AI 中文总结
本研究在惠勒-德维特散射语境下，基于协变标量时钟可观测量定义关系性维格纳-史密斯时长，推导其解析表达式与量子修正，扩展至多通道量子探测器，证明其可观测量可由定态约束态的散射关联记录定义，无需引入背景时钟。
AI 中文摘要
我们将闭合的弗里德曼-勒梅特-罗伯逊-沃尔克惠勒-德维特模型构建为一个精确的反射问题。其反射相位的导数定义了一个关系性穿越时长，该时长的前两个时钟矩源自协变标量时钟可观测量。我们获得了该时长的解析表达式、其经典再坍缩极限以及主导量子修正。有限谱包络也给出了一种可操作的、等先验的最小错误概率，用于通过几何读数区分再坍缩的两种取向。该构造被扩展到有界有限量子探测器，其多通道反射矩阵产生探针跃迁、谱-探针关联以及矩阵时长。直接的弱耦合计算验证了预测的跃迁和时长标度。标量时钟条件化和定向几何截面被证明是同一正频率狄拉克区的局域表示。这些结果完全通过定态约束态的关联和散射记录定义了时长与跃迁可观测量，未引入背景时钟。
英文摘要
A closed Friedmann-Lemaitre-Robertson-Walker Wheeler-DeWitt model is formulated as an exact reflection problem. The derivative of its reflection phase defines a relational crossing duration whose first two clock moments follow from a covariant scalar-clock observable. An analytic expression is obtained for this duration, its classical recollapse limit, and the leading quantum correction. A finite spectral packet also gives an operational, equal-prior minimum error probability for distinguishing the two orientations of recollapse with a geometric reading. The construction is extended to a bounded finite quantum detector. Its multichannel reflection matrix yields probe transitions, spectral-probe correlations, and a matrix duration. A direct weak-coupling calculation verifies the predicted transition and duration scalings. Scalar-clock conditioning and oriented geometric sections are shown to be local representations of the same positive-frequency Dirac sector. These results define duration and transition observables entirely through correlations and scattering records of a stationary constrained state, without introducing a background clock.
Comments9 pages, 5 figures
