Physicists have challenged a long-standing postulate of quantum mechanics: are imaginary numbers actually necessary? A team from Heinrich Heine University Düsseldorf (HHU) and the German Aerospace Center (DLR) has demonstrated something unexpected—quantum mechanics can be fully described using only standard real numbers. The research was published in Physical Review Letters and designated as a Highlight by the American Physical Society.
For decades, the theory has rested on complex numbers, where the real part encodes the amplitude of a quantum state and the imaginary part captures its phase. These "strange" numbers—whose squares result in negative values—were considered indispensable, as they seemed vital for describing key quantum phenomena ranging from interference to entanglement. In 2021, an international team led by Marc-Olivier Renou published a paper in Nature arguing that any version of quantum mechanics based solely on real numbers could be experimentally disproven. This appeared to be the final verdict on the matter.
However, Professor Dagmar Bruß and her doctoral student Pedro Barrios Hita re-examined one of the fundamental assumptions. Rather than demanding total mathematical identity when combining quantum systems, they applied a different approach based on physical meaning rather than formal postulates: if an operation acts on only one of two independent subsystems, it should have no measurable effect on the other. This simple, logical condition proved to be the decisive factor.
The result stunned the team: an entire family of quantum theories emerged, formulated exclusively with real numbers, yet predicting exactly the same outcomes as standard quantum mechanics for every conceivable experiment.
"Both frameworks yield identical predictions for any imaginable experiment," explained Professor Bruß. "This means that within this framework, imaginary numbers are not fundamentally necessary in quantum mechanics and could, in principle, be replaced by alternative formulations using real numbers."
What does this mean for practical applications, from quantum computers to secure communication? This remains an open question, and experimentalists are only just beginning to grapple with the implications. Yet the very existence of such an equivalent formulation is set to overturn our understanding of the theory's mathematical foundations, revealing that what seemed like a fundamental feature of physical reality might simply be a convenient calculation tool.
