Decoherence, Epistemic Coarse-Graining, and the Emergence of Classical Causal Structure

Boduen Wang

本文證明古典因果結構可在有限代理者的資源限制與環境交互作用下自洽湧現。不同於將退相干理解為客觀物理狀態的坍縮,本文將偏跡運算形式化為保持 Born rule 預測一致性的最小熵增CPTP 粗粒化映射 E = Trε,其熵增 ∆S 與跡距離界 D ≤ O(e−t/τD) 提供了知識論視界的量化邊界。Kochen-Specker 與 Bell 定理顯示,純量子層級缺乏全局 Kolmogorov 聯合機率與 Reichenbach 共同原因原則,使得 Pearl 的 do-演算在未退相干代數 ASE中缺乏定義基礎。透過結合量子達爾文主義冗餘度 Rδ1 與退相干歷史泛函 D(⃗α,⃗β) = O(ε),本文構造性證明了近似指針代數 Ap在 O(ε +δ) 誤差內可滿足近似 Markov 性與模組性,並建構出滿足 Pearl 截斷積公式的有效 do-操作。因果非對稱性因此可合理溯源於粗粒化映射 E 的不可逆資訊壓縮,而非微觀哈密頓量的時間箭頭。宏觀因果結構可被視為有限主體在資訊存取受限條件下,為維持 Dutch-book 預測自洽所採用的有效經驗拓樸。

Hongfang Li

Eduardo Lorca

Emergent Causality Through Decoherence

David Gutierrez Ule

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.

Peter James Dodd

Murray Gell‐Mann, James B. Hartle

The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. A formulation of quantum mechanics is used that predicts probabilities for the individual members of a set of alternative coarse-grained histories that decohere, which means that there is negligible quantum interference between the individual histories in the set. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e., such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of the noise consisting of the fluctuations that typical mechanisms of decoherence produce. We describe the derivation of phenomenological equations of motion explicitly for a particular class of models. Those models assume configuration space and a fundamental Lagrangian that is the difference between a kinetic energy quadratic in the velocities and a potential energy. The distinguished variables are taken to be a fixed subset of coordinates of configuration space. The initial density matrix of the closed system is assumed to factor into a product of a density matrix in the distinguished subset and another in the rest of the coordinates. With these restrictions, we improve the derivation from quantum mechanics of the phenomenological equations of motion governing a quasiclassical domain in the following respects: Probabilities of the correlations in time that define equations of motion are explicitly considered. Fully nonlinear cases are studied. Methods are exhibited for finding the form of the phenomenological equations of motion even when these are only distantly related to those of the fundamental action. The demonstration of the connection between quantum-mechanical causality and causality in classical phenomenological equations of motion is generalized. The connections among decoherence, noise, dissipation, and the amount of coarse graining necessary to achieve classical predictability are investigated quantitatively. Routes to removing the restrictions on the models in order to deal with more realistic coarse grainings are described.