The Imaginary Heart of Reality
Since its inception in the 1920s, quantum mechanics has been unsettling. Not just for its weirdness, like particles being in two places at once, but for its mathematical foundation. The theory's central pillar, the Schrödinger equation, relies on complex
numbers — numbers that include the 'imaginary' unit, 'i', the square root of -1. For many physicists, including Schrödinger himself, this was a sticking point. How could a number with 'imaginary' in its name be essential to describing tangible reality? For decades, the consensus was that complex numbers, while philosophically strange, were an indispensable tool. They are perfectly suited for describing waves and phases, which are central to quantum behaviour. The question of whether they were just a convenient shortcut or a fundamental feature of the universe remained a topic for debate, but one without a clear experimental answer.
The Quest for a Realer Theory
The desire for a more intuitive theory, one built entirely on the 'real' numbers we use to measure everyday quantities, never fully disappeared. A 'real quantum theory' would, for its proponents, feel more philosophically sound. The challenge was formidable. How could you replicate the predictive power of standard quantum mechanics without its most powerful mathematical tool? Early attempts showed that a real-number framework could handle many situations, but it struggled in others. The core of the problem lies in how quantum states are described and combined, particularly when dealing with entangled particles—the so-called 'spooky action at a distance' that links particles no matter how far apart they are. For a long time, it was generally accepted that a real-only version was experimentally indistinguishable from the complex version, leaving the choice between them a matter of taste rather than necessity.
An Experiment Seemed to Settle It
The debate dramatically shifted around 2021. A team of physicists devised a clever theoretical experiment, akin to a sophisticated game of Bell's inequality test, designed to distinguish between the two theories. The setup involved multiple, independent sources of entangled particles distributed among several parties. The theorists calculated that if quantum mechanics were based on real numbers, the correlations between the measurement outcomes would have a specific ceiling. Standard, complex-number quantum mechanics, however, predicted correlations that could breach that ceiling. When the experiments were carried out by two independent teams using light and superconducting qubits, the results were clear: the real-world data broke the real-number limit and agreed perfectly with the complex-number theory. It seemed the case was closed. Nature, at its deepest level, really did run on imaginary numbers.
A Crack in the Foundation
However, science is a process of constant questioning. In the years following that landmark result, physicists took a closer look at the assumptions baked into the 2021 experiment. They found a potential weakness. The 'no-go' theorem for real-number QM relied on a specific mathematical rule for combining different quantum systems, known as the tensor product. This is the standard textbook method used in complex quantum mechanics. But was it fair to assume that a completely different formulation of physics—one based only on real numbers—must use the exact same combination rule? Several researchers argued that this was an unfair constraint. They suggested that the original experiment didn't prove real-number QM was impossible; it only proved that a specific, perhaps naive, version of it was impossible. This opened the door for a comeback.
The Real Comeback
That comeback arrived very recently. In new work published in 2026, research teams have successfully developed a version of quantum mechanics using only real numbers that fully reproduces all the predictions of the standard theory. As one physicist involved in the work stated, "Complex numbers are not needed for quantum mechanics." They achieved this by creating a different, more sophisticated mathematical rule for combining quantum systems—one that is natural within the real-number framework. This new formulation successfully explains the results of the 2021 experiment without needing 'i'. It turns out the limits found previously were not limits of real numbers themselves, but limits of using a mathematical tool (the standard tensor product) in a context for which it wasn't designed. The debate, once thought settled, has been blown wide open.
