Study Finds Imaginary Numbers May Not Be Essential to Quantum Mechanics

Insider BriefPress release – Physicists at Heinrich Heine University Düsseldorf (HHU), in collaboration with the German Aerospace Center (DLR), have been investigating a fundamental property of quantum mechanics. In the journal Physical Review Letters, they show that this theory does not necessarily have to be formulated with imaginary numbers, but that this is also possible with real numbers.

The American Physical Society also dedicates a „highlight“ to these results in its Physics Magazine.The physical theory of quantum mechanics describes the world of atomic and subatomic particles. It was developed from the 1900s onwards by physicists such as Max Planck, Niels Bohr, Werner Heisenberg and Erwin Schrödinger. Quantum mechanics is successful in describing phenomena on microscopic scales. This includes, for example, the diffraction of particles at a double slit – particles also exhibit wave-like characteristics afterwards – and the tunneling effect, according to which particles can penetrate a barrier with a certain probability, even if their energy is too low. Today, particularly important phenomena are so-called entanglement and coherence, which are crucial in applications such as quantum computers and communication.A central tool of quantum mechanics are the so-called complex numbers. Here, a number is represented by two coordinates – a real and an imaginary part –; a quantum state has an amplitude represented by the real component and a phase represented by the imaginary part. Without this construct, many processes could not previously be described quantum mechanically. However, it is controversial whether quantum mechanics cannot fundamentally do without complex numbers, or whether these numbers are merely a practical computational tool. Consequently, the question is: Is quantum mechanics conceivable using only real numbers?In a paper published in 2021, the authors concluded that complex numbers are indispensable for quantum mechanics among standard postulates (Renou et al., Nature 600, 625 (2021)). This was also confirmed experimentally.Now, a team of physicists from HHU and DLR, led by Prof. Dr. Dagmar Bruß and her doctoral student Pedro Barrios Hita used the postulates employed in the earlier study. In a publication now appearing in Physical Review Letters, they show that one of these postulates is too restrictive. Instead, the authors identified a physically motivated alternative to formalize the system composition. As a result, this leads to a class of theories that can be formulated entirely with real numbers and that cannot be experimentally distinguished from standard quantum mechanics.Prof. Bruß: “The result is that both frameworks provide identical predictions for every conceivable experiment. Within this framework, imaginary numbers are therefore not fundamentally necessary in quantum mechanics, but can basically be replaced by alternative formulations with real numbers.“TopicsShare Get the latest research, company news, and market intelligence every week. MENTIONED IN THE ARTICLEHeinrich Heine University Düsseldorf, located in North Rhine-Westphalia, Germany, is a public university established in 1965. It succeeded Düsseldorf's Medical Academy from 1907 and was named in honor of the German poet Heinrich Heine.More in Research 2026 © Resonance Alliance Inc.

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