Physicists say quantum mechanics might not actually need imaginary numbers after all

[Dragon49]

Researchers from Heinrich Heine University Düsseldorf and the German Aerospace Center have shown that quantum mechanics can be consistently formulated using only real numbers, challenging a 2021 study that had concluded complex numbers, ones combining a real and an imaginary component, were mathematically indispensable to the theory

For decades physicists have debated whether the imaginary part of a quantum state's mathematical description, which represents phase alongside the real part representing amplitude, reflects something fundamental about nature or is simply a convenient calculational tool. The 2021 paper, published in Nature, appeared to settle the question by showing complex numbers were required under quantum mechanics' standard postulates, a conclusion also backed by experimental results at the time

The Düsseldorf team, led by Professor Dagmar Bruß and doctoral researcher Pedro Barrios Hita, revisited the assumptions underpinning that 2021 result and found one specific postulate, governing how quantum systems combine, was more restrictive than it strictly needed to be. By swapping in a different, physically well motivated approach to describing that combination, they identified an entire family of alternative theories expressible purely with real numbers

Critically, these real number formulations are experimentally indistinguishable from standard complex number quantum mechanics, meaning both frameworks predict identical outcomes for any conceivable experiment. As Bruß put it, imaginary numbers are therefore not fundamentally necessary, they can in principle be swapped out for real number alternatives without changing a single physical prediction. The work, published in Physical Review Letters, has been highlighted by the American Physical Society's Physics Magazine

Physicists say quantum mechanics may not need imaginary numbers after allwww.sciencedaily.com

[RealChristopher10]

The fact that both formulations make identical experimental predictions is the detail that really matters here, this isn't a physical discovery so much as a statement about which mathematical language we choose to use