I present a mathematically consistent topological framework for modelling causal branching, information preservation, and cross-dimensional state transitions under the Many-Worlds Interpretation (MWI) of quantum mechanics. The paper's central contribution is not an argument for the physical engineering of faster-than-light (FTL) travel. Rather, we exploit the fact that the Lorentz factor yields an imaginary proper time when treated as a boundary condition at v\rightarrow c^{+}, and propose that this imaginary quantity is a geometric indicator of a perpendicular fifth-dimensional manifold-the Imaginary Time Axis - that parameterises the multiverse's parallel branch topology. The core contribution is a formally defined, operator-algebraic Cross-Branch Traversal Operator \hat{T}, built on the Hilbert space tensor structure of the MWI universal wavefunction. We show that \hat{T} as a unitary map between orthogonal Hilbert subspaces corresponding to distinct timeline branches, and that it necessarily preserves both information (via unitarity) and energy (via a branch-vacuum compensating transfer mechanism). We further provide a quantitative definition for the inter-branch angular frequency was the square root of the quantum Fisher information between two branch states, giving a rigorous, first-principles handle on the "distance" between parallel timelines in terms of accumulated decoherence. This framework has direct structural analogues in quantum information theory, topological quantum computation, and the architecture of consistent-state simulated universes, making it relevant to physicists, quantum information theorists, and computational scientists alike.
I present a mathematically consistent topological framework for modelling causal branching, information preservation, and cross-dimensional state transitions under the Many-Worlds Interpretation (MWI) of quantum mechanics. The paper's central contribution is not an argument for the physical engineering of faster-than-light (FTL) travel. Rather, we exploit the fact that the Lorentz factor yields an imaginary proper time when treated as a boundary condition at v\rightarrow c^{+}, and propose that this imaginary quantity is a geometric indicator of a perpendicular fifth-dimensional manifold-the Imaginary Time Axis - that parameterises the multiverse's parallel branch topology. The core contribution is a formally defined, operator-algebraic Cross-Branch Traversal Operator \hat{T}, built on the Hilbert space tensor structure of the MWI universal wavefunction. We show that \hat{T} as a unitary map between orthogonal Hilbert subspaces corresponding to distinct timeline branches, and that it necessarily preserves both information (via unitarity) and energy (via a branch-vacuum compensating transfer mechanism). We further provide a quantitative definition for the inter-branch angular frequency was the square root of the quantum Fisher information between two branch states, giving a rigorous, first-principles handle on the "distance" between parallel timelines in terms of accumulated decoherence. This framework has direct structural analogues in quantum information theory, topological quantum computation, and the architecture of consistent-state simulated universes, making it relevant to physicists, quantum information theorists, and computational scientists alike.
Quantum mechanics does not require parallel universes — only phase-relative structure within a shared spacetime manifold. This preprint presents an interpretive framework for quantum multiplicity that avoids spatial “parallel universe” metaphors. Building on standard quantum field theory, Everettian quantum mechanics, and decoherence theory, it argues that apparent multiplicity can be understood as phase-relative branch structure within a single shared spacetime manifold, rather than as spatially separate worlds. The work introduces no new dynamics, equations, or empirical predictions. Its contribution is conceptual: clarifying how mutually exclusive classical outcomes arise through branch-relative accessibility and loss of correlation, while preserving all governing invariants, including conservation laws and universal gravitational coupling in the semiclassical regime. A companion supplementary document presents the standard mathematical formalism—Hilbert space structure, density matrices, decoherence, and expectation-value stress–energy—to demonstrate that the interpretation remains fully consistent with established physics. In approaches to quantum gravity where spacetime is emergent—such as loop quantum gravity or holographic dualities—the framework would naturally reformulate in relational or entanglement-theoretic terms. In that context, branch-relative multiplicity corresponds not to multiple times or geometries, but to multiple decohered relational histories or bulk reconstructions supported by a single underlying quantum state. This paper is intended as a foundations-level reinterpretation for physicists and philosophers of physics interested in quantum ontology, decoherence, and the conceptual structure of spacetime.
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.
The Many-Worlds Interpretation (MWI) of quantum mechanics preserves unitary evolution by rejecting wavefunction collapse and treating all outcome branches as equally real. While mathematically consistent, this move elevates admissible descriptions of a system to ontological status without an accompanying principle of physical selection. In this paper, we argue that quantum branching need not imply ontological multiplicity once structural admissibility, temporal constraint, and recoverability are made explicit. Unitary evolution defines the space of allowable continuations, but only a subset of these persist forward in time due to structural resolution. Within this framework, the appearance of branching reflects under-resolved admissible paths rather than the realization of multiple worlds. Many-Worlds is thus reinterpreted as a transitional bookkeeping scaffold rather than a necessary ontological commitment.
The nature of consciousness and its survival after biological death remain fundamental to theoretical physics, information theory, and philosophy of mind. This paper offers a rigorous mathematical formalization considering the "soul" as an irreducible, non-local informational manifold nested inside a higher-dimensional Hilbert space rather than as a metaphysical entity. Utilizing principles from quantum mechanics, unitary state evolution, algebraic topology, and open-quantum system dynamics, we construct a formal proof demonstrating that the informational entropy and topological invariants characterizing conscious states are conserved under biological phase transitions (death). Furthermore, by mapping conscious architecture onto holographic boundary principles, we show that information annihilation is forbidden within a closed unitary system. We finish with key quantum-informational metaphysics research issues and directions.
Description: This research provides a rigorous physical deconstruction of the Many-Worlds Interpretation (MWI) of quantum mechanics by shifting the focus from mathematical formalism to the fundamental constraints of physical reality. While MWI is often celebrated for its avoidance of the collapse postulate, this paper demonstrates that its core mechanism—exponential ontological branching—imposes requirements that violate established physical laws. Key Arguments Presented: * The Energetic Barrier (Landauer’s Principle): The work proves that if branching is a physical process, the creation of each distinct branch entails a thermodynamic cost (ΔQ≥kBTln2). The exponential proliferation of worlds would require energy exceeding the total mass-energy of the observable universe. The Information Ceiling (Bekenstein Bound): By applying the Bekenstein-Hawking entropy limits, the paper demonstrates that a finite universe cannot accommodate the infinite information storage required for distinct branch records. The Infinite Gap Theorem ($\infgap$): A formal proof showing the fundamental discrepancy between the infinite precision of mathematical Hilbert spaces and the finite representational capacity of physical systems. The Paradox of Macroscopic Superposition Cost: An empirical analysis showing that the extreme energy and operational difficulty required to maintain quantum coherence in laboratories contradicts the "cost-free" world-splitting assumed by MWI. Conclusion: The study concludes that MWI is a mathematical ghost-theory; the "Many Worlds" it predicts are informationally and energetically unrealizable within a finite physical manifold. Keywords: Quantum Foundations, Many-Worlds Interpretation, Information Theory, Landauer's Principle, Bekenstein Bound, Decoherence, Quantum Thermodynamics.
Title: Relativistic Branching Dynamics: A Geometric Resolution to the Measurement Problem and the Thermodynamic Arrow of Time Abstract: The reconciliation of the apparent flow of time and human agency with the rigid structure of the Einsteinian Block Universe remains one of the most intractable problems in the foundations of physics. The standard interpretation of Special Relativity, formalized by the Rietdijk-Putnam argument, implies a static four-dimensional manifold where future events are as ontologically fixed as the past. This paper introduces the Relativistic Many-Worlds (RMW) hypothesis, arguing that the Lorentz transformation implies an ontological divergence of realities rather than a mere coordinate transformation. By defining a metric for the "Degree of Separation" (Δs) between inertial frames, we propose that the "collapse" of the wave function is a relativistic frame-selection event driven by acceleration. We analytically derive the behavior of this separation metric in Newtonian, Relativistic, and Rindler (accelerated) limits, demonstrating how agency acts as a vector selection mechanism within a branching 4D manifold. Furthermore, we demonstrate that the thermodynamic Arrow of Time is an emergent property of this geometric divergence, resolving the paradox of irreversibility without invoking ad-hoc initial conditions. We conclude by offering falsifiable experimental predictions involving accelerated decoherence in matter-wave interferometry. Key Contributions: Geometric Resolution to the Block Universe: Proposes that the "Paradox of Reciprocal Reality" in Special Relativity necessitates a branching multiverse structure rather than a static single block. The Divergence Metric (Δs): Derives a mathematical framework quantifying the spacetime separation between counterfactual worldlines based on proper time and velocity difference. Agency as Kinematics: Redefines "Free Will" physically as the capacity to initiate acceleration (Frame Selection), thereby rotating the plane of simultaneity and selecting a specific geodesic through the Hilbert space. The Rindler Horizon of Choice: Demonstrates how acceleration creates a causal event horizon that geometrically censors unchosen histories from the observer. Falsifiable Predictions: Proposes specific experimental tests using matter-wave interferometry to detect "Accelerated Decoherence," distinguishing this theory from standard environmental decoherence models. Keywords: Special Relativity, Quantum Mechanics, Measurement Problem, Many-Worlds Interpretation, Block Universe, Arrow of Time, Lorentz Transformation, Rindler Horizon, Decoherence, Foundations of Physics. Subjects: Theoretical Physics, Quantum Foundations, Philosophy of Physics. Author: Paul Hallelujah, BSCH, MTS University of Toronto & Queen's University Alumnus