Physicists question if quantum mechanics requires imaginary numbers
8 reported
Physicists from Heinrich Heine University Düsseldorf (HHU) and the German Aerospace Center (DLR) have published a study in Physical Review Letters suggesting that quantum mechanics may not need to be formulated with imaginary numbers. The researchers reexamined a 2021 study that concluded complex numbers were indispensable under standard quantum mechanics postulates. They found that one of the postulates used in that earlier analysis was more restrictive than necessary. By replacing it with a different approach for describing how quantum systems combine, they identified a family of theories that can be expressed entirely with real numbers while remaining experimentally indistinguishable from conventional quantum mechanics. The American Physical Society has dedicated a “Highlight” to these findings in its Physics Magazine.
What’s reported
The study was conducted by researchers from Heinrich Heine University Düsseldorf (HHU) and the German Aerospace Center (DLR).
The lead researchers are Professor Dr Dagmar Bruß and doctoral researcher Pedro Barrios Hita.
The study was published in Physical Review Letters on July 13, 2026.
A 2021 study (Renou et al., Nature 600, 625) had concluded that complex numbers are indispensable under standard quantum mechanics postulates.
The new study found that one postulate from the 2021 analysis was more restrictive than necessary.
The researchers replaced that postulate with a different, physically motivated approach for describing how quantum systems combine.
The resulting framework can be expressed entirely with real numbers and yields identical predictions to conventional quantum mechanics.
Professor Bruß stated: "This means that both frameworks yield identical predictions for any conceivable experiment."
Key figures
Professor Dr Dagmar Bruß, researcher at Heinrich Heine University Düsseldorf (HHU)
Pedro Barrios Hita, doctoral researcher at Heinrich Heine University Düsseldorf (HHU)
Anton Trushechkin, Hermann Kampermann, Michael Epping (co-authors listed in journal reference)
Sources: ScienceDaily
