Axiomatic Emergence AB; The Physical Origin of Quantum Logic

This paper, based on two fundamental physical axioms—Information Conservation (A1) and Computability (A2)—systematically argues for the intrinsic logical structure necessary for describing physical reality. Research shows that in aself-referential universe model constrained by local observations, the truth-valuejudgment logic of physical propositions necessarily deviates from classical Booleanlogic. The core root lies in the “local-global inequivalence” of physical systems: theinformation contained in the global physical state cannot be completely determinedby any finite observational procedure within a finite spacetime region. This leads tothe invalidity of the law of excluded middle within the system, and consequently,the logical structure mathematically manifests as a non-distributive orthomodularlattice, i.e., Birkhoff–von Neumann quantum logic. This structure is proven tocorrespond exactly to the subobject lattice in the ∞-topos TA constructed previously. This theoretical framework finally leads to a testable cosmological prediction:the central value of the non-Gaussianity parameter fNL of the cosmic microwavebackground (CMB) temperature fluctuations is about −3.2. Next-generation CMBexperiments (such as CMB-S4) will be able to test this prediction precisely, andthe results can be used to evaluate whether the quantum logical structure emergingfrom the basic axioms is suitable for describing the real universe.