Alternatives to standard quantum theory ruled out

Wootters, William K.

doi:10.1038/d41586-021-03678-x

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15 December 2021

Alternatives to standard quantum theory ruled out

Standard quantum theory contains square roots of negative numbers. But how essential are these ‘imaginary’ numbers? A way of disproving analogous theories that omit them has been proposed — and confirmed experimentally.

William K. Wootters⁰

William K. Wootters
1. William K. Wootters is in the Department of Physics, Williams College, Williamstown, Massachusetts 01267, USA.
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The square root of a negative number could easily be regarded as a curious mathematical construction that has little bearing on real life. Indeed, the French polymath René Descartes gave such numbers the derogatory name ‘imaginary’, reserving the term ‘real numbers’ for those that occur on an ordinary number line. However, since the development of quantum theory nearly a century ago, it has seemed likely that complex numbers — which combine imaginary and real numbers — are deeply embedded in the structure of the physical world. Indeed, the imaginary unit that represents the square root of minus one occurs prominently in the basic equations of quantum theory. Writing in Nature, Renou et al.¹ show how experiments could strengthen the evidence that complex numbers are key to describing the quantum world, by eliminating a class of theory that contains only real numbers. And two versions of the experiment they propose have already been implemented²^,³.

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Nature 600, 607-608 (2021)

doi: https://doi.org/10.1038/d41586-021-03678-x

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