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The quantum physicists Sandu Popescu, Yakir Aharonov and Daniel Rohrlich have been troubled by the same scenario for three decades.

It started when they wrote about a surprising wave phenomenon called superoscillation in 1990. “We were never able to really tell what exactly was bothering us,” said Popescu, a professor at the University of Bristol. “Since then, every year we come back and we see it from a different angle.”

Finally, in December 2020, the trio published a paper in the Proceedings of the National Academy of Sciences explaining what the problem is: In quantum systems, superoscillation appears to violate the law of conservation of energy. This law, which states that the energy of an isolated system never changes, is more than a bedrock physical principle. It’s now understood to be an expression of the fundamental symmetries of the universe — a “very important part of the edifice of physics,” said Chiara Marletto, a physicist at the University of Oxford.

Physicists are divided as to whether the new paradox exposes a genuine violation of the conservation of energy. Their attitudes toward the problem depend in part on whether individual experimental outcomes in quantum mechanics should be considered seriously, no matter how improbable they may be. The hope is that by putting in the effort to resolve the puzzle, researchers will be able to clarify some of the most subtle and strange aspects of quantum theory.

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