Quantum theory based on real numbers can be experimentally falsified.

@article{Renou2021QuantumTB,
  title={Quantum theory based on real numbers can be experimentally falsified.},
  author={Marc-Olivier Renou and David Trillo and Mirjam Weilenmann and Thinh P Le and Armin Tavakoli and Nicolas Gisin and Antonio Ac{\'i}n and Miguel Navascu{\'e}s},
  journal={Nature},
  year={2021}
}
Although complex numbers are essential in mathematics, they are not needed to describe physical experiments, as those are expressed in terms of probabilities, hence real numbers. Physics, however, aims to explain, rather than describe, experiments through theories. Although most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces1,2. This has puzzled countless physicists, including the fathers of the… 
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