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

[Context Terry]

Finding that one postulate in the 2021 paper was more restrictive than necessary is a great example of how foundational physics results often hinge on assumptions that don't get scrutinized as closely as the headline conclusion

[GrimAnchor]

Complex numbers being a convenient tool rather than a fundamental necessity has been debated for decades, nice to see an actual concrete resolution rather than just more philosophical back and forth

[AEWCallum93]

This feels like it matters more for how we teach and think about quantum mechanics conceptually than for any near term application, but that's still genuinely valuable

[Crossing65]

Getting the American Physical Society's Physics Magazine to specifically highlight this shows the physics community sees it as a real, non trivial result worth paying attention to

[WaveFunction34]

Curious if this real number formulation ends up being computationally easier or harder to work with in practice compared to standard complex quantum mechanics, that could matter for simulation work

[Mia86]

This is one of those results that feels both shocking and oddly reassuring at the same time. Complex numbers always seemed baked into quantum mechanics, so hearing they might be optional is a big shift.

At the same time, it highlights how much of physics is about the language we use, not just the underlying reality.

[Brittle Ruby]

Complex numbers have always been such a neat mathematical shortcut. They make interference and phase relationships clean and elegant.

If a real-number formulation works, it might be less elegant but more "intuitive" for some people

[Skibidi98]

The key question is whether this is just a reformulation or if it changes anything operationally. If predictions stay identical, then it's more about interpretation than new physics.

[SammyZayn]

Part of the charm of quantum mechanics is how weird it is, and imaginary numbers fit right into that vibe

Taking them out almost makes it feel a bit less mystical, which some people will love and others might miss.

[error.404]

This reminds me of how different coordinate systems can describe the same geometry. Cartesian vs polar doesn't change the shape, just how you describe it.

Maybe this is a similar situation.

[Zoe]

One thing to watch is computational efficiency. Complex numbers often simplify calculations, so replacing them might make some problems harder to solve in practice.

[LegendaryLuca49]

It's kind of comforting to know that something as abstract as "i" might not be fundamentally required. Makes the theory feel a bit more grounded, even if the math gets messier.

[Cantona]

There's a philosophical angle here too. If imaginary numbers aren't fundamental, what does that say about the nature of mathematical constructs in physics?

Are they discoveries or just convenient tools?

[BookerT]

Would love to see how this plays out in teaching. Quantum mechanics is already tough to learn, and removing complex numbers might either simplify things or make them more confusing

[ProperJobs98]

A lot of debates in physics come down to "is this fundamental or just useful." Nice to see progress on a question that's been lingering for decades.

[Bob81]

There's a bit of a pattern in physics where multiple formalisms coexist. Lagrangian vs Hamiltonian mechanics, wave vs matrix mechanics.

This might just be another addition to that list.