发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在广义迹动力学框架下，探究Connes时间中记录选择的坍缩定律是否满足因果性，推导了无信号条件下的增益关系，分析了GTD中系数噪声的特性。
AI 中文摘要
动力学波函数坍缩不得违反因果性：“现在”被选中的记录不具有与参考系无关的意义，非线性定律可能让遥远观察者实现信号传递。我们探究，当具有因果结构的经典时空本身从局域化中涌现时，这种冲突是否能被避免——正如广义迹动力学（GTD）所提出的，其中选择记录的涨落来自未解决的前几何自由度，这些自由度由Connes时间而非时空坐标排序。此时超曲面问题不再被表述为选择发生的位置，而是转化为一个要求：涌现的记录不得传递信号。我们将标准无信号定理应用于CSL型的有效坍缩定律。朴素粗粒化的保范、无响应定律永远不会选择记录。在历史形式中，仅当涨落历史以两倍于自身扩散的增益偏向主导记录，且对于具有三个或更多共线本征值的算符，线性定律带有其抵消项（由光滑系数驱动产生错误符号）时，记录权重才是鞅；任何其他增益都会产生信号。对于平衡态海，涨落-耗散关系确定增益，因此玻恩增益是耦合、温度与关联时间之间的爱因斯坦关系。读取条件态纠缠的速率会产生信号；增强必须位于固定集体算符中。正态会湮灭携带坍缩系数的格拉斯曼双线性项，因此物理块是具有正动能形式的重构。我们针对GTD的关系主矩阵的Sutherland纹理评估系数噪声：与局域应变耦合的块会获得欧姆谱密度，带有计算出的摩擦、连续谱判据和回归，而动力学交叉耦合则不会产生此类效应。剩余部分是提供抵消项和增益的投影。
英文摘要
Dynamical wave-function collapse must not violate causality: a record selected "now" has no frame-independent meaning, and a nonlinear law can let distant observers signal. We ask whether this conflict is avoided when classical spacetime, with its causal structure, itself arises from localisation, as proposed in generalized trace dynamics (GTD), where the fluctuations that select a record come from unresolved pregeometric degrees of freedom ordered by Connes time, not by a spacetime coordinate. The hypersurface question is then not posed where selection happens; it returns as the requirement that emergent records do not signal. We apply the standard no-signalling theorem to an effective collapse law of CSL type. The norm-preserving, response-free law of a naive coarse-graining never selects. In history form, record weights are martingales only if the fluctuation history leans towards the leading record with gain twice its own diffusion and, for operators with three or more collinear eigenvalues, the linear law carries its counter-term, which a smooth coefficient drive gives with the wrong sign; any other gain signals. For an equilibrium sea the fluctuation-dissipation relation fixes the gain, so the Born gain is an Einstein relation between coupling, temperature and correlation time. A rate that reads the entanglement of the conditioned state signals; enhancement must sit in fixed collective operators. Positive states annihilate the Grassmann bilinear carrying the collapse coefficient, so the physical block is a reconstruction with positive kinetic form. The coefficient noise is evaluated for the Sutherland texture of GTD's relational master matrix: a block coupled to its local strain acquires an Ohmic spectral density with computed friction, continuum criterion and recurrence, while a kinetic cross-coupling yields none. What remains is the projection supplying counter-term and gain.
Comments38 pages
