MOND 是马赫式宇宙参考系拖曳效应吗？
Is MOND an effect of cosmic frame-dragging à la Mach?
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中文总结 AI 辅助
本文提出MOND的修正惯性起源，将$a_0$与宇宙视界退行加速度关联，通过因果体积假设推导插值函数，表明其源于膨胀宇宙的线性惯性参考系拖曳。
中文摘要 AI 辅助
修正牛顿动力学（MOND）的物理起源仍然未知，它通过单一经验加速度常数 $a_0$ 预测星系旋转曲线，而无需暗物质。我在一个与引力电磁学（广义相对论的线性化极限）密切相关的框架内，为 MOND 的插值函数和 $a_0$ 提出了一个修正惯性的起源。遵循夏玛（Sciama）统一引力与惯性的模型（该模型通过引力电感应实现马赫原理和加速度的相对性），我考虑一个经历恒定哈勃膨胀的理想化均匀宇宙。我确定 $a_0 \sim H_0^2R_u \sim c^2/R_u$ 与视界附近宇宙物质的相对退行加速度相对应，该加速度主导宇宙学贡献。我表明，只有当宇宙的相对加速度变得各向异性，且林德勒视界与宇宙哈勃视界相当或更大时（加速度量级为 $a_0$ 及以下），这一尺度才进入局部惯性动力学。通过观测者加速度依赖因果体积的最简单假设，考虑宇宙视界与林德勒视界之间的相互作用，我推导出 MOND 的简单插值函数作为修正惯性定律，无需人为插入或进行任何额外的特设调整。物理上，加速观测者前方因宇宙视界变形而进入因果联系的区域，其贡献的惯性阻力小于观测者后方因林德勒视界而失去的区域所损失的惯性阻力。这一概念验证表明，MOND 可能源于广义相对论中膨胀宇宙引起的大尺度线性惯性参考系拖曳效应。
英文摘要
The physical origin of Modified Newtonian Dynamics (MOND), which predicts galaxy rotation curves via a single empirical acceleration constant $a_0$ without the need for dark matter, remains unknown. I propose a modified-inertia origin for both MOND's interpolating function and $a_0$ within a framework closely related to Gravitoelectromagnetism, the linearized limit of General Relativity. Following Sciama's model unifying gravity and inertia, which implements Mach's principle and the relativity of acceleration through gravitoelectric induction, I consider an idealized homogeneous universe undergoing constant Hubble expansion. I identify $a_0 \sim H_0^2R_u \sim c^2/R_u$ with the relative recession acceleration of cosmic matter near the horizon, which dominates the cosmological contribution. I show that this scale enters local inertial dynamics only when the relative acceleration of the universe becomes anisotropic and the Rindler horizon is comparable to or larger than the cosmic Hubble horizon, at accelerations of order $a_0$ and below. By the simplest Ansatz for the observer's acceleration-dependent causal volume, accounting for the interplay between the cosmic and Rindler horizons, I derive MOND's simple interpolating function as a modified inertia law without the need to insert it by hand or make any further ad hoc adjustments. Physically, the region brought into causal connection ahead of the accelerating observer by the deformation of the cosmic horizon contributes less inertial drag than is lost from the region removed behind him by the Rindler horizon. This proof of concept motivates the possibility that MOND arises from large-scale linear inertial frame-dragging induced by the expanding universe within General Relativity.
发表机构
- Universität Leipzig（莱比锡大学）
机构由 AI 辅助整理，请以论文原文为准。
