Quantum mechanics, the mind-bending physics of the super small, might not need imaginary numbers after all, according to a new study. Developed in the early 1900s, this theory has been incredibly successful in explaining everything from particle behavior in the famous double-slit experiment to quantum tunneling. It even powers emerging tech like quantum computing and communication.
For decades, the standard way to describe quantum states has involved complex numbers, which have both a real and an imaginary part. The real part usually handles amplitude, and the imaginary part handles phase. While this setup has been considered fundamental for describing quantum processes, physicists have long pondered if complex numbers are a core feature of nature or just a handy math trick.
This question naturally leads to another: Could quantum mechanics be rephrased using only real numbers? A 2021 study suggested complex numbers were essential under the usual rules of quantum mechanics, with experimental results backing that up.
However, researchers from Heinrich Heine University Düsseldorf (HHU) and the German Aerospace Center (DLR) decided to dig deeper. They re-examined the assumptions of that earlier work and, in a new study published in Physical Review Letters, found that one of the postulates used was actually more restrictive than it needed to be.
By swapping out that postulate for a physically motivated approach to combining quantum systems, they've identified a set of theories that can be described entirely with real numbers. Crucially, these real-number theories produce the exact same predictions for any experiment as the standard, complex-number version of quantum mechanics.
"This means that both frameworks yield identical predictions for any conceivable experiment," explained Professor Dagmar 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."
