that it’s possible to play Beethoven’s Ninth Symphony by combining only sound waves below 1 hertz—frequencies so low that, individually, they would be imperceptible to the human ear. This rediscovery of superoscillation, which was already known to some signal processing experts, inspired physicists to invent an array of applications, from high-resolution imaging to new radio designs.
A wave’s energy is proportional to its frequency. This means that, when a wave function is a combination of multiple sine waves, the particle is in a “superposition” of energies. When its energy is measured, the wave function seems to mysteriously “collapse” to one of the energies in the superposition.
Because this superoscillatory piece has been plucked from the rest of the wave function, it is now identical to a photon of much higher energy. When this piece hits the detector, the entire wave function collapses. When it does, there’s a small but real chance that the detector will register a high-energy photon. It’s like the gamma ray emerging from a box of red light. “This is shocking,” said Popescu.
The problem is, the thought experiment suggests that energy conservation can be violated in individual instances—something many physicists object to., a professor emeritus at Reed College in Oregon and author of standard textbooks on quantum mechanics, maintains that energy must be conserved in each individual experimental run .
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