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Why Physics Should Use Simple Numbers, Not Real Ones

A plain-language version of “The Adelic Physics Program: Epistemological Foundations and Communications Framework”

3 min readNo jargon, no mathematicsPhysics

The short version

A long research paper argues that physics has used the wrong kind of numbers for 150 years. It says we should use simple fractions instead of infinite decimals, and a proven math rule then forces us to take other number systems seriously too.

The problem no one noticed

Physics today uses "real numbers." These include endless decimals like pi. But no one ever proved nature needs them. This choice came from math, not from experiments.

Every measurement gives a simple fraction. Every computer uses simple fractions. Every number in physics can be approximated by simple fractions. The paper asks: show one physical prediction that needs endless decimals. No one has done this.

The paper says we should start with the smallest number system that works. That is the fractions. We should only add more if forced by experiments.

A proven rule changes everything

In 1916, a mathematician named Ostrowski proved something important. He showed that fractions have only two kinds of completions. One gives the usual endless decimals. The other gives "p-adic numbers," one for each prime number.

If fractions are the physical starting point, then this old math result becomes a rule about nature. It says the endless decimals and all the p-adic systems are equally valid. Physics has ignored all but one.

Building numbers from scratch

The paper shows how to build numbers from the simplest act: drawing a line to separate "this" from "that." Marking and enclosing let us build counting numbers, then fractions, then approximations of endless decimals.

One step is different. It projects a tree shape onto a smooth surface. This step loses information. It creates endless decimals that cannot be reached by any finite building process. These lost-forever numbers are artifacts of the method, not things we can actually build.

Others reached the same conclusion

Two other researchers, Gisin and Del Santo, argued that endless decimals act like "hidden variables." These are extra facts that supposedly exist but cannot be measured. Their theory says some digits are not merely unknown. They are genuinely undefined until a measurement makes them real.

This matches the paper's view. It also matches a bound from gravity theory: any space region can hold only finite information. Endless decimals need infinite information, so they cannot fit in any real place.

New shapes for space and time

The p-adic systems come with tree shapes called Bruhat-Tits trees. These may be the true shape of space and time, not smooth surfaces. The paper reports that some particle mass ratios fit a pattern based on these trees. Another research group independently used these trees to study black holes.

A fast electron wiggle called Zitterbewegung may show mixing between the usual number system and the simplest p-adic one. This idea awaits experimental testing.

Computing with trees

The paper proposes quantum computers built on tree shapes. These would use a special distance rule where small errors cannot add up. A processor doing math on all number systems at once could work at room temperature. This hardware design is not yet tested.

Connecting to a grand math bridge

A famous math program links number theory and geometry. Physicists found that a symmetry in particle theory matches this program. The paper says this is not coincidence. It is a deep structural match. Even the fast Fourier transform, known to engineers everywhere, is secretly part of this bridge.

Why people misunderstand this work

The paper faces a language problem. It borrows words from number theory that most physicists never learned. The solution is to restate the core claim plainly: fractions, not endless decimals, are the physical starting point. No fancy vocabulary is needed to say this.

What this does and does not show

The paper does not present new experiments. It provides a way to understand a theoretical program. Independent tests of specific predictions remain an open challenge. The core math anchor is proven and old. The convergence with other researchers' work supports the broad idea. But room-temperature quantum devices and mass ratio predictions need their own validation.

The burden of proof has shifted. Those who defend endless decimals must now find a physical prediction that requires them. Until then, the simpler starting point wins.

Words used here

p-adic numbers
number systems built from fractions using a different way to measure size, one for each prime number
Bruhat-Tits tree
a branching shape that comes with each p-adic number system, like a family tree that spreads forever
completion
a way to fill gaps in a number system so certain sequences settle down
hidden variables
supposed extra facts that would fully determine outcomes, but cannot be measured

Learn more in plain language

This plain-language version was written by an AI model from the text of the paper and checked against plain-language rules: everyday words, no mathematics, no unexplained names. It leaves details out and can still be wrong; the paper is the source of record. To report a problem, open the paper, select the passage and choose Report.

For specialists: the technical digest, quoted from the paper

In the paper's words

The QNFO Adelic Physics Program proposes that the physically accessible base field of physics is Q (the rational numbers), not R (the real numbers). Ostrowskis theorem demands all p-adic completions of Q be physically meaningful. This paper provides the epistemological and pedagogical infrastructure.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

  1. The Adelic Cross-Domain Program reports that 11 Standard Model mass ratios fit this scheme to approximately 2%, with specific examples including: $m_{\tau } / m_{c} = 136.63$ vs. $3^{7} / 2^{4} = 136.7$ (deviation 0.07%) $m_{\tau } / m_{d} = 20.02$ vs. $2^{2} \cdot 5 = 20$ (exact) Convergent evidence (independent of QNFO): Chen, Liu, and Hung (2024) independently treat the Bruhat-Tits tree as a physical geometry, constructing a p-adic BTZ black hole on $T_{p}$.

    from 6.1 Discrete Substrate of Spacetime

  2. The adelic programme is not "new physics" — it is the removal of an unjustified assumption that has constrained physics for 150 years.

    from 11. Conclusion: What Changes

How it is done

  1. Ostrowski's theorem — a proven result in number theory — then demands that all p-adic completions of $\mathbb{Q}$ be physically meaningful, transforming the Adelic Physics Program from mathematical speculation into a physical programme.

    from Abstract

  2. The physically accessible numbers are rational — every measurement produces a rational number, every computer simulation operates on finite-precision approximations, and every number that has ever appeared in a physics paper ($\pi , e, \sqrt{2}$, the fine-structure constant $\alpha$) is computable — meaning it can be approximated to arbitrary precision by a finite rational procedure.

    from 1. Introduction

  3. Physics inherited $\mathbb{R}$ from mathematics, not from experiment.

    from $2.1 \mathbb{R}$ Is Not Forced by Physical Necessity

  4. A computable real number is one for which there exists a finite Turing-machine procedure (a D/R procedure in the terminology of Autaxys Ontological Closure) that approximates it with a computable modulus of convergence.

    from 2.2 The Computable Reals Argument

What would falsify it

  1. The burden of proof therefore shifts to the advocate of $\mathbb{R}$: demonstrate a physical prediction that requires infinite-precision real numbers and cannot be reproduced by any finite-precision rational computation.

    from $2.1 \mathbb{R}$ Is Not Forced by Physical Necessity

  2. To our knowledge, no such prediction exists [untested — open research question] [proposed — this is a methodological stance, not an established fact that $\mathbb{Q}$ is sufficient for all physics].

    from $2.1 \mathbb{R}$ Is Not Forced by Physical Necessity

  3. The non-computable reals (Chaitin's $\Omega$, etc.) have never appeared in any physical prediction [established].

    from 2.2 The Computable Reals Argument

Where the claim stops

  1. The adelic programme is not "new physics" — it is the removal of an unjustified assumption that has constrained physics for 150 years.

    from 11. Conclusion: What Changes

  2. The advocate of $\mathbb{R}$ must now demonstrate a physical prediction that requires infinite-precision real numbers and cannot be reproduced by any finite-precision rational computation.

    from 11. Conclusion: What Changes

  3. Until such a prediction is found — and none has been found to date — the working assumption should be that $\mathbb{Q}$ is the physical base field, and that Ostrowski's theorem applies.

    from 11. Conclusion: What Changes

Where to read

  1. Abstract236 words · 1 min
  2. 1. Introduction585 words · 3 min
  3. 2. The Unjustified Assumption637 words · 3 min
  4. 3. Number-Theoretic Foundations336 words · 1 min
  5. 4. Constructing Numbers from Distinctions348 words · 2 min
  6. 5. The Gisin–Del Santo Programme: Independent Convergence424 words · 2 min
  7. 6. Bruhat-Tits Trees as Physical Geometry348 words · 2 min
  8. 7. Ultrametric Quantum Computation266 words · 1 min
  9. 8. The Langlands Bridge240 words · 1 min
  10. 9. Domain Translation Errors: A Communications Framework295 words · 1 min
  11. 10. Observer-Centered Epistemology274 words · 1 min
  12. 11. Conclusion: What Changes223 words · 1 min

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