Quantum mechanics may work without imaginary numbers, physicists report
A new Physical Review Letters study says real-number versions of quantum mechanics can match standard predictions.
By Priya Raghavan · Science Reporter
3 min read
Physicists at Heinrich Heine University Düsseldorf and the German Aerospace Center say quantum mechanics can be formulated without imaginary numbers under a revised set of assumptions. The result matters because complex numbers have long been treated as part of the standard mathematical language used to describe quantum systems.
The work, published in Physical Review Letters, was led by Professor Dagmar Bruß and doctoral researcher Pedro Barrios Hita, according to Heinrich Heine University Düsseldorf. The American Physical Society also selected the study for a Highlight in its Physics Magazine, the university said.
Quantum mechanics describes matter and energy at atomic and subatomic scales. Heinrich Heine University Düsseldorf said the theory, developed in the early 20th century by scientists including Max Planck, Niels Bohr, Werner Heisenberg and Erwin Schrödinger, has become one of science’s most successful frameworks.
The theory accounts for effects such as the double-slit experiment, where particles show wave-like behavior, and quantum tunneling, where particles can pass through barriers they could not cross under classical physics. The university said quantum effects including entanglement and coherence now underpin fields such as quantum computing and quantum communication.
A challenge to a standard assumption
Standard quantum mechanics uses complex numbers, which contain both real and imaginary components. In that description, the real part is tied to amplitude and the imaginary part to phase, according to Heinrich Heine University Düsseldorf.
Physicists have debated whether complex numbers are a feature of nature itself or a highly effective mathematical tool. The new study addresses that question by asking whether quantum mechanics can be rebuilt using only real numbers while keeping the same observable results.
A 2021 study in Nature by Renou and colleagues concluded that complex numbers were required under the usual postulates of quantum mechanics. Heinrich Heine University Düsseldorf said experiments also supported that conclusion.
Bruß, Barrios Hita and their collaborators re-examined the assumptions behind that earlier argument. The team found that one postulate used in the 2021 analysis placed tighter limits on the theory than necessary, according to the university.
By replacing that postulate with another physically motivated way to describe how quantum systems combine, the researchers identified a family of theories that use only real numbers. The university said those theories cannot be distinguished experimentally from conventional quantum mechanics.
Same predictions, different mathematics
The study’s journal reference lists Pedro Barrios Hita, Anton Trushechkin, Hermann Kampermann, Michael Epping and Dagmar Bruß as authors. The paper is titled “Quantum Mechanics Based on Real Numbers: A Consistent Description.”
According to Heinrich Heine University Düsseldorf, Bruß said the two frameworks produce the same predictions for every possible experiment within the study’s framework. She said that means imaginary numbers are not necessary at a fundamental level in that formulation and can be replaced by real-number alternatives.
The finding does not discard quantum mechanics. Instead, it changes what may be required in its mathematical foundation, according to the university’s summary of the research.
This story draws on original reporting from ScienceDaily.