Why some physicists want to banish irrational numbers from quantum theory entirely

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A growing thread of research in quantum foundations, most prominently associated with physicist Nicolas Gisin at the University of Geneva and Constructor University, argues that the mathematical real numbers physicists have relied on for centuries, including irrational numbers with infinitely long, non repeating decimal expansions, may not actually describe anything physically meaningful. The argument centers on a deceptively simple observation, almost every real number contains an infinite amount of information encoded in its endless digits, and a finite region of physical space simply cannot contain infinite information.

Gisin's proposed alternative treats physical quantities as having only finite information content rather than the infinitely precise values classical and quantum theory both traditionally assume. Instead of a particle's position being represented by a real number with infinitely many decimal digits all specified at once, Gisin's framework treats those digits as only partially determined at any given moment, becoming more defined over time as new information effectively gets created rather than merely revealed by measurement. That reframing has significant philosophical stakes, since it reintroduces a kind of genuine indeterminism into physics that doesn't rely purely on quantum mechanical uncertainty specifically.

This connects to a related but distinct line of research Gisin has pursued alongside collaborators concerning whether quantum theory actually requires complex numbers rather than just real ones. A 2021 paper in Nature, coauthored with Marc-Olivier Renou and several others, proposed an experiment specifically designed to determine whether quantum correlations could be reproduced using only real number Hilbert spaces rather than the complex number formalism standard quantum mechanics has used since its earliest days. That experiment was subsequently performed, and follow up work has continued refining exactly what assumptions are needed to rule out a real number only version of quantum theory conclusively.

The broader philosophical framework underlying this research draws on intuitionistic mathematics, a school of thought developed originally by mathematician L.E.J. Brouwer in the early twentieth century that treats mathematics as fundamentally a construction of the human mind rather than a fixed, eternal truth waiting to be discovered. Applying that intuitionistic lens to physics specifically suggests that treating time as an open, ongoing process of information becoming determined, rather than a fixed block universe where every future digit of every physical quantity already exists in some completed sense, might resolve certain longstanding tensions between our lived experience of an open future and a purely deterministic physical description of reality.

Whether any of this actually changes how physicists calculate anything in practice remains genuinely unclear, and mainstream physics continues to operate successfully using standard real and complex number mathematics regardless of these foundational debates. But the research represents a serious, mathematically rigorous attempt to question an assumption so basic that most physicists never think to examine it at all, treating the specific number system used to describe reality as itself an open scientific question rather than a fixed, unquestionable mathematical backdrop that physics simply operates within

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