Pedro Barrios Hita, a doctoral researcher in Düsseldorf, sketches equations on a chalkboard where every number is real—no imaginary units in sight—challenging a century-old assumption at the heart of quantum mechanics. Alongside his advisor, Professor Dr. Dagmar Bruß at Heinrich Heine University Düsseldorf and collaborators at the German Aerospace Center (DLR), Barrios Hita has helped demonstrate that quantum mechanics, the theory governing the bizarre behavior of particles at atomic and subatomic scales, can be fully described using only real numbers. This finding reopens a foundational debate: are imaginary numbers—a mathematical staple since Schrödinger’s equation—a necessity of nature, or merely a convenient tool?
For decades, complex numbers, which combine real and imaginary components, have been considered essential to quantum theory. They encode both the amplitude and phase of quantum states, enabling accurate predictions of phenomena like wave-particle duality, quantum tunneling, and entanglement—the very features powering emerging technologies like quantum computing. A 2021 study reinforced this view, concluding that complex numbers were indispensable under standard quantum postulates. But the HHU-DLR team questioned one key assumption in that analysis: how quantum systems are composed when combined. They proposed a physically motivated alternative to the standard composition rule, revealing a new class of theories that rely solely on real numbers while matching all experimental predictions of conventional quantum mechanics.
Their paper, published in Physical Review Letters in 2026, shows that with this revised framework, every known quantum phenomenon—from double-slit interference to quantum entanglement—can be reproduced without invoking imaginary numbers. “This means that both frameworks yield identical predictions for any conceivable experiment,” explains Professor Bruß. “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.” The result doesn’t invalidate standard quantum mechanics; rather, it reveals a deeper flexibility in how we mathematize reality.
The implications are profound for both physics and philosophy. If two mathematically distinct theories predict the same outcomes, the choice between them may come down to elegance, pedagogy, or computational efficiency—not truth. For students struggling with imaginary numbers, a real-number formulation could make quantum theory more accessible. For theorists, it opens new pathways to unify quantum mechanics with gravity or to explore hidden-variable models.
As quantum technologies advance, so too does our understanding of the theory behind them. This work reminds us that even the most entrenched ideas in science remain open to reimagining—sometimes with nothing more than a shift in perspective, and a few well-placed real numbers.