The Imaginary World of Quantum Mechanics
Ever since quantum mechanics was developed in the 1920s, it has relied on a strange mathematical tool: complex numbers. A complex number is part 'real' (the numbers we use every day) and part 'imaginary'. The imaginary part is a multiple of the square
root of -1, a concept that has no equivalent in the physical world of countable objects. Despite their name, these numbers are indispensable for describing things like waves and rotations. In quantum mechanics, they are baked into the fundamental equations that describe the wave-like nature and probabilistic behavior of particles. For decades, physicists wondered if these imaginary components were a true feature of reality or just a convenient shortcut. Erwin Schrödinger, one of the theory's founders, hoped it was the latter.
A Challenge to Orthodoxy
The long-standing debate was mostly philosophical until recently. A key question emerged: could you build a version of quantum mechanics that works using only real numbers? Theorists proposed that this might be possible, but it wasn't a simple substitution. Getting rid of complex numbers seemed to require tweaking other fundamental assumptions about how quantum systems are combined. In 2021, a group of physicists devised a clever theoretical test, inspired by the famous Bell's inequality experiments, to settle the matter. Their work suggested that a quantum world based only on real numbers would produce slightly different experimental results than one based on complex numbers. This transformed the philosophical debate into a question that could be answered with an experiment.
Putting Reality to the Test
Soon after the theoretical test was proposed, two independent teams of physicists set up experiments to carry it out. One experiment used entangled photons (particles of light), while another used superconducting quantum bits, or qubits. The setup involved creating complex networks of entangled particles and measuring the correlations between them. The theoretical work predicted that if reality could be described by real numbers alone, the strength of these correlations would have a specific maximum limit. However, if complex numbers were truly necessary, the correlations could exceed that limit. The results were definitive. Both experiments observed correlations that were impossible to explain with a real-number-only quantum theory. The verdict seemed clear: the imaginary part of quantum mechanics was here to stay.
A New 'Real' Twist
Just when the case seemed closed, the story took another turn. In a paper published in June 2026 and highlighted by the American Physical Society, a team of physicists in Germany showed that the previous experiments had a loophole. The 2021 analysis that concluded complex numbers were essential relied on a standard, but not required, assumption about how to combine quantum systems. By using a different, but still valid, rule, the German team successfully formulated a version of quantum mechanics using only real numbers that gives the exact same predictions as the standard, complex version for all possible experiments. According to this latest research, complex numbers might just be a matter of convenience after all, not a fundamental necessity.
Why This Abstract Debate Matters
This back-and-forth might seem like a purely academic exercise, but it cuts to the heart of our understanding of reality. Questioning fundamental assumptions is a core part of the scientific process. By pushing these boundaries, physicists gain a deeper understanding of the structures that underpin our most successful theories. Even if the standard formulation of quantum mechanics remains the easiest to use in practice, knowing that it can be reformulated without complex numbers forces a re-evaluation of what is truly essential versus what is simply a convenient mathematical tool. This deeper insight could prove valuable in the development of future technologies like quantum computing, where a complete grasp of the theory's foundations is critical to pushing the limits of what's possible.
