The Imaginary Requirement
To understand the breakthrough, we first have to talk about something called complex numbers. These aren't just very large numbers; they are numbers that have two parts: a 'real' part and an 'imaginary' part. The imaginary part is a multiple of the square
root of -1, a concept represented by the symbol 'i'. Since you can't have negative one of a physical object, mathematicians called this concept imaginary. But these numbers are incredibly useful. Engineers use them to analyze electrical currents, and physicists use them to describe waves. When quantum mechanics was developed in the 1920s by pioneers like Erwin Schrödinger, these complex numbers were baked right into its core equations. It was believed they were fundamental to describing quantum states, and that the theory simply wouldn't work without them.
Challenging a Century of Physics
The idea that complex numbers were essential was so strong that experiments were designed to prove it. As recently as 2022, experiments seemed to confirm that a version of quantum theory using only real numbers would make incorrect predictions. Those experiments effectively ruled out earlier, simpler attempts at a real-number quantum theory. However, those tests rested on a key assumption about how to mathematically combine multiple quantum particles. A new study, published in June 2026 in the journal Physical Review Letters, took a different approach. A team of physicists from Germany found a way around the old problem. By changing the rule for combining particles, they successfully built a version of quantum mechanics that uses only real numbers but makes all the same predictions as the standard, complex-number theory.
So, Are Imaginary Numbers Not Real?
This discovery doesn't mean that a century of physics is wrong. The standard formulation of quantum mechanics with complex numbers still works perfectly. Rather, this new work shows that complex numbers are not as fundamental as once believed. They can be seen as a convenient mathematical tool rather than an essential ingredient of reality itself. Professor Dagmar Bruß of Heinrich Heine University Düsseldorf, one of the study's authors, explained that both frameworks—the old complex one and the new real one—yield identical predictions for any experiment. The finding is less about changing our picture of the physical world and more about deepening our understanding of the mathematical language required to describe it. It forces physicists to reconsider which parts of their theories are truly essential and which are just artifacts of a chosen mathematical representation.
Why This Matters for Future Technology
While this is a deeply fundamental discovery, it could have long-term practical implications. Quantum mechanics is the foundation for technologies like quantum computing and quantum communication. Having a new, potentially simpler mathematical framework could be invaluable. Understanding the absolute essentials of the theory could help engineers and physicists find more efficient ways to design and control quantum systems. While the new formulation doesn't immediately change any experimental predictions or point to new devices, it opens up new avenues of research. Extending this new real-number theory to cover all possible quantum systems is a natural next step for researchers. A clearer understanding of the foundations of quantum mechanics could ultimately accelerate the development of next-generation technologies that will define the future of business and information.
