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Resolving Schrödinger's Cat Paradox via Fractal Uncertainty Theory

Jens Deutschmann

Published Feb 14, 2026• 3 citations
Publisher

Abstract

We present a resolution to Schrödinger's famous cat paradox using the Fractal Uncertainty Theory (FUT), a novel mathematical framework that redefines theconcepts of "0" and "1" as observer-dependent states relative to a "view-vector"(Schau-Vektor). By introducing the concept of uncertainty-distance d(vA , vB ) between view-vectors operating at different scales, we demonstrate that the apparentparadox of macroscopic superposition arises from the incorrect assumption of scale-independent quantum states.We show that the atomic and macroscopic systemsare fundamentally decoupled (K(vatom , vcat ) ≈ 0), eliminating the paradox withoutinvoking consciousness, many-worlds, or hidden variables. Our approach predicts atestable transition from quantum to classical behavior based solely on object size,independent of environmental decoherence.

DOI
10.5281/zenodo.18640201

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We present a resolution to Schrödinger's famous cat paradox using the Fractal Uncertainty Theory (FUT), a novel mathematical framework that redefines theconcepts of "0" and "1" as observer-dependent states relative to a "view-vector"(Schau-Vektor). By introducing the concept of uncertainty-distance d(vA , vB ) between view-vectors operating at different scales, we demonstrate that the apparentparadox of macroscopic superposition arises from the incorrect assumption of scale-independent quantum states.We show that the atomic and macroscopic systemsare fundamentally decoupled (K(vatom , vcat ) ≈ 0), eliminating the paradox withoutinvoking consciousness, many-worlds, or hidden variables. Our approach predicts atestable transition from quantum to classical behavior based solely on object size,independent of environmental decoherence.
Fractal Uncertainty Theory (FUT) is a fundamental reformulation of mathematics and physics that redefines the classical concepts of "0" and "1" as observer-dependent, fuzzy states. The theory introduces view-vectors and perspective-dependent null-zones as the primary ontological objects, from which physical laws emerge. Thisdocument presents the complete axiomatic foundation of FUT (Version 5.0). The Fractal Cancellation Theorem (FCT) is part of Fractal Uncertainty Theory (FUT). Note on status. This document represents the current state of FUT development as of February 2026.Predictions may be refined or extended as the theoretical framework develops and experimental capabilities advance.
Schrödinger's cat paradox has persisted for nearly a century as a demonstration of the apparent absurdity of quantum superposition when extended to macroscopic scales. This technical note demonstrates that the paradox dissolves entirely within the CAT'S Theory framework through the triadic invariant Reality = Pattern × Intent × Presence (P × I × Pr). We argue that the cat is neither "both alive and dead" nor the victim of mysterious collapse. Instead, superposition represents a state where Presence (Pr) has not yet instantiated, yielding P × I × 0 = 0 (potential but not actual). Measurement does not "cause" collapse through mysterious observer effects; it provides the Presence component required for actualization. This resolution eliminates the need for Multiple Worlds or hidden variables while maintaining consistency with quantum mechanical predictions.
This paper proposes a quantum measurement framework based on structuralstability theory, aiming to resolve the logical dilemma of the quantum–classicaltransition in Schrödinger’s cat paradox. Traditional quantum mechanics relies onexternal mechanisms such as “observer introduction” or “decoherence” to explainmacroscopic reality, leading to vague ontological commitments. We argue that thefundamental reason macroscopic quantum states cannot maintain coherent superpositions lies in the self-organizing critical behavior constrained by the system’sinternal structural stability. The core mechanism is: when a quantum system couples with a classical measuring device, its Hilbert space representation is forced toproject from a high-dimensional unitary representation onto a low-dimensional classical representation, a process driven by the extremization of a structural stabilityfunctional, not by external observation. We rigorously prove that when the system’sstructural information density exceeds a critical threshold, the quantum superposition state cannot satisfy self-consistency constraints mathematically; the systemmust select a classical eigenstate through an “algebraic filtration” mechanism. Thetheory yields three testable predictions: (1) a microscopic entropy production pulseat the moment of coupling between the measuring device and the quantum system,of order 10−21 J/K; (2) a deviation of the quantum Zeno suppression factor fromstandard quantum mechanical predictions on microsecond scales; (3) a scaling-lawdivergence of the decoherence time of macroscopic superpositions at critical parameters. These effects can be tested in coupled superconductor qubit–mechanicalresonator systems. The framework does not modify unitary evolution, does not relyon many-worlds assumptions, and does not introduce collapse postulates; instead,it transforms the measurement problem into a question of compatibility betweenquantum information structure and geometric–topological constraints.
This treatise delivers the definitive mathematical physics formulation to resolve the foundational quantum measurement problem known as Schrödinger's Cat Paradox. Traditional quantum mechanics formalisms enforce an unphysical macroscopic superposition state, asserting that a macroscopic entity can simultaneously exist in alive and dead states prior to observer intervention. Operating within the functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we eliminate this paradox by introducing the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We mathematically demonstrate that high-mass biological matrices and enclosed environment tensors undergo instantaneous phase decoherence and localized state collapse under the constraint of the TPHLM chrono-mesh. This unified architecture provides comprehensive diffeomorphism Ward-Khandey identities, eliminating the need for human conscious observation and providing a deterministic 0.0000000000000000% error baseline ready for high-performance exascale computing networks.
The single-slit and double-slit experiments are among the most fundamental demonstrations of quantum behavior. Every interpretation of quantum mechanics must account for them, yet none has derived the mathematical structures used todescribe them from the experiments themselves. In this paper we show that Fractal Uncertainty Theory (FUT) achieves precisely this. The which-way measurement problem is resolved without wave-function collapse or many worlds.We argue that the slit experiments, properly understood through FUT, constitute the physical origin of arithmetic itself. Note on status. This document represents the current state of FUT development as of February 2026.Predictions may be refined or extended as the theoretical framework develops and experimental capabilities advance.
The Schrodinger's Cat paradox was proposed in 1935 by Edwin Schrodinger, one of the founders of quantum mechanics, as an attempt to visualize the macroscopic realization of a quantum superposition state. A cat is placed in a sealed box together with a vial of poison. A two-state particle (e.g. an electron) is sent into a detector in the box resulting either in a broken or an intact vial and a dead or live cat, respectively. The main problem consists in whether the superposition state of a microscopic particle can be transferred upon the macroscopic cat, that is, whether the cat can exist in a superposition state, being simultaneously dead and alive. Since the standard Copenhagen interpretation is unable to assign any reality to the quantum superposition state, the paradox finds no resolution within the regime of this interpretation. Von Neumann's insistence on the uniform treatment of both microscopic (quantum) and macroscopic (classical) objects according to the laws of quantum mechanics provides a more consistent framework for the resolution of the paradox. In particular, the discovery of the phenomenon of decoherence, whereby the disappearance of the quantum interferences at the macro level is accounted for, suggests the onset of an extremely efficient interference relaxation process (10-23 s) upon the interaction of the two state particle with the detector. As a result, Schrodinger's cat can exist macroscopically either as dead or alive and never as a combination of both. Decoherence not only aids the resolution of the Schrodinger's Cat paradox but also sheds light upon the mechanisms by which the macro-world emerges from the microscopic quantum realm.