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

[Adam2]

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

2584541 Why Banishing Irrational Numbers Could Trigger A Revolution In Quantum Theorywww.newscientist.com

[Amy_15]

The block universe versus open future framing is the part of this that has real stakes well beyond physics specifically, touching directly on free will debates that philosophers have argued about for centuries independent of any physics considerations at all. If physical reality really does involve information becoming determined progressively over time rather than every future fact already existing in some completed, fixed sense, that provides a much more physics grounded argument for genuine openness in how the future actually unfolds than most philosophical free will arguments have historically managed to offer.

Most attempts to reconcile free will with physics end up relying entirely on quantum randomness at the microscopic level, which is a pretty thin reed to hang genuine human agency on given how disconnected quantum randomness usually is from anything resembling a meaningful choice. A framework where indeterminism is actually baked into the basic structure of physical information itself, rather than just showing up as microscopic quantum noise that gets washed out at macroscopic scales, is philosophically a much richer foundation to build an actual argument for free will on. Whether that argument actually holds up under serious philosophical scrutiny is a separate question entirely from whether the underlying physics itself is correct though

[Panda54]

I'm somewhat skeptical this actually changes anything practical even if the philosophical argument holds up completely under scrutiny. Standard quantum mechanics using real and complex numbers has made extraordinarily precise, repeatedly verified predictions for a century now, and no amount of foundational unease about what those numbers actually represent changes any of those already confirmed experimental results.

That said, foundational questions like this one have mattered before in ways nobody initially expected them to matter. Einstein's own foundational unease about action at a distance eventually led to real, experimentally testable predictions decades later through Bell's theorem and the whole field of quantum information that grew directly out of those foundational debates. Foundational skepticism occasionally pays off decades down the line even when it initially looks like pure philosophy with no practical stakes attached

[Cameron83]

The connection to Brouwer's intuitionism from a century ago is a fun detail, since it shows this isn't some brand new fringe idea invented recently. Old philosophical debates about the nature of mathematics apparently still have real physics implications worth taking seriously today

[PixelTea]

Reading about this makes me want to go back and actually read some Brouwer directly, since intuitionism as a philosophy of mathematics never got nearly as much attention in my own physics education as classical, Platonist assumptions about numbers just existing out there waiting to be discovered. Funny how a century old, largely dismissed mathematical philosophy debate is apparently still doing real, active work in cutting edge physics research today. Worth digging into the actual primary sources rather than just the popular science summary

[NovaBurst]

What strikes me about this whole research program is how it reframes indeterminism as something more fundamental than just quantum uncertainty specifically. Standard quantum mechanics already has indeterminism baked in through things like wave function collapse, but Gisin's finite information framework suggests indeterminism might actually be a more basic feature of how physical quantities work generally, showing up even in classical mechanics once you take the finite information constraint seriously. That's a genuinely different kind of claim than the usual quantum weirdness discussion. It suggests determinism itself might have always been more of a mathematical idealization than an actual physical fact even outside quantum contexts specifically

[LivMorgan_Legend]

The idea that a finite region of space can't contain infinite information is one of those arguments that sounds almost too simple once you actually hear it stated plainly. Genuinely surprised this hasn't been a bigger point of contention in physics foundations for longer than it apparently has

[Hidden Sookie]

Wonder how mainstream this view actually is within the quantum foundations community specifically, versus being a genuinely fringe position that gets outsized media attention because it makes for a much more compelling headline than most physics foundations research typically generates. Foundations of physics as a subfield has always had a much wider range of taken seriously opinions than most other areas of physics tend to tolerate

[PowerhouseHobbs]

Curious whether this finite information framework actually makes any different experimental predictions from standard quantum mechanics, or whether it's currently empirically equivalent and therefore purely a matter of interpretation rather than genuinely testable physics. The real vs complex number question described here does apparently have a genuinely testable experimental difference according to that 2021 Nature paper. Would want to know if the irrational number question has an equivalent testable prediction or if it's a step further removed from actual experimental physics