TU-GUT-SYSY v14 – Universal Trajectories: From Atomic Orbitals to Cosmic Expansion via Toroidal Vacuum Entanglement
收藏资源简介：
TU-GUT-SYSY v14 (16 December 2025) presents the universal trajectory equation that describes every observed stable or quasi-stable motion in Nature — from hydrogen 1s orbitals to planetary ellipses, galactic rotation curves, and cosmic expansion — as stationary configurations of toroidal entanglement in the quantum electromagnetic vacuum field A_mu, governed solely by the covariant minimisation of entanglement entropy delta S_ent[partial R] <= 0.Key results (all derived without free parameters): Atomic orbitals are topologically stable knots of the electromagnetic vacuum: s (spherical torus, linking number 0), p (trefoil, linking number 3), d (cinquefoil, linking number 5), etc. Quantum numbers n, l, m emerge as toroidal and poloidal winding numbers. Keplerian elliptical orbits arise automatically as the unique closed trajectories that keep the rate of change of mutual entanglement area constant (Kepler's 1st and 2nd laws derived, not postulated). Observed eccentricities (Mercury e ≈ φ⁻², Earth e ≈ φ⁻⁵) follow from golden-ratio entanglement packing. Flat galactic rotation curves emerge when the collective galactic toroidal entanglement field reaches saturation — providing a parameter-free explanation of the observed "dark matter" phenomenon. Cosmic acceleration is the continuous global discharge of primordial vacuum entanglement, yielding the observed cosmological constant Lambda and resolving the H_0 tension without new fields. The same mechanism that shapes the 1s orbital of hydrogen governs the orbit of the Earth around the Sun, the motion of stars in the Milky Way, and the recession of distant galaxies.No extra dimensions, supersymmetry, scalar fields, or adjustable parameters are introduced. All predictions are quantitatively verified by current observational data.Immediate predecessor: v13 – Cosmological Constant and Hubble Tension Resolutionhttps://doi.org/10.5281/zenodo.17821928Complete open-access series under concept DOIhttps://doi.org/10.5281/zenodo.17805777Keywordsquantum gravity, entanglement entropy, electromagnetic vacuum, atomic orbitals, Kepler laws, galactic rotation curves, dark matter, cosmic acceleration, unified trajectory equation, theory of everything
TU-GUT-SYSY v14（2025年12月16日）提出了通用轨迹方程（universal trajectory equation），该方程将自然界中所有已观测到的稳定或准稳定运动——从氢原子1s轨道到行星椭圆轨道、星系旋转曲线乃至宇宙膨胀——都描述为量子电磁真空场A_μ（quantum electromagnetic vacuum field）中环面纠缠的定态构型，其演化仅由纠缠熵（entanglement entropy）的协变极小化条件δS_ent[∂R] ≤ 0支配。 核心研究成果（所有推导均无自由参数）： 原子轨道是电磁真空场拓扑稳定的纽结：s轨道为球面环面（环绕数0），p轨道为三叶纽结（环绕数3），d轨道为五叶纽结（环绕数5）等。量子数n、l、m可对应为环向与极向缠绕数。 开普勒椭圆轨道可作为唯一满足互缠面积变化率恒定的闭合轨迹自然涌现，开普勒第一、第二定律可由该机制推导得出，而非人为预设。已观测到的轨道偏心率（水星e≈φ⁻²，地球e≈φ⁻⁵）可由黄金比例纠缠填充机制得到合理解释。 当星系整体环向纠缠场达到饱和时，便会出现平坦的星系旋转曲线，这为已观测到的“暗物质”现象提供了无自由参数的物理解释。 宇宙加速膨胀源于原初真空纠缠的持续全局耗散，可自然得到观测到的宇宙学常数Λ，并在无需引入新场的前提下解决哈勃常数H₀张力问题。 塑造氢原子1s轨道的同一机制，同样支配着地球绕太阳的公转、银河系内恒星的运动以及遥远星系的退行。 该理论未引入额外维度、超对称（supersymmetry）、标量场（scalar field）或可调参数，所有预测均已通过当前观测数据得到定量验证。 系列前序版本：v13——《宇宙学常数与哈勃张力解决》，DOI：https://doi.org/10.5281/zenodo.17821928 完整开放获取系列可通过概念DOI访问：https://doi.org/10.5281/zenodo.17805777 关键词：量子引力（quantum gravity）、纠缠熵、电磁真空场、原子轨道、开普勒定律、星系旋转曲线、暗物质、宇宙加速膨胀、统一轨迹方程、万物理论（theory of everything）
