A new analysis conducted by researchers at the Heinrich Heine University (HHU) Düsseldorf and the German Aerospace Center (DLR) in Germany has shown that quantum mechanics could work without imaginary numbers too. This allows quantum mechanics theory to be formulated using real numbers, marking a major shift in how the science is carried out. 

In the early years of science, we were looking to answer questions like why do objects fall on the ground or why do certain chemicals react. To answer such questions, scientists developed theories that could explain the observations we made. As is the case with science, solving some problems raises new ones, and scientists now need to probe deeper to answer them. 

In the 1900s, physicists like Max Planck, Niels Bohr, Erwin Schrondinger, and others developed theories to explain the world of atomic and subatomic particles, leading to the development of quantum mechanics, which has opened up fields like quantum computing and sensing in recent years. 

Need for complex numbers

The field of quantum mechanics arose as physicists struggled to explain the behavior of phenomena in which particles displayed wave-like behavior, such as in the double-slit experiment. In another phenomenon like the quantum tunneling effect, particles display the ability to penetrate a barrier even when they do not have the energy to do so. 

In quantum physics, particles can combine to create an additive effect or even cancel each other out as opposite phases of a wave. To represent such behavior mathematically, physicists used complex numbers, which consist of two components: a real and an imaginary part. 

The amplitude is represented by the real number (1,2,3, so on), while its phase is represented using the imaginary part (-1,-2,-3, and so on). Using this construct, it has been possible to mathematically explain how wave-like behavior has canceling effects. 

Physicists have debated whether this is a fundamental necessity of quantum mechanics or simply a tool for simplifying calculations. In 2021, a team of researchers from Austria even published a paper demonstrating experimentally that complex numbers are necessary for quantum mechanics.

Not really

Dagmar Bruss, professor and Head of the Quantum Information Theory group at HHU, and her doctoral researcher, Pedro Barrios Hita, conducted a new analysis of the postulates used in the 2021 paper and found one to be too restrictive. 

Bruss and colleagues identified a physically motivated alternative that formalizes system composition and gives rise to a class of theories that can be formulated with real numbers and yet are indistinguishable from standard quantum mechanics, even at the experimental level. 

“This means that both frameworks yield identical predictions for any conceivable experiment,” said Professor Bruss in a press release. “Within this framework, imaginary numbers are thus not fundamentally necessary in quantum mechanics and can in principle be replaced by alternative formulations using real numbers.”

The research study was published in the journal Physical Review Letters. 

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