
Explanatory diagram for the research question – is quantum mechanics possible with only real numbers? – and results of the study.
Image Credit: © HHU / Pedro Barrios Hita
Scientific Frontline: Extended "At a Glance" Summary: Real-Number Quantum Mechanics
The Core Concept: Quantum mechanics, the physical theory describing the behavior of atomic and subatomic particles, can be successfully formulated using solely real numbers. This mathematically rigorous alternative challenges the traditional reliance on complex numbers, which incorporate both real and imaginary components, to describe quantum states.
Key Distinction/Mechanism: Standard quantum mechanics uses complex numbers where a state's amplitude is represented by the real part and its phase by the imaginary part. By utilizing a physically motivated, less restrictive postulate for system composition, researchers have developed an alternative framework that strictly uses real numbers while remaining experimentally indistinguishable from standard quantum mechanics.
Origin/History: The development of quantum mechanics began in the 1900s through the foundational work of physicists such as Max Planck, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger. The modern debate over the mathematical necessity of imaginary numbers was highlighted by a 2021 study declaring them essential, which was subsequently overturned in 2026 by physicists from Heinrich Heine University Düsseldorf and the German Aerospace Center.












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