Is Reality ‘Imaginary’? Physicists Just Settled One of Quantum Theory’s Weirdest Debates.

4 min readHere’s what you’ll learn when you read this story:A team of German physicists has built a fully working version of quantum mechanics that uses only real numbers.Complex numbers, built from a combination of real and imaginary numbers, have long seemed essential to the theory’s math.The result answers a fundamental question: is the math of reality truly “imaginary,” or just easier that way?In a newly published study in the journal Physical Review Letters, a group of German physicists have laid out the case that we can all do quantum physics without needing to use complex numbers. The work comes from a collaboration between Heinrich Heine University Dusseldorf and the German Aerospace Center.The paper, titled “Quantum Mechanics Based on Real Numbers: A Consistent Description,” is a response to other physicists’ recent work on equivalence—that is, whether a real-number version of quantum theory can make all the same experimental predictions as the standard complex-number version. In several previous studies, different scientists have tried to write out the math of quantum physics scenarios without using complex numbers, but they found that their results couldn’t match complex quantum mechanics’ predictions. Those results, they suggested, showed that it may not be possible to build quantum physics without using complex numbers.So, what’s a complex number, and why is it good or bad to use them in quantum mechanics? Most of us meet the idea at some point in our education, when we learn that the square root of a negative number isn’t a real number at all. Instead, it’s an “imaginary” one, written with the symbol ⁠𝒾. A complex number combines a real value and an imaginary one, like 2 + 𝒾. In quantum mechanics, these numbers are important because quantum states behave like waves, and a complex number neatly captures both a wave’s strength and its timing in a single unit. However, everything we actually measure in quantum experiments comes out as an ordinary real number, which raises the question at the heart of the new paper: If the answers in quantum mechanical equations are always real, do the calculations really need to be complex?But we also must ask: Is that notation a stopgap? Math has never needed to perfectly mirror reality to be useful. For example, in geometry, no square you draw or build will ever match the flawless one in the textbook, yet the textbook math describes your wobbly square just fine. The square root of –1 may work the same way, since it’s not an object you’ll find anywhere in nature, but a tool that makes the description work. The real test of any such tool is that the formula has to hold up across every possible case—not just convenient ones. And if you swap the tool out for another, the new version has to predict every experimental outcome exactly as well as the old one did.There are a few ways that scientists have suggested we can do quantum mechanics using only real—and not complex—numbers. None of these was perfect, and none have proved to be true in the generalizable way that “complex quantum mechanics” (using complex numbers) is. In a sense, it’s like our real world square compared with the perfect square in a geometry book. We can’t successfully make an approximation match the theoretical formulas. The approximations, so far, were not adequate to predict experimental outcomes.With those partial ideas in mind, physicists Pedro Barrios Hita, Anton Trushechkin, Hermann Kampermann, Michael Epping, and Dagmar Bruß have now built a mathematical model that aims to take out these limitations. They swapped pieces of math with equivalent relationships or formulas, resulting in a final product that can predict the same outcomes from experiments that the complex quantum math does.The scientists highlight their many peers who are doing similar work, which set the stage for them to piece together this new step forward. There’s also no compelling reason to take complex numbers out of quantum mechanics as of yet—it’s more a matter of discussion among scientists, though “real number quantum mechanics” could be needed at some point.At the beginning of their article, the scientists wonder whether complex numbers are “fundamental or merely convenient.” After several pages of math-wrangling and taking the long way, they conclude: “[C]omplex numbers are not necessary to describe quantum mechanics—but they are certainly very useful.” In 2021, a study in Nature suggested that real-number quantum mechanics could be experimentally disproven using entangled particles, leading many to conclude that imaginary numbers are fundamental to the universe. However, the new research demonstrates that the 2021 argument relied on an unnecessarily strict mathematical rule for combining quantum systems. By replacing this with a physically motivated alternative, the German physicists have developed a real-number formulation that yields the same predictions as standard quantum mechanics. Because no experiment can distinguish between the two versions, the use of imaginary numbers is a choice of mathematical language rather than an experimental fact, serving as a convenient option rather than a physical necessity.Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all.