The uncertainty principle of quantum mechanics is often regarded as a fundamental postulate or an ontological property of the microscopic world. This paperproposes a unified interpretative framework based on information constraints, arguing that uncertainty relations are essentially an inevitable consequence of thetwo operational boundaries in the process of physical cognition: finite informationcapacity and feasibility of finite steps. By introducing the Noetherian property ofalgebraic structures and the discretization of information hierarchies, a rigorouscorrespondence from operational constraints to subfactor towers and informationgeometry is constructed. Within this framework, uncertainty relations naturallyemerge from the geometric rigidity of the information hierarchical structure, andtheir mathematical form is locked by algebraic invariants such as the Jones index. The theory not only coherently derives the standard Heisenberg relations butalso predicts testable modifications at extremely high energies and in strong gravitational fields, providing a clear mechanism for the quantum-classical transitionbased on information accumulation phase transitions. This work indicates that uncertainty is not an inherent fuzziness of nature but a structural boundary of physicaldescription under information constraints, thereby establishing a new foundationfor understanding the continuity between quantum theory and classical physics.
The uncertainty principle of quantum mechanics is often regarded as a fundamental postulate or an ontological property of the microscopic world. This paperproposes a unified interpretative framework based on information constraints, arguing that uncertainty relations are essentially an inevitable consequence of thetwo operational boundaries in the process of physical cognition: finite informationcapacity and feasibility of finite steps. By introducing the Noetherian property ofalgebraic structures and the discretization of information hierarchies, a rigorouscorrespondence from operational constraints to subfactor towers and informationgeometry is constructed. Within this framework, uncertainty relations naturallyemerge from the geometric rigidity of the information hierarchical structure, andtheir mathematical form is locked by algebraic invariants such as the Jones index. The theory not only coherently derives the standard Heisenberg relations butalso predicts testable modifications at extremely high energies and in strong gravitational fields, providing a clear mechanism for the quantum-classical transitionbased on information accumulation phase transitions. This work indicates that uncertainty is not an inherent fuzziness of nature but a structural boundary of physicaldescription under information constraints, thereby establishing a new foundationfor understanding the continuity between quantum theory and classical physics.
The Heisenberg uncertainty principle constitutes one of the foundational pillars of quantum mechanics and represents a definitive rupture with the deterministic ideal of classical physics. This work develops a comprehensive analysis of the uncertainty principle from a mathematical, physical, and philosophical perspective, demonstrating that it should not be interpreted as an instrumental or epistemological limitation, but rather as an ontological property inherent to the formalstructure of quantum theory.Within the framework of Hilbert spaces, self-adjoint operators, and non-commutative algebras, it is shown that uncertainty emerges necessarily as a consequence of the structural incompatibility between conjugate observables. The study articulates the uncertainty principle with classical chaos theory and the sciences of complexity, establishing a fundamental distinction between epistemological unpredictability and ontological indeterminacy. While classical chaos preserves well-defined trajectories that are practically inaccessible, quantum mechanics eliminates the very notion of trajectory as a fundamental entity.This rupture manifests itself in the granularity of phase space, the impossibility of defining exact initial conditions, and the consequent reformulation of determinism. Contemporary experimental developments designed to exclude instrumental disturbances are analyzed, reinforcing the ontological interpretation of the uncertainty principle.Finally, the implications for simulation, predictability, and quantumOverall, this work argues that the uncertainty principle does not undermine scientific rationality, but rather redefines itsscope and deepens our understanding of physical reality. Keywords: uncertainty principle; quantum mechanics; mathematical structure; non-commutative operators; chaos theory; complexity; determinism; physical ontology.
We derive the structural modifications and physical implications of the Heisenberg Uncertainty Principle under the framework of the Three-Dimensional Complex Necessity (3DCN) principle. In standard quantum mechanics, the uncertainty relation is bounded by a constant scalar value derived from the axiomatic commutation relation [x, p] = i*hbar. By replacing the static imaginary unit i with the dynamically locked universal complex structure operator J_U, we prove that the commutator deforms into a state-dependent operator equation [x, p] = J_U*hbar. We demonstrate that the lower bound of quantum uncertainty is no longer invariant, but fluctuates based on the local geometry of the real phase space substrate and the energy density of the flavor-locking mechanism. This deformation naturally regularizes sub-Planckian spatial measurements, establishing a fundamental physical cutoff that prevents infinite information density localized in real space, thereby avoiding gravitational collapses at the quantum level.
The Heisenberg Uncertainty Principle is conventionally interpreted as a fundamental limit of nature's precision or as a consequence of measurement disturbance. In this paper, we propose a structural reinterpretation within the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that quantum uncertainty is mathematically isomorphic to the Time-Bandwidth Product in signal processing. By modeling the vacuum as a discrete information grid, we identify the uncertainty relation not as an intrinsic indeterminism of the object, but as a Representation Limit arising from the projection of infinite information onto a finite-bandwidth substrate. Key Results: Geometric Derivation: We derive the uncertainty inequality σxσk≥1/2 strictly from the properties of the Fourier Transform on a lattice, identifying the Planck constant ℏ as the scaling parameter converting grid bandwidth into physical momentum (p=ℏk). Numerical Verification: Included Python simulations (FFT) confirm that Gaussian wavepackets minimize the uncertainty product to exactly 0.5. This proves that "fuzziness" is effectively the compression artifact of a finite-resolution universe. Ontological Shift: The paper recovers the standard quantum mechanical limit while providing a rigorous geometric foundation based on discrete signal theory, removing the need for an axiomatic "indeterminacy principle." Includes: Full mathematical derivation (Fourier Duality). Python Simulation Notebook (102_18116715_SDRIS_Born_Rule_Simulation_Code_v1_0.ipynb) verifying the lower bound.
This work develops a unified structural explanation of Heisenberg’s uncertainty principle based onthe infinite-dimensional nature of physical reality and its mathematical representation. Quantumstates are intrinsically wave-like and must be described by functions rather than finite-dimensionalvectors, forcing the use of an infinite-dimensional Hilbert space. Within this framework, fourindependent but mutually reinforcing structures emerge: analytic non-commutativity ofmultiplication and differentiation, Fourier duality and the mutual broadening of a function and itstransform, the symplectic geometry of phase space and its minimal area constraint, and thealgebraic rigidity encoded in the Weyl relations and the Stone–von Neumann theorem. Theselayers form a logical chain from finite-dimensional impossibility to infinite-dimensional necessity,revealing the uncertainty principle as a structural feature of the physical world. The paper furtherdiscusses extensions to the generalized uncertainty principle and the infinite-dimensionalstructure of quantum field theory.
The indispensability of the complex structure in quantum mechanics has beenexperimentally confirmed, yet its ontological status—whether complex numbers aremerely a mathematical tool or a constitutive element of physical reality—has longremained undecided. Starting from mathematical necessity, this paper argues thatthe complex structure is not only the descriptive language of quantum mechanicsbut also an ontological constraint condition of physical reality. Based on Frobenius’ theorem on the classification of division algebras over the real numbers, wereveal: if the descriptive framework is required to be both commutative and algebraically closed, then the complex structure is the unique logically necessary choice.This mathematical constraint, when mapped onto physical reality, implies that the”imaginary part” corresponds to a modal dimension that is not directly observablebut constrains observable phenomena. The measurement process is thus reconceptualized as a projection from the complex structure onto a real subspace, whereinformation loss is an inherent feature of the mathematical structure rather thanan additional dynamical assumption. We demonstrate that this framework is compatible with research on imaginarity as a resource in quantum resource theory andwith analyses of Fisher information limits in quantum metrology, and we proposethree testable predictions with quantum metrological precision. This interpretationadvances the quantum measurement problem from a matter of interpretational debate to a level of structural analysis, providing a rigorous mathematical foundationfor understanding the quantum-classical transition.
This paper proposes a fundamental framework based on information geometry that unifies quantum mechanics, thermodynamics, and spacetime geometry into a single foundational theory. Starting from three elementary axioms regarding information as the primary physical ontology, we derive the universal information metric, construct the information action functional, and show that all known physical laws emerge as extremal conditions of this functional. The theory recovers standard quantum mechanics, classical thermodynamics, and general relativity in appropriate limits, while predicting new relations between quantum entanglement, gravitational curvature, and entropy. We conclude that all physical phenomena—matter, energy, spacetime, and interactions—are equivalent to geometric structures on the space of quantum information states.