Quantum physicists Sandu Popesque, Yakir Aharonov and Daniel Rorlich have been haunted by the same situation for the past 30 years.

It all started in 1990 when they wrote about super oscillations (an unusual wave phenomenon). Popesque, a professor at the University of Bristol at the time, said: “We’ve never told you what’s bothering us. Every year since then, we’ve come back and see it from another angle.”

In December 2020, the trio published a paper explaining the problem in the proceedings of the National Academy of Sciences: In Quantum Systems, Super Oscillations seem to violate the Energy Conservation Act.

The law states that the energy of an isolated system never changes. This is not only a basic principle of physics, says Chiara Marleto, a physicist at Oxford University, who now understands it as a manifestation of the basic symmetry of the universe and an important part of physics.

Physicists differ as to whether the new paradox exposes the real violation of energy conservation. Their attitude toward the question depends on whether the individual experimental results in quantum mechanics should be taken seriously, no matter how improbable. It is hoped that by working to solve this puzzle, researchers will be able to clarify some of the most subtle and strange aspects of quantum theory.

The main factor is superposition, an effect that every physics student feels is contradictory to learning about waves.

Any wave, no matter how complex, can be represented as a sum of sine waves of different frequencies. A wave can only oscillate up to its high frequency sine wave component. So in combination with a beam of red light, it should logically remain red.

By the 1990s, however, Aaronov and Popesk had discovered that specific combinations of sine waves created regions of collective waves that oscillate faster than any other element. Their colleague Michael Berry pointed out that Beethoven’s ninth symphony could be played by combining sound waves below 1 Hz. As some signal processing experts already know, this rediscovery of super oscillations has inspired physicists to discover numerous applications ranging from high-resolution imaging to newer radio designs.

Just as super oscillation is amazing, it does not violate any laws of physics. But when Akhalonov, Popesque, and Rohlich applied this idea to quantum mechanics, they encountered a completely paradoxical situation.

In quantum mechanics, a particle is described by the action of a wave, and its varying magnitude indicates the possibility of finding that particle in different places. Like any other wave, one wave activity can be represented as the sum of the sine waves.

The energy of a wave is proportional to its frequency. This means that when a wave function is a combination of multiple sine waves, the particles are in a “superposition” state of energy. When its energy is measured, the wave activity appears as a mysterious “breakdown” of energy in a superposition.

Popesque, Aharonov, and Rohlich exposed this paradox in an excellent experiment. Suppose you have a photon trapped in a box, and this photon has a super oscillating area for wave action. Quickly place a mirror in the path of the photon, where the wave activity is superosylating, and place the mirror there for a while. If the photon comes close to the mirror at this point, the photon will be taken out of the mirror box.

Since the bounce does not form a scale, the wave function does not collapse. Instead, it is divided into two parts. Most of the wave function remains in the box, but a small portion of the rapidly oscillating wave activity near the mirror insert goes out of the box and into the detector.

Since this super oscillating part is extracted from the rest of the wave function, it is now equivalent to a very high energy photon. When this piece falls on the detector, the whole wave function breaks down. When it crashes, the detector has a small but real potential to record high-energy photons. It’s like gamma rays coming out of a box of red light.

The problem is, this thought experiment shows that energy conservation can be violated in individual situations – something that many physicists oppose.

Marleto believed that the Energy Conservation Act was right. In her opinion, if your experiment seems to violate this protection law, you are not looking carefully enough. The extra energy has to come from somewhere. “This so-called violation of energy conservation can have many avenues, one of which is not taking the environment into account,” she said.