally checks on the cat, the observation instantaneously settles the quantum stalemate, rendering the cat either 100% alive or 100% dead.

Collapsing Cats

One way to interpret this is that the observation caused the cat’s wavefunction—the mathematical expression of the cat’s possible states and how likely they are—to "collapse" into a single outcome. But today many theorists favor a different way of thinking, called the "many worlds" interpretation. In this view of things, observing the cat makes reality branch into two separate but equally valid realities. In one, the cat lives; in the other, it dies.

Which brings us back to the quantum theater, where the audience is never passive. Simply by their presence, they affect the turns the story takes, the way the characters behave, and the way the play goes. It’s a perfectly Shakespearean insight. After all, historians think that, back in Shakespeare’s day, the cheap seats (which weren’t seats at all) were filled with rowdy hecklers who were happy to interrupt the show, or even get up on stage themselves. The invisible "wall" that separates actors from audience simply wasn’t there. All the world was a stage, and the stage was all the world.

Each time I measure
time, my clock… is a
bit degraded.
- Renato Renner
So how do you choose which quantum interpretation is correct? Renner and del Rio think that may be the wrong question to ask. With support from a $60,000 grant from FQXi, they are exploring what it means to tear down that invisible wall between the observers and the observed. By recasting objective "observers" as subjective "agents" who can’t help but participate in the quantum action that they are studying, del Rio and Renner think that they may be able to resolve paradoxes like Schrödinger’s cat and better understand how classical reality emerges from quantum theory.

Once you start thinking of an agent as a quantum system in his or her own right, says Renner, things get complicated. Imagine an experiment in which one scientist tries to use quantum mechanics to make predictions about other scientists who, in turn, use quantum mechanics to make predictions, like a play within a play within a play. Because the experimenters are all quantum systems, they must model not just the quantum state of the equipment and particles in each others’ labs, but each other as well. In certain circumstances, the result will be a contradiction, as if one member of the audience wept to see Romeo and Juliet die, while another cried happy tears when she saw the lovebirds live happily ever after.

Quantum Clock

Removing the wall between actors and audience also means eliminating the wristwatches that the audience members keep glancing at and admitting that the only time that matters is time as it passes inside the play. It’s an idea that was first introduced in the 1980s, when FQXi members Don Page, now at the University of Alberta, Canada, and William Wootters, at Williams College, in Williamstown, Massachusetts, suggested nixing the notion of a "universal" clock that exists independently of the system being studied and replacing it with a "quantum" clock. Instead of ticking away off-stage, the quantum clock is itself a quantum system. It could be as simple as a single photon or as elaborate as the movement of a Swiss clock—the more complicated the system, the more precise the clock—but whatever it is, it runs on the same quantum rules as the rest of the world.

That means that, no matter how massive or elaborate it is, a quantum clock cannot be infinitely precise. "If you measure a quantum system, you necessarily disturb it," says Renner. "Each time I measure time, my clock that gives me the time information is a bit degraded."

Time Distortion
Without an accurate clock, the difference between
various interpretations of quantum paradoxes
First-generation quantum theorists like Erwin Schrödinger realized more than 90 years ago that you could not build a perfect quantum clock. But, says Renner, no one has ever figured out how precise the very best quantum clock could be.

"What we are now trying to do is to find out what it is that bounds the ultimate accuracy of clocks," says Renner. They are using an approach based on information theory to try and understand the physical principles that are responsible for the fundamental limits on time measurements.

"Let’s say we would like to decide whether there’s really a superposition of the dead cat and living cat," says Renner, returning to the Schrödinger’s cat paradox. "If we want to do that we have to control the system extremely well," in particular the wavefunction, says Renner. That level of control would require an exquisitely precise clock—one that might be impossible to build.

If Renner and del Rio can show that such a precise quantum clock is a physical impossibility, that would meant that there is no way to discriminate between a superposition and a mixture in a "macroscopic" object like a cat, and the difference between the two states would lose its meaning. "Then the distinction between superpositions and mixtures is just a mathematical curiosity without a ’physically existing’ counterpart," says Renner. "The paradox would dissolve."

That would also resolve the play-within-a-play problem. If there are limits on how well we can measure time, that means that there are also limits on how well quantum mechanics can describe the world. That innate inexactness might not matter on small scales, but it could compound for large systems, like scientists. "If we give up the idea that there is a perfectly precise time then the predictions that (current) quantum theory makes about scientists who use quantum theory may be wrong," Renner says.

Theorists working on quantum gravity—the problem of reconciling quantum theory with Einstein’s description of gravity—are also eager for new ways to think about time. "The goal of quantum gravity is to describe space-time itself—and thus, in some sense, the whole universe—quantum mechanically, and then there is no space for external clocks or observers," says Markus Müller, a quantum physicist at the Austrian Academy of Sciences in Vienna. "Instead, one has to treat clocks as part of the quantum-mechanical system"—just as del Rio and Renner are doing.

Matthew Leifer, a quantum physicist at Chapman University, also hopes that del Rio and Renner’s work could solve multiple longstanding theoretical puzzles at once. "The approach seems very ambitious in that they are trying to tie together several problems that are usually thought of separately, and thought to be very difficult on their own," he says. "Maybe thinking about these as instances of the same general problem will lead to new insights."

No one knows how this particular play will turn out, including del Rio and Renner. "In such conceptual work, it is always hard to say how close one is to a result," says Renner. So, for now, we’ll stay on the edge of our seats, waiting to find out what happens before the curtain falls.

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