Quantum Mechanics May Work With Real Numbers After All

For nearly 100 years, physicists thought imaginary numbers were essential to quantum mechanics, the theory explaining how atoms and particles behave. A team from Heinrich Heine University Düsseldorf just proved that assumption wrong.

Quantum mechanics is one of science's greatest success stories. It explains everything from how particles can act like waves to how they tunnel through barriers they shouldn't be able to cross, and it powers emerging technologies like quantum computers.

But the theory has always used complex numbers, which combine regular numbers with imaginary ones (based on the square root of negative one). Scientists debated whether nature truly requires these imaginary numbers or if they're just a handy mathematical shortcut.

Professor Dagmar Bruß and doctoral researcher Pedro Barrios Hita decided to revisit that question. They examined a 2021 study that concluded imaginary numbers were absolutely necessary for quantum mechanics to work.

The team discovered something surprising. One of the assumptions in that earlier study was more restrictive than it needed to be.

By replacing it with a different approach for describing how quantum systems combine, they found you can write quantum mechanics entirely with real numbers. The kicker? This new framework makes identical predictions to conventional quantum mechanics for every possible 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," Professor Bruß explained. Their findings appeared in Physical Review Letters, and the American Physical Society featured the work in Physics Magazine.

Why This Inspires

This discovery reminds us that even our most established scientific theories still hold surprises. After a century of assuming imaginary numbers were fundamental to quantum mechanics, researchers found a simpler path hiding in plain sight.

The work also shows how questioning basic assumptions drives science forward. The 2021 study seemed definitive, but the German team looked closer and found wiggle room in the foundations.

While this won't change how quantum computers work tomorrow, it deepens our understanding of reality itself. Sometimes the most profound breakthroughs come from asking whether the tools we've always used are truly necessary.

The research joins other recent quantum advances, including new experimental systems bringing quantum technologies to students and studies testing whether large quantum systems truly follow quantum rules. Each discovery builds our grasp of nature's smallest scales.

This breakthrough proves there's always room to rethink what we thought we knew.