![]() But this real-number approach has now been squashed by two independent experiments, performed by Ming-Cheng Chen of the University of Science and Technology of China and by Zheng-Da Li of the Southern University of Science and Technology, China. However, the possibility of using real numbers was never formally ruled out, and recent theoretical results suggested that a real-valued quantum theory could describe an unexpectedly broad range of quantum systems. But early on, the pioneers of quantum mechanics abandoned the attempt to develop a quantum theory based on real numbers because they thought it impractical. But are complex numbers essential in quantum physics-where the mathematics (the Schrödinger equation, the Hilbert space, etc.) is intrinsically complex-valued? This simple question has accompanied the development of quantum mechanics since its origins, when Schrödinger, Lorentz, and Planck debated it in their correspondence. Thus, complex analysis is just a powerful computational tool. However, in these physical theories, complex numbers aren’t strictly needed, as all meaningful observables can be expressed in terms of real numbers. ![]() In electromagnetism, for instance, they tremendously simplify the description of wave-like phenomena. ![]() ×Ĭomplex numbers are widely exploited in classical and relativistic physics. In both experiments, the obtained score isn’t compatible with a real-valued, traditional formulation of quantum mechanics. ![]() The game involves two sources distributing entangled qubits to three observers, who calculate a “score” from measurements performed on the qubits. APS/ Carin Cain Figure 1: Conceptual sketch of the three-party game used by Chen and colleagues and Li and colleagues to demonstrate that a real quantum theory cannot describe certain measurements on small quantum networks. ![]()
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