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PreprintCC BY-NC-ND 4.0HAL

Ontological Constraints on Epistemic Syntax: How Informationally-Constrained Access to Reality Shaped the Axiomatic Structure of Quantum, Relativistic, and Gravitational Theories

  • Fabien Déchery
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Abstract

Three physical properties of any measurement probe π in a substrate 𝒢 --- non-zero energy cost (A1: Eπ > 0), finite propagation speed (A2: vπ ≤ c), and constitutive excitation (A3: π ∈ 𝒢) --- tightly constrain the axiomatic structures of quantum mechanics, relativity, and quantum field theory. A1 ∧ A3 tightly constrains non-commutativity and the Born rule; A2 entails Lorentz invariance and microcausality; their conjunction yields the Wightman axioms and CPT. A3 enriches both registers: complexification in 𝒟QM and curvature in 𝒟GR. Each major step is grounded in a published theorem (Ignatowski, Gleason, Jost, Malament, Jacobson). The linearity of quantum mechanics is identified as a screening artefact of the Hilbert-space habitat. A classification criterion for the mass gap --- nonlinearity plus non-trivial homotopy --- is consistent with all six known test cases (consistency checks, not blind predictions).

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Cite

BibTeXRIS
BibTeX
@misc{dechery2026ontological,
  title = {{Ontological Constraints on Epistemic Syntax: How Informationally-Constrained Access to Reality Shaped the Axiomatic Structure of Quantum, Relativistic, and Gravitational Theories}},
  author = {Fabien Déchery},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05854375v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Ontological Constraints on Epistemic Syntax: How Informationally-Constrained Access to Reality Shaped the Axiomatic Structure of Quantum, Relativistic, and Gravitational Theories
AU  - Fabien Déchery
PY  - 2026
DA  - 2026/10/29
PB  - HAL
UR  - https://hal.science/hal-05854375v1
AB  - Three physical properties of any measurement probe π in a substrate 𝒢 --- non-zero energy cost (A1: E_π > 0), finite propagation speed (A2: v_π ≤ c), and constitutive excitation (A3: π ∈ 𝒢) --- tightly constrain the axiomatic structures of quantum mechanics, relativity, and quantum field theory. A1 ∧ A3 tightly constrains non-commutativity and the Born rule; A2 entails Lorentz invariance and microcausality; their conjunction yields the Wightman axioms and CPT. A3 enriches both registers: complexification in 𝒟_QM and curvature in 𝒟_GR. Each major step is grounded in a published theorem (Ignatowski, Gleason, Jost, Malament, Jacobson). The linearity of quantum mechanics is identified as a screening artefact of the Hilbert-space habitat. A classification criterion for the mass gap --- nonlinearity plus non-trivial homotopy --- is consistent with all six known test cases (consistency checks, not blind predictions).
ER  -