Informational Causal Branching in Quantum Informational Geometrodynamics: Decoherent Histories, Branch-Relative Spacetimes, and the Status of an Emergent Multiverse
Quantum Informational Geometrodynamics (QI-G) treats spacetime, matter, and interactions as emergent structures of a discrete causal network carrying quantum information. This paper investigates whether a multiplicity of effectively autonomous realities can arise within QI-G without postulating a fundamental multiverse. We formulate a kinematic space permitting superpositions of causal-network configurations, introduce coarse-grained causal histories and their decoherence functional, and define an informational causal branch through three jointly necessary conditions: suppressed interference, stable causal records, and approximate dynamical autonomy. Each branch may admit its own coarse-grained Lorentzian geometry and intrinsic causal time, so that no external simultaneity relation between branches is required. An exact sector-decomposition result is established for block-diagonal dynamics. A redundant-record model further yields the suppression law η_N = ∏_{j=1}^{N}|r_j| and the threshold ∑_j[-ln|r_j|] ≥ ln(ε^{-1}) for effective branching at tolerance ε. We also propose, as a testable but presently unproved QI-G-specific ansatz, that the decoherence rate is controlled by an informational separation functional combining quantum Jensen–Shannon divergence, causal-structure mismatch, and emergent-curvature mismatch. The resulting framework supports emergent effective multiversality but does not establish a literal or empirically distinct multiverse. Such a conclusion would require a derivation of branch-selection scales, probabilities, and residual recoherence directly from the QI-G action.
Quantum Informational Geometrodynamics (QI-G) treats spacetime, matter, and interactions as emergent structures of a discrete causal network carrying quantum information. This paper investigates whether a multiplicity of effectively autonomous realities can arise within QI-G without postulating a fundamental multiverse. We formulate a kinematic space permitting superpositions of causal-network configurations, introduce coarse-grained causal histories and their decoherence functional, and define an informational causal branch through three jointly necessary conditions: suppressed interference, stable causal records, and approximate dynamical autonomy. Each branch may admit its own coarse-grained Lorentzian geometry and intrinsic causal time, so that no external simultaneity relation between branches is required. An exact sector-decomposition result is established for block-diagonal dynamics. A redundant-record model further yields the suppression law η_N = ∏_{j=1}^{N}|r_j| and the threshold ∑_j[-ln|r_j|] ≥ ln(ε^{-1}) for effective branching at tolerance ε. We also propose, as a testable but presently unproved QI-G-specific ansatz, that the decoherence rate is controlled by an informational separation functional combining quantum Jensen–Shannon divergence, causal-structure mismatch, and emergent-curvature mismatch. The resulting framework supports emergent effective multiversality but does not establish a literal or empirically distinct multiverse. Such a conclusion would require a derivation of branch-selection scales, probabilities, and residual recoherence directly from the QI-G action.
The series Time as Phase Flow (Papers I–IV) established that time is not fundamental but emerges from the geometric phase flow of quantum information, providing a unified account of dynamically generated cosmological constants, informational temporal viscosity, and the suppression of large-scale structure. Despite these successes, a fundamental mechanism explaining why a single, stable observable reality emerges from the space of quantum informational states has remained unresolved. In this work, we introduce the framework of Information-Geometric Spacetime (IGS), in which spacetime itself emerges from the geometry of quantum information, entanglement, and modular flow. Within IGS, we define an Actualization Operator that mediates between quantum informational states and observable spacetime geometry. Derived from first principles, the operator combines entropy-based suppression with modular evolution, governed by a universal geometric constant β = 1/(π√3) ≈ 0.1837 fixed by the geometry of causal diamonds and the associated modular Hamiltonian. We show that actualization preserves information conservation and quantum unitarity, acting as a structural filter that selectively stabilizes informational states capable of forming consistent geometric reality, in close analogy with decoherence-driven classical emergence. Under this mechanism, previously identified cosmological effects—most notably the suppression of the matter power spectrum and the S_8 tension—are reinterpreted as observational consequences of information actualization rather than modifications of gravity or exotic matter. This framework also offers a geometric reformulation of the quantum measurement problem, in which the observer is not an external agent but an emergent process associated with modular structure and entanglement thermodynamics. The theory yields testable predictions in controlled quantum systems and forthcoming cosmological surveys, providing a concrete pathway toward empirical tests of spacetime emergence from quantum information.
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
Description This work presents a process-based quantum framework in which causality, gravity, time, and three-dimensional space emerge from discrete quantum processes (P-tacts). A P-tact is defined as a minimal unit of quantum evolution combining a local superposition operation and an entangling unitary transformation. The global dynamics of a system is described as a graph of P-tacts, where causal order, branching, and relational structure arise intrinsically, without introducing an external time parameter. The framework demonstrates that causal branching appears first, followed by emergent quantum gravity as an effect of entanglement density and network connectivity. From this structure, relational time emerges as a discrete sequence of P-tacts, and only at later stages does three-dimensional space arise from the global topology of the process graph. Space, time, and gravity are thus shown to be mutually emergent properties of a single discrete quantum process network. This work directly builds upon the previously published concept of the quantum switch as an emergent process structure from discrete P-tacts (see Ref. [1]) and extends it toward a unified description of spacetime emergence. The formalism provides a concrete realization of Everettian branching, making the many-worlds interpretation operational and graph-theoretic. The proposed framework connects quantum information theory, indefinite causal order, quantum gravity, and emergent spacetime, offering both conceptual clarity and experimental relevance. It is applicable to quantum switches, multi-qubit entanglement, quantum networks, and quantum simulations, and provides a testable route toward understanding spacetime as a derived structure rather than a fundamental background. Reference to previous foundational work: DOI 10.5281/zenodo.18498181.
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.
We develop an extended formulation of Universal Modular Dynamics (UMD) in which physical law is organized as a hierarchy of nested, renormalization-stable informational phases emerging from a pre-quantum domain of distinguishability. The construction does not assume spacetime, locality, quantum fields, or graph structure as fundamental. Instead, the primitive level is defined through relations of distinguishability between pre-physical configurations, whose dynamically persistent sectors provide the substrate from which effective operator states and subsequent physical structures emerge. Within this architecture, previously derived pre-string configurations are interpreted as a particular low-dimensional stable sector of the broader UMD pre-quantum state space, rather than as the universal starting point of the theory. Their collective scaling behavior admits an effective graph limit, providing a controlled route from pre-string organization to relational connectivity and, subsequently, to operational subsystem structure. This graph limit is therefore emergent and sector-dependent, rather than ontologically primitive. At the operator level, the density matrix ρ becomes the carrier of distinguishability and generates modular structure through K = −log ρ, Kρ|σ = −log ρ + log σ. Relative modular dynamics, together with completely positive open-system flows, defines a sequence of scale-dependent transformations through which stable subsystem decompositions, operational locality, and finite-speed information propagation emerge. The resulting causal structure is established before continuum spacetime geometry and is governed by Lieb– Robinson-type bounds on the transport of quantum correlations. A central aim of the present work is to sharpen the transition from discrete relational organization to continuum spacetime. We explicitly distinguish the geometry of quantum state space from physical spacetime geometry and formulate the intermediate coarse-graining and scaling conditions required to connect Bogoliubov–Kubo–Mori information geometry, correlation-based relational distances, and an effective continuum metric. Einstein-type dynamics is then interpreted as an entropic consistency condition of the emergent geometric phase, arising from local information balance and variational stability rather than from a fundamental spacetime background. The same hierarchical framework is extended to access-relative vacuum structure and hidden-sector dynamics. Dark-energy-like behavior is associated with stable entropic vacuum drift relative to an observer-accessible algebra, while dark-matter-like effects arise from correlations and backreaction between visible and inaccessible sectors. These mechanisms are embedded within the same renormalization hierarchy rather than introduced as independent cosmological components. We further characterize regimes in which metricity, causal ordering, and stable factorization fail, defining non-geometric phases relevant to the breakdown of the spacetime description in extreme gravitational and early-universe regimes. Throughout the construction, we distinguish theorem-level results, conditional emergence statements, numerical evidence, and phenomenological predictions, and we identify explicit falsifiability conditions for the principal UMD claims. The resulting picture is that physical law is not represented by a single primitive dynamical equation imposed on a pre-existing arena, but by a recursively organized hierarchy of informational structures whose stable renormalization sectors generate quantum states, locality, causality, geometry, gravitation, and effective dark-sector phenomena.
We introduce a framework in which spacetime locality and geometric causal structure are not assumed as fundamental, but instead emerge conditionally from quantum dynamics under restricted observational access. We define depth as a restriction on the set of observables accessible to an observer and show that, un- der appropriate conditions of redundancy and decoherence, effective locality and finite propagation speed arise from intrinsically nonlocal quantum systems. Con- versely, locality degrades when these conditions fail. Using simple toy models, we demonstrate threshold behavior separating regimes with and without stable causal structure. This approach reframes spacetime geometry as an emergent description rather than a primitive input, while remaining compatible with standard quantum mechanics and general relativity within their respective domains of validity.