# Imaginary numbers turned out to be necessary to describe reality by quantum theory

(ORDO NEWS) — Imaginary numbers appear when we take the root of minus one. Together with real numbers, they make up the so-called complex numbers, which are widely used in mathematics, but about the role of which in quantum theory – service or fundamental – there has been an ongoing debate for a long time. SchrÃ¶dinger, the author of the famous wave equation, for example, believed that the complex numbers appearing in his equation play only an auxiliary role and are not related to the properties of nature.

Now, in two new studies, physicists have decided to test how fundamental complex numbers are to nature in an experiment that is a variation on Bell’s classic experiment. This test was created to test the hypothesis of quantum entanglement, a mysterious connection between two separated particles that is deduced from quantum theory.

In this new modification of Bell’s experiment, physicists placed two independent sources, S and R, between three detectors, A, B, and C, thus creating an elementary quantum network. Source S sends two particles of light, or two photons: one to detector A, and the other to detector B.

The emitted photons are then in a state of quantum entanglement. Source R similarly emits two photons, only directs them to sources B and C. If the Universe is described by standard quantum mechanics based on complex numbers, then the photons arriving at detectors A and C should not be in an entangled state between themselves, but if the quantum theory is built only on real numbers, then confusion should be observed.

For the test, the authors of the second of these studies conducted an experiment in which they irradiated crystals with laser beams. The energy transferred from the laser to the crystal was then re-emitted in the form of entangled photons.

By observing the states of the photons arriving at all three detectors, the researchers found that the photons arriving at the detectors A and C are not entangled, which implies that the data they obtained are based on quantum theory, which includes the use of complex numbers.

Research published in the journals Nature and Physical Review Letters; research team leader Marc-Olivier Renou.

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