ARC Corpus · Volume 7

Physics Reread

Measurement as projection: Tsirelson without Hilbert, the wave, the quantum, the proton and the strings

« Classique : mesurer les côtés. Quantique : mesurer les diagonales. La différence est √2. Rien de plus, et la lecture paie la moitié. »

Filipe Bastos, Tsirelson sans Hilbert, v4.1, juillet 2026

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Abstract

What the ARC corpus says about physics, in one sentence: measurement is projection. A complete state is read by an instrument that keeps only part of it, and what is called randomness, indeterminacy or collapse is the price of that reading, not a property of what is read. The first chapter decomposes the Tsirelson bound 2√2 into three exact factors. The following chapters apply the same grammar to the quantum of action, Heisenberg, the tunnel effect, the proton as axis, the Standard Model, the nested atom, strings and E = Dc². Two rules hold throughout: Bell's theorem is not contested, and a Reading remains a Reading; a reading that reproduces the numbers of received physics earns its place only through its predictions.

Keywords: quantum mechanics, Tsirelson bound, measurement, Heisenberg, tunnelling, proton, Standard Model, string theory

The chapters themselves are in French. Open any chapter and use the Translate links in the header for a machine translation; the abstract and the table of statements on this page are translated by hand.

Résumé (français)

Ce que le corpus ARC dit de la physique, en une phrase : la mesure est une projection. Un état complet est lu par un instrument qui n'en retient qu'une partie, et ce que l'on appelle aléa, indétermination ou effondrement est le prix de cette lecture, non une propriété de ce qui est lu. Le premier chapitre décompose la borne de Tsirelson 2√2 en trois facteurs exacts. Les suivants appliquent la même grammaire au quantum d'action, à Heisenberg, à l'effet tunnel, au proton comme axe, au Modèle standard, à l'atome matriochka, aux cordes et à E = Dc². Deux règles tiennent le volume : le théorème de Bell n'est pas contesté, et ce qui est Lecture reste Lecture ; une lecture qui reproduit les nombres de la physique reçue ne gagne sa place que par ses prédictions.

Keywords: mécanique quantique, borne de Tsirelson, mesure, Heisenberg, effet tunnel, proton, Modèle standard, théorie des cordes

Contents

  1. Foreword
  2. Chapter 1. The Tsirelson bound without a Hilbert space
    • 1.1 The model
    • 1.2 The singlet correlation
    • 1.3 The erratum: the pure sign is the Popescu-Rohrlich box
    • 1.4 The arithmetic foundation of k = 1/2
    • 1.5 The geometric derivation of the bound
    • 1.6 The three ceilings
    • 1.7 No-signaling, Born rule, entanglement
    • 1.8 Five constants, one mechanism
    • 1.9 Scope and limits
    • 1.10 Falsifiable predictions
    • 1.11 The double derivation
    • 1.12 The hourglass of pairs
    • 1.13 The same bound read by Book VIII
  3. Chapter 2. Quantum correlations by sequential projection
    • 2.1 The four principles
    • 2.2 The global state and the sequential order
    • 2.3 The classical objections
    • 2.4 The ternary structure beneath binary measurements
    • 2.5 Half-integer spin as geometric necessity
    • 2.6 The uniqueness of the update
    • 2.7 The comparison with the received interpretations
    • 2.8 Falsification
  4. Chapter 3. The wave does not collapse, it inverts
    • 3.1 The measurement problem
    • 3.2 The six principles
    • 3.3 The ontological sequence 2 → 1∞ → 3 → 6 → 5 → 4
    • 3.4 The wave as relational product
    • 3.5 The inversion: the third term binds
    • 3.6 The arithmetic signature: 5 × 5 = 25 → 7
    • 3.7 The observer as degree of binding
    • 3.8 Wave-particle duality as rotation
    • 3.9 Continuity with sequential projection
    • 3.10 The objections
    • 3.11 The comparison of frameworks
    • 3.12 Predictions
    • 3.13 Scope
  5. Chapter 4. Heisenberg's indeterminacy as projection cost
    • 4.1 The theorem and its reading
    • 4.2 The paths of k = 1/2
    • 4.3 The same 1/2 in every domain
    • 4.4 Measurement as projection
    • 4.5 The commutator reread
    • 4.6 Stevin's residue
    • 4.7 Predictions
    • 4.8 Determinism restored
  6. Chapter 5. The tunnel effect: the barrier as a switch
    • 5.1 The established facts
    • 5.2 The geometric reading
    • 5.3 Recoverability: the rotated component exists
    • 5.4 Predictions
    • 5.5 What version 2.0 no longer claims
    • 5.6 Conclusion
  7. Chapter 6. The Planck cross: the quantum is an area
    • 6.1 The quantum is an area, not a sphere
    • 6.2 The enclosed area: states inhabit the halves
    • 6.3 The phase cross and the four inversion pairs
    • 6.4 Excitation opens the span
    • 6.5 The square is seen as a trapezoid
    • 6.6 Liouville: the area holds, the shape deforms
    • 6.7 The half is not the quantum, it is the conjugate face
    • 6.8 Indeterminacy as projection cost
    • 6.9 Particles are functions
    • 6.10 Synthesis
  8. Chapter 7. The proton as axis
    • 7.1 The table everyone owns
    • 7.2 The two names and the double turn
    • 7.3 First fact: the spin crisis, the 3 seen and the 6 hidden
    • 7.4 Second fact: confinement, the axis cannot be visited
    • 7.5 Third fact: the gauge octet, 9 = 8 + 1
    • 7.6 Mass: the massively relational object
    • 7.7 The commitment: the 2/9 versus 3/9 test
    • 7.8 The epistemic status
    • 7.9 Conclusion
  9. Chapter 8. The Standard Model reread: the arithmetic collapse
    • 8.1 The six founding errors
    • 8.2 Planck's constant as the resolution of the system
    • 8.3 Heisenberg's inequality
    • 8.4 The photon as state interval
    • 8.5 Mass as winding number
    • 8.6 The reduction of the particle spectrum
    • 8.7 The redundancy of the infinite-dimensional space
    • 8.8 Determinism restored
    • 8.9 Synthesis and predictions
  10. Chapter 9. Principia relationalis: the overall plan
    • 9.1 The preamble: the epistemological break
    • 9.2 The six pillars
    • 9.3 Internal coherence
    • 9.4 The predictions by domain
    • 9.5 The final declaration
  11. Chapter 10. The atom is not a brick: the matryoshka
    • 10.1 The atom is the relation between two poles
    • 10.2 The self-coded matryoshka
    • 10.3 The refusal of division
    • 10.4 Fission: inversion, not destruction
    • 10.5 Two illusions eliminated
    • 10.6 The end of the accelerator
    • 10.7 Predictions
    • 10.8 Conclusion
  12. Chapter 11. Strings without strings
    • 11.1 The problem and the diagnosis
    • 11.2 The axioms
    • 11.3 The number 496
    • 11.4 The gradient 198, the axis 595 and the string
    • 11.5 The sealing of the string
    • 11.6 The curled-up dimensions as inscribed circles
    • 11.7 The two bricks and the birth of the square
    • 11.8 The rewriting piece by piece
    • 11.9 The theorems of the rewriting
    • 11.10 The three engravings corrected
    • 11.11 The head and the legs: where the grammar touches the world
    • 11.12 The April predictions, with their statuses
    • 11.13 Conclusion
  13. Chapter 12. E = Dc²: density, not mass
    • 12.1 The thesis
    • 12.2 The operative criterion of D
    • 12.3 The dynamic enrichment of D
    • 12.4 Falsification
  14. Chapter 13. Book VIII of the Quantum Bible: physics without amputation
    • 13.1 The end of integral calculus for solids of revolution
    • 13.2 The amputation by Newton and Leibniz, and the recovery of Pappus
    • 13.3 Mendeleev's fold and the Ni-Co-Fe triad
    • 13.4 The 137/163 couple
    • 13.5 Gravity at the two scales
    • 13.6 LIEM: Light = Information = Energy = Magnetism
    • 13.7 The cosmic dipole and the primordial asymmetry
    • 13.8 The anomalous magnetic moment of the muon
    • 13.9 Riemann's critical line
    • 13.10 Synthesis of the book
  15. Appendix A: Table of statements
  16. Appendix B: Withdrawals and corrections
  17. Appendix C: Merged sources
  18. Appendix D: Verifications redone

Version 1.0, octobre 2026 · 63 497 mots · 132 pages · Licence CC BY 4.0