The Bounded Quantum Reality: Integrating the Infinite Gap (ε∞) with Spacetime Constraints Against Ontological Branching

This work presents a revolutionary unified framework that fundamentally challenges the Many-Worlds Interpretation (MWI) of quantum mechanics through two complementary and mutually reinforcing approaches: the information-theoretic Infinite Gap (ε∞) analysis and the spacetime-constrained single-outcome framework. **Core Contributions:** 1. **The Infinite Gap (ε∞) Concept**: We introduce and formally define ε∞ as the fundamental discrepancy between ideal mathematical structures and physically realizable representations. Through rigorous mathematical analysis, we demonstrate that MWI's infinite branching violates: - The Bekenstein entropy bound: I ≤ 2πRE/ħc ln 2 - The holographic principle: S ≤ k_B A/4ℓ_P² - Landauer's thermodynamic principle: E ≥ k_B T ln 2 per bit - Quantum representation capacity limits 2. **Spacetime Continuity Constraints**: We establish that quantum realization is inherently restricted to single causal histories within a connected spacetime manifold. Environmental interactions—far from creating multiple branches—actively prevent multiple outcomes through decoherence, which we reinterpret as a prevention mechanism rather than a selection process. 3. **Three Unified Principles**: - **Information-Spacetime Unity**: Physical realization must satisfy both information-theoretic bounds and spacetime continuity constraints - **Interaction-Primacy**: Environmental interaction is fundamental while superposition represents temporary mathematical idealization - **Representational Economy**: Mathematical descriptions should minimize ontological commitments while maintaining empirical adequacy **Systematic Critique of MWI:**The research provides a comprehensive six-point critique demonstrating that MWI:1. Violates fundamental information capacity limits2. Suffers from probability incoherence (the Born rule problem)3. Lacks a non-arbitrary preferred basis4. Breaches spacetime continuity and causal structure5. Imposes exponential ontological cost without empirical justification6. Is empirically undecidable and therefore non-falsifiable **Alternative Framework:**We propose the Single-Outcome Information-Conscious Interpretation, which:- Respects all information-theoretic and spacetime constraints- Maintains empirical adequacy with quantum mechanics- Provides natural explanations for quantum coherence and decoherence- Offers testable predictions about physical limits **Testable Predictions:**The framework generates specific, falsifiable predictions including:- Decoherence timescale scaling: τ_D ∝ (Δx)^{-2}- Maximal maintainable superposition sizes (~10⁶ amu with current technology)- Information capacity limits for physical systems- Mutual consistency of all environmental records- Absence of branching signals or interference between macroscopically distinct states **Implications:**This work fundamentally reorients the quantum foundations debate by showing that physical realizability constraints—not just mathematical consistency—must guide interpretive choices. The Infinite Gap ε∞ marks where mathematical possibility meets physical impossibility, and spacetime continuity ensures this meeting occurs only once in our single, causally connected reality. **Keywords:** Infinite Gap, ε∞, Bekenstein Bound, Many-Worlds Interpretation, Quantum Foundations, Information Theory, Spacetime Constraints, Decoherence, Holographic Principle, Quantum Measurement, Ontological Economy