The Numbers We Take for Granted
Since the dawn of physics, scientists have used mathematics as the fundamental language to describe the universe. For most of history, this meant using “real” numbers—the familiar values on a number line, including integers, fractions, and irrational
numbers like pi. They are the bedrock of classical mechanics, used to measure everything from the speed of a falling apple to the orbit of a planet. But in the 1920s, the development of quantum mechanics introduced a wrinkle. To make the equations work, physicists like Erwin Schrödinger had to use “complex numbers,” which combine a real number with an “imaginary” one (a multiple of the square root of -1). These numbers have been considered essential to the theory ever since, yet they’ve always been a bit unsettling. After all, physical measurements always give real-number results.
A Debate Reborn
The question of whether complex numbers are a fundamental part of nature or just a convenient mathematical shortcut has simmered for decades. In 2021, it seemed the debate was settled. A landmark experiment appeared to show that a version of quantum theory built using only real numbers would make incorrect predictions. The results suggested that complex numbers were, in fact, indispensable. However, new research published in July 2026 in the journal Physical Review Letters has challenged that conclusion. A team of physicists from Heinrich Heine University Düsseldorf and the German Aerospace Center took a closer look at the assumptions behind the 2021 study. They discovered that one of the postulates was more restrictive than necessary.
Finding a 'Real' Alternative
The German research team, led by Professor Dr. Dagmar Bruß, developed a new approach. By modifying a rule for how separate quantum systems are combined, they built a working version of quantum mechanics using only real numbers. Crucially, this new formulation makes all the same predictions as the standard, complex-number-based theory. According to Professor Bruß, this means that for any experiment you can imagine, both frameworks would give you identical predictions. In this sense, imaginary numbers are not fundamentally necessary and can be replaced. This doesn't mean the old math is wrong, but rather that it might be just one possible dialect for speaking the language of the universe. The new model essentially creates a bookkeeping system that tracks the components of complex numbers separately, using only real values.
Beyond Real and Complex: A Finite Universe?
The discussion doesn't even stop at real versus complex numbers. Some physicists argue for an even more radical idea: that the universe, at its most fundamental level, is described by finite mathematics. This approach gets rid of the concept of infinity altogether. Proponents of this view, sometimes called Finite Quantum Theory (FQT), argue that concepts like infinitely small or infinitely large are artifacts of classical mathematics that don't apply to a world made of discrete particles. In FQT, infinities—a major headache in standard physics—cannot exist. Some theorists, like Oxford physicist Tim Palmer, go further, suggesting that abandoning the continuum of real numbers could resolve many of quantum mechanics' famous paradoxes, like Schrödinger's cat. This approach even makes a testable prediction: that quantum computers might hit a fundamental wall, unable to scale beyond a certain size.
