Quantum mechanics can be built from real numbers without losing any of its predictive power. That is the central result from a paper published on 18 June 2026 in Physical Review Letters by physicists at Heinrich Heine University Düsseldorf and the German Aerospace Center.
The work, titled Quantum Mechanics Based on Real Numbers: A Consistent Description, replaces one postulate governing composite quantum systems with a physically motivated alternative. Authors Pedro Barrios Hita, Anton Trushechkin, Hermann Kampermann, Michael Epping, and Dagmar Bruß demonstrate that the resulting family of real-number theories matches the experimental predictions of conventional quantum mechanics exactly.
This finding directly addresses a 2021 study in Nature that had argued real-number formulations satisfying certain standard postulates could be ruled out by experiment. By modifying the rule for how separate quantum systems combine, the Düsseldorf team sidesteps that limitation while preserving full consistency with observed data.
Imaginary numbers as convenience
The American Physical Society selected the paper as a highlight in its Physics magazine, signalling its interest to the broader physics community. The result carries implications for how theorists conceptualise the deepest layer of physical law and for how quantum mechanics is taught.
Dagmar Bruß, professor at Heinrich Heine University Düsseldorf, put the outcome plainly: This means that both frameworks yield identical predictions for any conceivable experiment. 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.
Traditional quantum theory relies on complex numbers to capture amplitudes and phases in interference, tunnelling, entanglement and coherence. These phenomena drive technologies from quantum computers to precision sensors. The new real-number construction shows the same empirical content can be recovered without invoking the imaginary unit.