The Imaginary Problem in the Real World
Quantum mechanics is famously weird. It’s the rulebook for how matter and energy behave at the smallest scales, and it’s responsible for everything from the existence of atoms to the development of technologies like quantum computing. But since its inception
in the 1920s, the theory has relied on a mathematical tool that even its founders found unsettling: complex numbers. These numbers combine a “real” part with a so-called “imaginary” part—a multiple of the square root of -1. While engineers use them to describe practical things like electrical currents, their role in fundamental physics has always been a puzzle. Are these unreal numbers a true feature of reality, or just a convenient crutch for our calculations?
A Radical New Formulation
A recent study published in the journal Physical Review Letters offers a groundbreaking answer. Researchers from Heinrich Heine University Düsseldorf and the German Aerospace Center have shown that quantum mechanics doesn't necessarily need imaginary numbers at all. They have successfully formulated a version of the theory using only real numbers—the kind we use to count and measure in everyday life. According to the study, led by Professor Dr Dagmar Bruß and doctoral researcher Pedro Barrios Hita, this new framework makes all the same predictions for experiments as standard quantum theory. In other words, for any conceivable test, the real-number version works just as well.
Rethinking a Key Assumption
This breakthrough was possible because the team questioned a long-held mathematical assumption. Previous attempts to build a real-number quantum theory had failed, and a key 2021 study seemed to prove that complex numbers were essential. That earlier work, however, relied on a specific rule for how to mathematically combine two separate quantum systems. The new research demonstrates that this rule, known as the tensor product, was more restrictive than necessary. By using a different, physically motivated approach to describe how quantum systems combine, the researchers were able to construct a consistent and complete theory based entirely on real numbers.
What This Means for Physics
This discovery doesn't mean that a century of physics textbooks are wrong. Instead, it deepens our understanding of the fundamental nature of reality. It shows that the mathematical language we use to describe the universe might be more flexible than previously believed. The fact that imaginary numbers aren't strictly necessary forces physicists to ask deeper questions about which mathematical structures are truly fundamental and which are simply convenient tools. While this new formulation doesn't immediately lead to a new type of quantum computer, it provides a new and potentially powerful lens through which to view the universe’s most profound mysteries. It simplifies the conceptual foundation of our most successful theory.
The Search for a Deeper Reality
The debate over the role of different types of numbers in physics is not new. Some theorists have even argued for abandoning the continuum of real numbers to solve problems in quantum gravity. This new study adds a significant chapter to that story. By showing that even the celebrated imaginary numbers might be optional, it pushes scientists to reconsider the relationship between the physical world and the abstract world of mathematics. The next step is for the wider physics community to explore this new real-number framework, testing its limits and searching for areas where it might offer new insights into long-standing problems. The result could be a more intuitive and elegant description of the quantum realm.
