Quantum Complexity, Undecidability & Quantum Gravity: Is Spacetime a Computation? (2025 Study) скачать в хорошем качестве

Quantum Complexity, Undecidability & Quantum Gravity: Is Spacetime a Computation? (2025 Study)

The quest for a unified theory of quantum gravity faces deep conceptual challenges, particularly where general relativity (GR) breaks down at singularities. This failure suggests that spacetime is not a fixed backdrop but emergent from deeper quantum degrees of freedom. This video explores how information-theoretic concepts like quantum complexity and entanglement are revolutionizing our understanding of gravity, extending the foundational AdS/CFT correspondence. Holographic Complexity and Spacetime Geometry Two leading proposals, the Complexity-Volume (CV) Duality and the Complexity-Action (CA) Duality, propose a quantitative link between computational complexity (the minimum number of quantum gates required to create a state) and geometric quantities in the bulk spacetime. The Complexity-Action duality, for instance, relates the complexity of a quantum state C(∣ψ⟩) to the gravitational action evaluated on the Wheeler-DeWitt (WDW) patch (IWDW). This framework suggests that the growth of quantum complexity is directly related to the growth of spatial volume or gravitational action, particularly within the interiors of black holes. Furthermore, the complexity-curvature correspondence suggests that scalar curvature (R) is related to the second time derivative of complexity (dt2d2 C). A unified approach, the Universal Holographic Principle, extends these ideas beyond AdS/CFT to arbitrary spacetimes. This principle requires extended Einstein field equations that incorporate corrections from entanglement entropy (S μν), quantum complexity (C μν), and quantum fluctuations (Q μν). This structure offers a potential resolution to the Black Hole Information Paradox by showing that quantum information is preserved in the complexity growth, even as the black hole evaporates. The Barrier of Undecidability (2025 Study) However, achieving a complete, wholly algorithmic "Theory of Everything" (ToE) is argued to be impossible due to intrinsic mathematical limits. Drawing on theorems by Gödel, Tarski, and Chaitin, recent research suggests that certain facts about reality—including specific black hole microstates—will remain computationally undecidable. The study published in August 2025 proposes that a fully foundational theory must be a Meta-Theory of Everything (MToE). The MToE must augment algorithmic deduction with non-algorithmic understanding (an external truth predicate) to certify truths that evade computable searches. This framework implies that since any putative simulation of the universe would itself be algorithmic, the universe cannot be a simulation.