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In the world’s most famous thought experiment, physicist Erwin Schrödinger described how a cat in a box could be in an uncertain predicament. The peculiar rules of quantum theory meant that it could be both dead and alive, until the box was opened and the cat’s state measured. Now, two physicists have devised a modern version of the paradox by replacing the cat with a physicist doing experiments — with shocking implications.

Quantum theory has a long history of thought experiments, and in most cases these are used to point to weaknesses in various interpretations of quantum mechanics. But the latest version, which involves multiple players, is unusual: it shows that if the standard interpretation of quantum mechanics is correct, then different experimenters can reach opposite conclusions about what the physicist in the box has measured. This means that quantum theory contradicts itself.

The conceptual experiment has been debated with gusto in physics circles for more than two years — and has left most researchers stumped, even in a field accustomed to weird concepts. “I think this is a whole new level of weirdness,” says Matthew Leifer, a theoretical physicist at Chapman University in Orange, California.

The authors, Daniela Frauchiger and Renato Renner of the Swiss Federal Institute of Technology (ETH) in Zurich, posted their first version of the argument online in April 2016. The final paper appears in Nature Communications on 18 September1. (Frauchiger has now left academia.)

Weird world

Quantum mechanics underlies nearly all of modern physics, explaining everything from the structure of atoms to why magnets stick to each other. But its conceptual foundations continue to leave researchers grasping for answers. Its equations cannot predict the exact outcome of a measurement — for example, of the position of an electron — only the probabilities that it can yield particular values.

Quantum objects such as electrons therefore live in a cloud of uncertainty, mathematically encoded in a ‘wavefunction’ that changes shape smoothly, much like ordinary waves in the sea. But when a property such as an electron’s position is measured, it always yields one precise value (and yields the same value again if measured immediately after).

The most common way of understanding this was formulated in the 1920s by quantum-theory pioneers Niels Bohr and Werner Heisenberg, and is called the Copenhagen interpretation, after the city where Bohr lived. It says that the act of observing a quantum system makes the wavefunction ‘collapse’ from a spread-out curve to a single data point.

The Copenhagen interpretation left open the question of why different rules should apply to the quantum world of the atom and the classical world of laboratory measurements (and of everyday experience). But it was also reassuring: although quantum objects live in uncertain states, experimental observation happens in the classical realm and gives unambiguous results.

Now, Frauchiger and Renner are shaking physicists out of this comforting position. Their theoretical reasoning says that the basic Copenhagen picture — as well as other interpretations that share some of its basic assumptions — is not internally consistent.

What’s in the box?

Their scenario is considerably more involved than Schrödinger’s cat — proposed in 1935 — in which the feline lived in a box with a mechanism that would release a poison on the basis of a random occurrence, such as the decay of an atomic nucleus. In that case, the state of the cat was uncertain until the experimenter opened the box and checked it.

In 1967, the Hungarian physicist Eugene Wigner proposed a version of the paradox in which he replaced the cat and the poison with a physicist friend who lived inside a box with a measuring device that could return one of two results, such as a coin showing heads or tails. Does the wavefunction collapse when Wigner’s friend becomes aware of the result? One school of thought says that it does, suggesting that consciousness is outside the quantum realm. But if quantum mechanics applies to the physicist, then she should be in an uncertain state that combines both outcomes until Wigner opens the box.

Frauchiger and Renner have a yet more sophisticated version (see ‘New cats in town’). They have two Wigners, each doing an experiment on a physicist friend whom they keep in a box. One of the two friends (call her Alice) can toss a coin and — using her knowledge of quantum physics — prepare a quantum message to send to the other friend (call him Bob). Using his knowledge of quantum theory, Bob can detect Alice’s message and guess the result of her coin toss. When the two Wigners open their boxes, in some situations they can conclude with certainty which side the coin landed on, Renner says — but occasionally their conclusions are inconsistent. “One says, ‘I’m sure it’s tails,’ and the other one says, ‘I’m sure it’s heads,’” Renner says.

The experiment cannot be put into practice, because it would require the Wigners to measure all quantum properties of their friends, which includes reading their minds, points out theorist Lídia Del Rio, a colleague of Renner’s at ETH Zurich.

Yet it might be feasible to make two quantum computers play the parts of Alice and Bob: the logic of the argument requires only that they know the rules of physics and make decisions based on them, and in principle one can detect the complete quantum state of a quantum computer. (Quantum computers sophisticated enough to do this do not yet exist, Renner points out.)

Duelling interpretations

Physicists are still coming to terms with the implications of the result. It has triggered heated responses from experts in the foundations of quantum theory, many of whom tend to be protective of their pet interpretation. “Some get emotional,” Renner says. And different researchers tend to draw different conclusions. “Most people claim that the experiment shows that their interpretation is the only one that is correct.”

For Leifer, producing inconsistent results should not necessarily be a deal breaker. Some interpretations of quantum mechanics already allow for views of reality that depend on perspective. That could be less unsavoury than having to admit that quantum theory does not apply to complex things such as people, he says.

Robert Spekkens, a theoretical physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, says that the way out of the paradox could hide in some subtle assumptions in the argument, in particular in the communication between Alice and Bob.

“To my mind, there’s a lot of situations where taking somebody’s knowledge on board involves some translation of their knowledge.” Perhaps the inconsistency arises from Bob not interpreting Alice's message properly, he says. But he admits that he has not found a solution yet.

For now, physicists are likely to continue debating. “I don’t think we’ve made sense of this,” Leifer says.