AI 中文总结
该研究探讨大质量测试粒子空间叠加的悬浮协议，对比CSL与DP指数，证明二者比率与粒子质量和询问时间无关，明确了区分相关动力学的决定性实验要求。
AI 中文摘要
我们研究了可产生大质量测试粒子空间叠加态的理想化悬浮协议。对于每个协议，我们将与质量成正比的连续自发局域化（CSL）的无量纲对比度损失指数，与迪奥西-彭罗斯（DP）自能指数$E_G\tau/\bar{h}$进行比较。我们首先证明，点粒子CSL分离核具有精确的随机幺正实现：在泊松分布时间到达的高斯动量冲量会产生空间相干性的相同无条件衰减，尽管基于完整冲量记录的纯态仍保持纯态。因此，分离核本身仅规定了一种可操作的退相干定律，而非客观坍缩的发生。随后我们表明，CSL与DP指数的比率与粒子质量和询问时间无关。在点粒子模型中，该比率仅取决于分支分离和有效距离；对于标准GRW参考参数，其可分辨叠加的交叉点为$x_*\boldsymbol{\times}1.91\boldsymbol{\times}\text{nm}$。对于具有任意归一化径向质量分布、总质量、整体密度尺度的刚性球体，以及询问时间同样会被抵消，仅留下无量纲几何因子。这些结果明确了决定性实验的三项要求：可检测的绝对效应、CSL与DP尺度的受控比较，以及能够区分具有相同系综退相干核的物理不同动力学的可观测量。
英文摘要
We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent $E_Gτ/\hbar$. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is $x_*\approx1.91\,\mathrm{nm}$. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.
Comments4 figures
