Imaginary numbers may be necessary to describe reality, according to new studies

An international team of researchers has shown through a theoretical experiment that the predictions of standard quantum theory cannot be explained without the help of complex numbers.

The approach and the demonstration of the result of the experiment, obtained by researchers from the Spanish Institute of Photonic Sciences (ICFO), the University of Geneva and the Schaffhausen Institute of Technology, the Vienna University of Technology and the IQOQI of the Academy of Sciences of Austria, were published in mid-December in the journal Nature. 

Physical theories are expressed in terms of mathematical objects, such as equations, integrals or derivatives, concepts that have evolved to explain increasingly complicated physical phenomena. 

Describing nature through theories is like using a map to go to the mountain: the map is a representation of the mountain, the houses, the rivers and the trails, but it is not the mountain, but the theory that is used to represent the reality of the mountain.

How essential are imaginary numbers for understanding the quantum world? Find out in this excellent N&V by William Wootters.
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Quantum Theory and Complex Numbers

But the advent of quantum theory, thought to represent the microscopic world, was a turning point for physics, since it was the first theory to be formulated in terms of complex numbers. 

And what are these complex numbers? They are numbers made up of a real part and an "imaginary" part, as the philosopher Descartes called it. 

The use of complex numbers is one of the anti-intuitive properties of quantum physics, and indeed some of the founding fathers of this theory, such as Schrödinger, expressed reservations.

However, several later results showed that it was possible to explain many quantum phenomena through a theory formulated with real numbers, and in this way the idea that complex numbers in quantum theory were just a convenient tool was accepted.

Now the study published in Nature shows that if quantum postulates are expressed in terms of real numbers rather than complex numbers, then some predictions about quantum networks would necessarily differ. 

In fact, the team of researchers presented a concrete experimental proposal, which included three interconnected parts and two sources of entangled particles, where the prediction of the standard complex quantum theory cannot be expressed by its real counterpart.

The subsequent experiment, carried out in collaboration with the University of Science and Technology of the South and the University of Electronic Science and Technology, has been published in Physical Review Letters, in parallel to the Nature article.

Bell's theorem

The results published in Nature can be seen as a generalization of Bell's theorem, which provides a quantum experiment that cannot be explained by any local quantum formalism.

The study also shows how outstanding the theory's predictions can be when combining the concept of a quantum network with Bell's ideas. 

Undoubtedly, the tools developed and used to obtain this first result are such that they will allow physicists to achieve a better understanding of quantum theory and will one day trigger the realization and materialization of applications hitherto unthinkable for the quantum Internet. 

FEW (EFE, Nature, Physical Review Letters)