Dec 22, 2021 17:00:00

Recent research shows that imaginary numbers are needed to explain reality

Two recent studies have shown that

imaginary numbers, which are 'numbers that shouldn't exist', are needed to explain reality accurately.

Quantum theory based on real numbers can be experimentally falsified | Nature
https://www.nature.com/articles/s41586-021-04160-4

Physical Review Letters --Accepted Paper: Testing real quantum theory in an optical quantum network
https://journals.aps.org/prl/accepted/0907bY08X531687d3971977071a6d5f742cb036ed

Imaginary numbers could be needed to describe reality, new studies find | Live Science
https://www.livescience.com/imaginary-numbers-needed-to-describe-reality

'A number that becomes negative when squared' is an imaginary number, which is used as part of the wave function that represents a pure state in quantum mechanics, which is a field of physics. It has long been argued whether imaginary numbers are used in equations used in quantum mechanics because 'the equations do not hold without imaginary numbers' or 'because simple equations can be easily explained by using imaginary numbers'. Where it has been done.

Even Erwin Schrödinger , the founder of quantum mechanics, is skeptical about the implications of including complex numbers in equations in a letter to a friend. In fact, Schrodinger has devised a way to express the wavefunction only with real numbers without imaginary numbers, and later physicists continue to try to replace imaginary numbers with real numbers in quantum theory.

The question here is whether quantum theory works correctly without imaginary numbers. Two of the studies that shed light on this were the study published in the academic journal Nature on December 15, 2021 and the study published in the Physical Review Letters on the same day. Through relatively simple experiments, the two studies prove that 'if quantum mechanics is correct, the reality cannot be realized without the existence of imaginary numbers', and Schrodinger's wave function imaginary numbers are converted into real numbers. The replacement attempt shows that it is wrong.

'Schrödinger, the founder of quantum mechanics, couldn't find a way to interpret the complex numbers that appear in the theory,' said Mark Olivier Lenow, a theoretical physicist at the Spanish Institute of Optical Sciences who was involved in the study. Probably, it makes a lot of sense to have (equations) imaginary numbers, but there is no clear way to identify imaginary numbers in terms of real elements, 'he told the scientific media Live Science. increase.

In the study published in Nature, a method was devised to add a slight twist to

the classical quantum experiment 'Bell's theorem ' in order to verify whether imaginary numbers are really important elements in wave functions. It has been. In the experiment, two independent light sources (S, R) are first placed between the three detectors (A, B, C) of the basic quantum network, and two light particles or photons are placed from the light source S, one is A. Emit in the direction and the other in the B direction. On the other hand, the light source R also emits two photons in the directions of B and C. If the universe is described by standard quantum mechanics based on imaginary numbers, photons reaching A and C will not cause entanglement. However, if all of quantum mechanics can be explained by real numbers, photons should be entangled.

In the second study, in order to demonstrate the first study, an experiment was conducted in which a laser beam was applied to the crystal. As a result of the experiment, it has been confirmed that the photons that caused the quantum entanglement were emitted, but the photons at the time of reaching the detectors A and C were not entangled. In other words, it was proved that quantum mechanics can only be explained correctly by using imaginary numbers.

'Just observing what comes out of some experiments and excluding many potential explanations without assuming the reliability of the physical devices used in the experiments,' said Lenow, who was involved in the study. In the future, physicists may need some experiments built from the first principles to reach complete quantum theory. '

He also notes that the results of this study may help outline the principles of the quantum Internet in the future.