The many-worlds interpretation holds an important position in foundationalstudies of quantum mechanics due to its ontological parsimony—adhering to theuniversality of the wave function and unitary evolution. However, this interpretation has long faced core challenges such as the fuzzy mathematical definition of”world branches” and the origin of probability. Within the framework of a ”faileduniverse,” this paper re-examines the generation conditions and existence formsof many-worlds structure. By introducing topological constraint phase transitionsand self-referential reconstruction dynamics, we prove that when the universe is in a”failed phase” caused by insufficient logical depth, the global many-worlds description collapses, but its topological order parameter—the second Chern number—localizes in a modularized discrete form within causal fragments. The many-worldsdo not disappear but exist in a fragmented, modalized manner; the quantum measurement process is reconstructed in this picture as a topological transition of theobserver on the boundaries of causal fragments, rather than instantaneous wavefunction collapse or global world splitting. This framework unifies quantum measurement, spacetime emergence, and cosmological observations into a self-consistenttheoretical system, and derives three experimentally distinguishable predictions:non-Gaussianity of the cosmic microwave background radiation, the logical noisespectrum of primordial gravitational waves, and a detectable discrete chiral currentin mesoscopic circuits.
The many-worlds interpretation holds an important position in foundationalstudies of quantum mechanics due to its ontological parsimony—adhering to theuniversality of the wave function and unitary evolution. However, this interpretation has long faced core challenges such as the fuzzy mathematical definition of”world branches” and the origin of probability. Within the framework of a ”faileduniverse,” this paper re-examines the generation conditions and existence formsof many-worlds structure. By introducing topological constraint phase transitionsand self-referential reconstruction dynamics, we prove that when the universe is in a”failed phase” caused by insufficient logical depth, the global many-worlds description collapses, but its topological order parameter—the second Chern number—localizes in a modularized discrete form within causal fragments. The many-worldsdo not disappear but exist in a fragmented, modalized manner; the quantum measurement process is reconstructed in this picture as a topological transition of theobserver on the boundaries of causal fragments, rather than instantaneous wavefunction collapse or global world splitting. This framework unifies quantum measurement, spacetime emergence, and cosmological observations into a self-consistenttheoretical system, and derives three experimentally distinguishable predictions:non-Gaussianity of the cosmic microwave background radiation, the logical noisespectrum of primordial gravitational waves, and a detectable discrete chiral currentin mesoscopic circuits.
Based on the mathematical framework established in the Observer Geometryseries (A-I), this paper proposes a novel structural resolution to Schrödinger’s catparadox and the many-worlds interpretation. By internalizing the observer as aself-referential subsystem of noncommutative algebras, we prove that the core ofthe quantum measurement problem is not ”how the wave function collapses” or”how worlds branch”, but rather the self-referential rupture and repair of the observer algebra structure at the micro-macro interface. This paper unifies six existing theories—Dynamic Time Algebra, Post-Markovian Paradigm, Temporal LayerCausal Evolution, Chronogroup Framework, Time Fiber Category, and Origin ofOrder—and demonstrates that they are all effective descriptions of observer geometry under different projections. We derive three testable predictions: logarithmicoscillatory patterns in CMB non-Gaussianity, topologically chiral currents without external fields in mesoscopic systems, and magic number resonance structuresin high-energy colliders. This framework elevates the many-worlds interpretationfrom ”metaphysics of parallel universes” to ”geometric realization of self-referentialalgebras”, providing a mathematically self-consistent and experimentally testableunified solution to the foundational problems of quantum mechanics.
This paper proposes a unified description framework for the quantum universebased on logical depth and topological invariants. By introducing logical depth as afundamental parameter and combining it with the topological constraint of secondChern number conservation, we prove that the single-world and many-worlds descriptions correspond to effective theories of the system at different logical depths,respectively. This framework is independent of observer consciousness and is strictlyestabllllished on topological field theory, quantum information geometry, and theprinciple of gauge invariance. It also presents experimentally testable predictionsthat can be examined through observations of topological currents in mesoscopicsystems and analysis of non-Gaussianity in the cosmic microwave background radiation.
This paper constructs a logically self-consistent emergent structural frameworkfor the Many-Worlds Interpretation (MWI) based on decoherence theory, quantum information geometry, and self-referential dynamics. Within this framework,a ”world” is rigorously defined as a quasi-classical branch formed in Hilbert spacethrough environmental decoherence and information-geometric boundaries. Its independence is quantitatively characterized by the branch separation degree Dab defined by the quantum relative entropy between branches. When Dab exceeds a critical value Dc determined jointly by the energy scale of environmental fluctuationsand the decoherence time, the branches separate irreversibly in the informationgeometric sense, constituting independent ”worlds”. Furthermore, by introducingthe concept of a self-consistent observer, this paper demonstrates the dynamic selection mechanism of cosmological laws within the string theory landscape: only thosevacuum branches that can support self-consistent observers (satisfying conditionssuch as the memory decoherence time being much greater than the cognitive operation time) have their wavefunction weights effectively preserved during evolution,thereby acquiring physical reality. Finally, combining Zurek’s envariance argumentwith the requirement of observer memory stability, we show that the Born ruleP(i) = |⟨i|ψ⟩|2 is not an additional assumption but a necessary consequence forthe stable existence of self-consistent observers. This framework provides an operational mathematical foundation for the many-worlds interpretation, transforms theanthropic principle into a dynamic selection problem, and offers an explanation forthe origin of probability based on quantum information principles.
This paper systematically elaborates on the structural interpretations of sixemerging mathematical physics frameworks for Everett’s many-worlds interpretation, including the branching structure of dynamic time algebra, the logical parallelism of the post-Markovian paradigm, the historical bifurcation of temporal layercausal evolution, the representation splitting of the time group framework, the section bundling of chronological fiber categories, and the stability selection in theorigin of order theory. These theories, from different perspectives, demonstratethe global unitarity of quantum state evolution, reinterpreting ”world splitting”as representation branching, logical parallelism, or fiber bundling on mathematical structures, thereby providing a mathematical foundation for the many-worldsinterpretation independent of philosophical assumptions. By comparing the coremechanisms, mathematical structures, and physical predictions of each theory, thispaper proposes a unified view: the many-worlds is not ”splitting” but a naturalresult of structural degeneration, and all branches are mathematically equal andco-existent. At the same time, this paper discusses feasible paths for experimentalverification and introduces the category of potential worlds to unify the six theories,clarifying how the condition of observer self-consistency leads to the Born rule.
This paper proposes a novel structural solution to the quantum measurementproblem based on the Bispectral-Covariant Constraint Quantum Decision (BCTCQD) framework. By systematically analyzing the reconstruction mechanism ofthe Schrödinger’s cat paradox within the many-worlds interpretation, we establish a complete theoretical system incorporating bispectral invariants, constraintphase transitions, and the three-boundary inequality. The research proves that thequantum-classical transition is essentially a self-organizing process driven by constraints inherent in the system’s internal mathematical structure, rather than anexternal observational act. The framework successfully unifies six mathematicalphysical methods: Dynamic Time Algebra, Post-Markovian Paradigm, TemporalLayer Causal Evolution, Chronogroup Framework, Chronological Fiber CategoryTheory, and Origin of Order Theory. It derives several testable experimental predictions, including an entropy production pulse (on the order of 10−21 J/K), a topological chiral current (19nA), and the logarithmic scaling of CMB non-Gaussianity(fNL(ℓ) ∝ 1/logℓ). The discrete numerical model in the appendix further verifiesthe computability of self-referential closed loops and constraint saturation, layingthe foundation for experimental tests of the theory.
This paper proposes a theoretical framework for quantum measurement basedon four-dimensional Chern-Simons topological field theory. The framework reconstructs the coupling between the measured system and the measuring apparatus asa unified gauge system, whose dynamics is governed by a topological action withboundary terms: S[A] = k 4π ∫M Tr(F ∧F)+ k 4π ∫ ∂M CS(A). We prove that the topological phase of the system is rigidly labeled by the integer topological invariant—the second Chern number Ch2(P): when Ch2(P) = 0, the system admits a globallyunique classical narrative (single-world description); when Ch2(P)= 0, the bulktopological nontriviality inevitably induces topologically protected chiral modes onthe boundary, rendering any single classical description incapable of accommodating all physical information, making the many-worlds description a mathematicalnecessity. Furthermore, we reconstruct the measurement process itself as the dynamics of a topological phase transition driven by coupling strength: the boundaryconditions of the measuring apparatus force the system to be defined on a manifold with boundary; adiabatic variation of the coupling parameter drives the systemacross a critical point, where the second Chern number jumps from zero to nonzero,and the branch of the transition is locked to the different eigenstates of the detector,thereby generating a chiral current on the boundary whose direction is locked bysgn(Ch2(P)) without external fields. Based on the Josephson junction array model,the typical magnitude of the chiral current is estimated to be ∼ 10nA, which lieswithin the detection range of existing nano-SQUID devices. Renormalization groupanalysis shows that Ch2 = 0 is an infrared stable fixed point, and the classicality ofmacroscopic apparatus originates from this dynamical hardening mechanism. Thistheory transforms the quantum measurement problem from philosophical speculation into a computable and experimentally testable physical proposition.