An Imaginary Foundation
Since its inception in the 1920s, quantum mechanics has been the most successful theory for describing the universe at the subatomic level. From the outset, its core equations, like the famous Schrödinger equation, relied on complex numbers. A complex number is
a combination of a regular 'real' number (like 3) and an 'imaginary' number — a multiple of the square root of -1, denoted by 'i'. While you can't hold an imaginary number of apples, these mathematical tools are incredibly useful for describing phenomena like waves and alternating electrical currents. For decades, physicists debated whether these numbers were just a convenient shortcut or a fundamental, non-negotiable feature of reality. Even Schrödinger himself hoped for a version of his theory that used only real numbers.
The Real Number Challenge
The debate seemed to be settled in 2021 and 2022. Researchers devised experiments involving entangled particles that, according to their theory, would produce different results depending on whether the underlying reality was based on real or complex numbers. When the experiments were run, the results perfectly matched the predictions of standard, complex-number quantum mechanics, appearing to rule out a real-number alternative. Complex numbers seemed unavoidable. However, this conclusion rested on a subtle but crucial assumption about how to mathematically combine separate quantum systems — a rule taught in every standard textbook called the tensor product.
A New Rule for Reality
Recently, physicists from Heinrich Heine University Düsseldorf and the German Aerospace Center took a fresh look. They questioned the necessity of the standard tensor product rule. By developing a different, physically motivated rule for combining quantum systems, they built a complete model of quantum mechanics using only real numbers. This new formulation makes all the same predictions as the standard theory, meaning it is experimentally indistinguishable from the complex-number version. As study author Pedro Barrios Hita explained, this means complex numbers are not fundamentally necessary, but rather helpful tools. Their work, published in the journal Physical Review Letters, effectively reopens a chapter everyone thought was closed.
What This Means for Physics
This discovery represents a significant conceptual shift. It places quantum mechanics in the same category as other areas of physics where complex numbers are used for convenience, not out of necessity. The breakthrough doesn't immediately lead to new technologies or change any experimental predictions, as the real-number version is designed to match the results of the established theory. However, it offers a new, potentially more intuitive way to think about the fundamental nature of reality. By stripping away the 'imaginary' component, physicists may gain deeper insights into the perplexing concepts of quantum theory, like entanglement and superposition. It provides a different lens through which to view the foundational rules of our universe.
