This paper presents the Pan-Information Unified Field Theory (PIUFT), a first-principles algebraic framework that reconstructs quantum mechanics from two core axioms: the confirmation operation and information truncation. Using Tomita-Takesaki modular flow, GNS construction, and fusion category theory, we derive all key postulates of quantum mechanics—including the Hilbert space structure, Born rule, unitary evolution, quantum entanglement, and the Schrödinger equation—without any additional assumptions. The theory reveals that quantum "weirdness" arises from the inherent information truncation of finite observers, rather than being fundamental to nature itself. We also discuss the potential implications for quantum gravity and experimental predictions beyond the standard model.
This paper presents the Pan-Information Unified Field Theory (PIUFT), a first-principles algebraic framework that reconstructs quantum mechanics from two core axioms: the confirmation operation and information truncation. Using Tomita-Takesaki modular flow, GNS construction, and fusion category theory, we derive all key postulates of quantum mechanics—including the Hilbert space structure, Born rule, unitary evolution, quantum entanglement, and the Schrödinger equation—without any additional assumptions. The theory reveals that quantum "weirdness" arises from the inherent information truncation of finite observers, rather than being fundamental to nature itself. We also discuss the potential implications for quantum gravity and experimental predictions beyond the standard model.
This paper presents a rigorous demonstration that the fundamental origin of the natural affinity between information ontology and quantum mechanics lies in the eternal asymmetry between global information (the full information algebra 𝔄) and local information (the observable algebra 𝒩). Starting from the core axioms of the Pan-Information Unified Field Theory (PIUFT)—idempotency of information confirmation and trace-preserving information conservation—the paper strictly proves that the kernel space ker(E) necessarily exists and that any observer is necessarily a local information structure, permanently unable to access the full information algebra. The conditional expectation E: 𝔄 → 𝒩 acts as the projection bridge, transforming the global structure of completeness, determinacy, commutativity, real numbers, and classicality into the local structure of incompleteness, indeterminacy, non-commutativity, complex numbers, and quantumness. All core features of quantum mechanics—the emergence of Hilbert space via the GNS construction, operator non-commutativity, complex probability amplitudes, the uniqueness of the Born rule, and quantum entanglement—are rigorously derived as inevitable algebraic consequences of local information incompleteness. The universal incompleteness of physical laws—singularity breakdown in general relativity, the quantum measurement problem, the redundancy of free parameters in the Standard Model, and the second law of thermodynamics—is unified under a single algebraic root: the asymmetric allocation of information quotas between the global and the local. The trace conservation law τ(𝔄) = τ(𝒩) + τ(ker(E)) guarantees that global and local information are not two independent worlds but two perspectives on the same hyperfinite type III₁ von Neumann factor, constituting a strict dialectical unity. The paper further derives a series of testable observational predictions, including the precise proportions of dark energy, dark matter, and ordinary matter, all algebraically determined by the Jones index χ = 4 of the A₁₁ subfactor with zero free parameters. This work establishes the first complete philosophical and mathematical framework that unifies quantum foundations, cosmological dark components, the incompleteness of physical laws, and the cognitive boundaries of observers under a single principle of information asymmetry.
We propose a self-consistent axiomatic framework that unifies quantum unitary evolution, thermal dissipation, and spacetime geometry based on three fundamental principles: the \emph{complex-time principle}, the \emph{information-geometry equivalence principle}, and the \emph{maximal entropy gradient principle}. Starting from these axioms, we rigorously derive three core equations: a complex-time quantum-thermal master equation, an information-induced gravitational field equation, and a unified gradient-flow dynamics that couples quantum states, thermodynamics, and curvature. From these, we further derive four key derived equations: a generalized Einstein field equation in the low-energy limit, a quantum-thermodynamic uncertainty relation, a relation between entropy production and curvature scalar, and a conservation law for quantum information current. The framework naturally recovers standard quantum mechanics, thermodynamics, and general relativity in appropriate limits, while offering new predictions about the relation between quantum entanglement and spacetime structure. All derivations are carried out in full mathematical detail, and the resulting equations are original, closed-form, and internally consistent.
The postulates of quantum mechanics — complex Hilbert space structure, unitary evolution, the Born rule, definite measurement outcomes, the canonical commutation relations, and the Pauli exclusion principle — have traditionally been taken as axioms. In this work we show that, within the framework of Modular Entropic Gravity (MEG), these structures admit a unified derivation from four geometric axioms governing the informational structure of the quantum vacuum.The framework is non-circular: its inputs are operator-algebraic structures of quantum field theory — including modular Hamiltonians, the JLMS identity, and the Bisognano–Wichmann theorem — which are defined independently of any probability interpretation. The probabilistic and dynamical rules of textbook quantum mechanics then arise as an infrared effective description of this underlying structure.The six results are obtained in logical order: (Q1) the emergence of complex structure from the entropion mass gap; (Q2) the L2 Hilbert space and Schrödinger equation from the long-wavelength limit of the vacuum propagator; (Q3) the Born rule from a relative entropy identity combined with the PLES–Petz correspondence; (Q4) definite measurement outcomes from PLES boundary conditions imposed by classical apparatus; (Q5) the canonical commutation relations from modular flow via the Bisognano–Wichmann and Araki reconstruction; and (Q6) the Pauli exclusion principle from the Z3 topological structure of the MEG vacuum.Three of these results (Q1, Q2, Q5) are established as complete theorems within the framework. The remaining three (Q3, Q4, Q6) are structurally complete derivations in which the underlying mechanism is fully identified, and any remaining conditions concern either formal infinite-dimensional extension or quantitative refinement.The paper therefore presents a coherent and non-circular programme in which the postulates of quantum mechanics are reconstructed from a smaller set of underlying principles, together with an explicit account of the remaining technical steps required for complete formalisation.
This paper provides a rigorous derivation of all core postulates of quantum mechanics from a single axiom: the existence of binary distinction. No prior assumptions—Hilbert space, wave function, probability amplitude, or unitary evolution—are introduced as external inputs. The derivation proceeds in six chapters: Chapter 1 establishes the axiom of binary distinction and proves that the imaginary unit i is the algebraic necessity of iterative distinction operations: Δ applied twice equals a reversal (-1), therefore one distinction corresponds to multiplication by i. Chapter 2 demonstrates that complex probability amplitudes are the unique algebraic carriers of the binary split between confirmed information (real part) and concealed information (imaginary part). Chapter 3 proves the Born rule as the unique solution to information deviation minimization under truncation constraints—the squared modulus is the sole functional form compatible with positivity, normalization, and classical-degenerate compatibility. Chapter 4 derives unitary evolution as the traversal of all indistinguishable paths during the suspension interval between confirmation operations. Schr\"{o}dinger's equation emerges as the differential limit of this traversal under modular flow. Chapter 5 establishes that measurement collapse is not a mysterious nonunitary process but the re-execution of the confirmation operation, projecting the suspended superposition onto a single confirmed eigenstate. The collapse probability is identical to the Born rule derived in Chapter 3. Chapter 6 demonstrates that quantum entanglement is the split-window projection of a shared confirmation projector—two entangled particles share the same confirmation projection in the full-dimensional information field, and spatial separation is merely the appearance of local windows in the observable domain. Bell inequality violation follows directly from the non-homomorphic property of the truncation projection. The entire formalism emerges without fitting parameters, without interpretation debates, and without external physical assumptions. Quantum mechanics is thus revealed not as the fundamental language of the universe, but as the inevitable cognitive structure of any finite observer executing information confirmation and truncation on the full-dimensional information field. All conclusions are strictly demarcated by a "boundary of honesty," distinguishing logically necessary deductions from directional inferences requiring further mathematical hardening.
We present a fundamental unified framework based on information geometry, in which quantum mechanics, statistical thermodynamics, and general relativity emerge from a single information-theoretic ontology. Starting from three rigorous axioms that establish quantum information as the primary physical substrate, we construct the universal information action functional using the Bures–Fisher–Rao metric on the manifold of quantum density matrices. Full variational derivation yields a unified field equation that governs the evolution of quantum information and emergent spacetime geometry. In appropriate limiting regimes, we recover the Schrödinger equation, equilibrium statistical mechanics, and the Einstein field equations. This work provides the foundational layer of a complete theory of everything based on the principle: geometry is information.
This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information.