A Puzzling Quantum Scenario Appears to Violate a Law of Physics

The physicists have been troubled by the same scenario for three decades.

They wrote about a wave phenomenon called superoscillation in 1990.

In December 2020, the trio published a paper in the Proceedings of the National Academy of Sciences explaining the problem of superoscillation in quantum systems. The law states that the energy of an isolated system is more than a physical principle. It is an expression of the fundamental symmetries of the universe, which is very important part of the edifice of physics.

Physicists are divided on whether the new paradoxes exposes a genuine violation of the conserved energy. Their attitudes toward the problem depend on whether individual experimental outcomes in quantum mechanics should be considered seriously. The hope is that by resolving the puzzle, researchers will be able to clarify some of the most subtle and strange aspects of quantum theory.

There is a mirror trick.

The scenario in question is similar to opening a box full of red light and seeing a high-energy radiation shoot out. How can this happen?

The key ingredient is a phenomenon called superoscillation, which seems to contradict what a physics student learns about waves.

Any wave can be represented as a sum of waves of different frequencies. The students learned that a wave can only be oscillated as fast as its component. It should stay red if you combine a bunch of red light.

The collective wave that wiggles faster than any of the others was discovered by Aharonov and Popescu around 1990. Their colleague Michael Berry showed that it is possible to combine sound waves below 1 hertz to play Beethoven's Ninth symphony. The rediscovery of superoscillation inspired physicists to invent new applications, from high-resolution images to new radio designs.

It doesn't contradict any laws of physics. The situation that they encountered when applying the concept to quantum mechanics was downright strange.

In quantum mechanics, a particle is described by a wave function, which is a kind of wave that varies in amplitude. Wave functions can be expressed as sums of waves.

The wave's energy is proportional to its Frequency. When a wave function is a combination of multiple waves, the particle is in a position of energies. The wave function seems to collapse to one of the energies in the superposition when it is measured.

The paradoxes were exposed using a thought experiment. If you have a photon trapped inside a box, the wave function has a superoscillatory region. Put a mirror in the photon's path where the wave function superoscillates, and keep it there for a short time. The mirror will bounce the photon out of the box if the photon is close enough to the mirror.