Quantum theory does not need complex numbers

Science
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In 2021, Renou et al. published a result in Nature arguing complex numbers are necessary for quantum mechanics — that a real-number-only theory can’t reproduce certain correlations in systems of three or more entangled particles, under the standard rule for combining separate quantum systems (the tensor product, the thing every QM textbook uses to build a multi-particle description out of single-particle ones). That result was taken fairly widely as settling the question. The new work doesn’t dispute the math of that result — it disputes the assumption underneath it. If you don’t insist on the standard tensor-product composition rule, and instead derive a different rule for how separate real-number quantum systems combine, you can build a fully real-valued theory that reproduces every prediction of ordinary complex quantum mechanics, multi-particle correlations included. The lesson isn’t “complex numbers are fake” — it’s “the necessity argument was conditional on a specific composition rule, and that rule turns out not to be forced.”