Image credit: Event Horizon Telescope collaboration

For three decades, similar conditions have plagued quantum physicists Sandu Popescu, Yakir Aharonov, and Daniel Rohrlich.

They started when they wrote about a great wave called superoscillation in 1990. “We could not say what was troubling us,” said Popescu, a professor at the University of Bristol. “Since then, we come back and see it differently every year.”

Finally, in December 2020, the three published a paper in Proceedings of the National Academy of Sciences outlining the problem: In quantum systems, superoscillation appears to violate energy conservation law. This law, which states that the power of a remote system does not change, is beyond the basal body. It is now understood to reflect the basic dimensions of the Universe – “the most important part of the physical structure,” said Chiara Marletto, a physicist at Oxford University.

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Physicists are divided on whether the new paradigm exposes a fundamental violation of energy conservation. Their attitudes toward the problem largely depend on how much each test results in quantum mechanics should be considered severe, no matter how improbable. The hope is that by making an effort to solve the puzzle, researchers will be able to unravel some of the hidden and complex aspects of quantum theory.

Mirror Trick: Aharonov described the situation as opening a box full of red light – powerful electric waves – and seeing a powerful gamma-ray explode. How is this possible?

The main ingredient is superoscillation, which seems to contradict what every physics student learns about waves.

No matter how complex, any wave can be represented as a total of four waves of different frequencies. Students learn that a lock can revolve around as fast as its most common sine waves. So add a lot of red light, and it should always be red.

But in about 1990, Aharonov and Popescu discovered that a unique combination of four waves produced regions of a combined wave that moved faster than any other element. His colleague Michael Berry demonstrated the power of superoscillation by showing the possibility (though not possible) of playing Beethoven’s Ninth Symphony by combining sound waves with less than 1 hertz – waves so low that, individually, they would not be visible to the human ear. This discovery of superoscillation, already known by some signal processing experts, has motivated physicists to develop applications ranging from high-definition graphics to new radio designs.

Photo of Sandu Popescu, a particularly bald man with glasses, wore a suit and tie.

Sandu Popescu, a quantum physicist at the University of Bristol, is known for inventing thought tests that reveal new details about contextual concepts.

Royal Society
Surprisingly as superoscillation is, it does not contradict any laws of physics. But when Aharonov, Popescu, and Rohrlich applied the concept to quantum mechanics, they encountered a dilemma.

In quantum mechanics, particles are defined by wave activity, a wave whose amplitude varies that transmits particle probability in different locations. Wave operations can be expressed as sine wave statistics, just as other waves can.

The power of a wave is equal to its frequency. This means that if wave activity combines multiple sine waves, the particle is “on top” of the force. When its power is measured, the function of the waves appears to be “falling” in a mysterious way to some of the troops in the superposition.

Popescu, Aharonov, and Rohrlich revealed a paradox in their use of imagination. Suppose you have a photon trapped inside a box, and the photon wave function has a superoscillatory space. Quickly insert the mirror into the photon path when the wave function superoscillates, keeping the mirror there for a short time. If the photon is close enough to the screen at that moment, the mirror will release the photon out of the box.

Remember, we are dealing with the work of the photon wave here. Since the bounce does not include measurements, the function of the tides does not fall. Instead, it splits in two: Most of the wave activity resides in the box, but a small, rotating piece, near the place where the mirror is placed, leaves the box and heads for the detector.

Because this part of the superoscillatory is released from all wave activity, it now resembles a high-energy photon. When this clip hits the detector, all the wave activity breaks down. There is a slight but real chance that the sensor will register a high-energy photon if possible. It is like a gamma-ray emanating from a box of red light. “This is shocking,” said Popescu.


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