迈向量子粒子的熵几何动力学：作为普朗克子的 Casimir 虫洞口
Towards an Entropic Geometrodynamics of Quantum Particles: Mouths of Casimir Wormholes as Planckeons
AI总结：
本文用共形引力、二阶 Ricci 流与 Casimir 负能量构建稳定普朗克虫洞网络，解释量子动力学及双缝干涉的熵、混沌与组合优化起源。
摘要：
本文提出一种共形引力方法，用以描述普朗克尺度下量子化时空如何从一个由可穿越虫洞口（作为 planckeons，普朗克子）构成的类晶格网络中涌现。这不同于 Licata 等人早期的工作；后者以 ER=EPR 猜想成立为出发点，并使用了来自 Ryu–Takayanagi 公式的纠缠熵。本文首先建立一个共形引力模型，假定其适用于普朗克尺度，并通过 Ricci 流的二阶形式（即度规张量的波动方程）来描述时空涨落。随后，我们考察其黑洞解，以说明普朗克虫洞可能形成。通过考虑 Casimir 效应产生的熵力作为负能量来源，我们提出普朗克虫洞将是稳定的，并可能允许场经由一系列 Casimir 虫洞传输；这些虫洞口在给定时间段内保持开放，而该时间段由修正的不确定性原理决定。基于普朗克尺度上的这一现象，我们表明它可以成为“量子动力学”涌现的基础，从而使 ER=EPR 猜想得以实现。最后，我们发展了一种新的量子诠释，聚焦于量子动力学的本质，尤其是其在宏观双缝实验中产生著名干涉图样的效应。我们表明，干涉图样的起源在本质上具有熵性和混沌性：量子粒子通过一系列虫洞的动力学不仅在本质上被视为概率性的，而且还需要组合优化。
英文摘要：
A conformal gravity approach is presented here to describe the emergence of a quantized spacetime at the Planck scale from a lattice-like network of mouths of traversable wormholes as planckeons. This differs from the earlier work of Licata et.al., which started with the assumption that ER=EPR conjecture is valid and used an entanglement entropy from the Ryu-Takayanagi formula. Here, we developed first a conformal gravity model that is postulated to apply at the Planck scale to describe the spacetime fluctuation via a second-order form of the Ricci Flow, i.e., a wave equation of the metric tensor. We then consider its black hole solution to suggest the possible formation of Planckian wormholes. By considering the role of the entropic force due to Casimir effect as the source of negative energy, we suggest that Planckian wormholes will be stable and may allow for the transfer of field through a series of Casimir wormholes with mouths that are open at a given period of time as dictated by a modified Uncertainty Principle. From this phenomena at Planck scale, we showed that it can be the basis from which "quantum dynamics" emerges and therefore ER=EPR conjencture can be realized. Lastly, we develop a new quantum interpretation that focuses on the nature of quantum dynamics, particularly with the effect of generating the famous interference pattern in a macroscopic double-slit experiment. We showed that the interference pattern's origin is entropic and chaotic in nature, where the dynamics of a quantum particle through a series of wormholes is not just considered to be probabilistic in nature but also requires a combinatorial optimization.
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