Quantum mechanics is a branch of physics that explains how matter and energy behave on atomic and subatomic scales. Developed in the early 1900s by pioneers such as Max Planck, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger, it became one of the most successful scientific theories ever created.
This theory accurately explains a wide range of microscopic phenomena. These include the famous double-slit experiment, in which particles behave like waves, and quantum tunneling, in which particles can pass through barriers even if they do not have enough energy to cross them in the classical sense. Other important quantum effects, such as entanglement and coherence, currently form the basis of emerging technologies such as quantum computing and quantum communications.
Are complex numbers really necessary?
For decades, quantum mechanics has relied on complex numbers, which combine real and imaginary components. In the mathematical description of a quantum state, the real part represents the amplitude and the imaginary part represents the phase. This framework has long been considered essential for describing many quantum processes.
Still, physicists have continued to debate whether complex numbers are truly a fundamental part of nature or just a convenient mathematical tool. This question naturally leads to another question. Can quantum mechanics be formulated using only real numbers?
Rethinking key quantum assumptions
A 2021 study concludes that complex numbers are essential under the standard postulates of quantum mechanics (Renou et al., Nature 600, 625 (2021)). Experimental results also support that conclusion.
Researchers at the Heinrich-Heine University (HHU) in Düsseldorf and the German Aerospace Center (DLR), led by Dr. Dagmar Bruce and postdoctoral researcher Pedro Barrios Hita, decided to revisit the assumptions behind previous studies.
In a new study published in physical review letterthey found that one of the postulates used in the 2021 analysis was more restrictive than necessary. By replacing this with an alternative physically motivated approach to explaining how quantum systems couple together, we have identified a set of theories that remain experimentally indistinguishable from classical quantum mechanics, yet can be expressed entirely in real numbers.
Professor Bruce said: “This means that both frameworks yield the same predictions for every possible experiment. Therefore, within this framework, imaginary numbers are not fundamentally necessary in quantum mechanics and could in principle be replaced by a different formulation using real numbers.”
