News summary produced by Claude AI
Quantum mechanics, developed in the early 1900s by pioneers including Max Planck, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger, has become one of the most successful scientific theories ever created. The theory accurately describes microscopic phenomena ranging from wave-particle duality demonstrated in the double slit experiment to quantum tunneling, where particles can pass through barriers despite lacking sufficient classical energy. Key quantum effects such as entanglement and coherence now form the foundation of emerging technologies in quantum computing and quantum communication.
For decades, quantum mechanics has relied on complex numbers—mathematical constructs combining real and imaginary components—to describe quantum states, with the real part representing amplitude and the imaginary part representing phase. This framework has long been considered essential for describing many quantum processes. However, physicists have long debated whether complex numbers represent a fundamental aspect of nature or merely serve as a convenient mathematical tool, raising the question of whether quantum mechanics could be reformulated using only real numbers.
A 2021 study concluded that complex numbers are indispensable under the standard postulates of quantum mechanics, a conclusion supported by experimental results. Recently, researchers from Heinrich Heine University Düsseldorf and the German Aerospace Center, led by Professor Dagmar Bruß and doctoral researcher Pedro Barrios Hita, reexamined the assumptions underlying that analysis. Their findings, published in Physical Review Letters, indicate that one of the postulates used in the earlier work was more restrictive than necessary.
By replacing it with an alternative approach grounded in physical principles for describing how quantum systems combine, the researchers identified a family of theories expressible entirely in real numbers while remaining experimentally indistinguishable from conventional quantum mechanics. Professor Bruß noted that both frameworks yield identical predictions for any possible experiment, suggesting that imaginary numbers are not fundamentally necessary in quantum mechanics and could in principle be replaced by alternative formulations using only real numbers.