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第一性原理:波函数的起源和实在性

Shanlin Zhu, K Chen

Published Jun 26, 2026• 0 citations
Publisher

Abstract

量子力学创立百余年,波函数的物理实在性始终是基础物理的核心争议。哥本哈根诠释将波函数视为抽象概率计算工具,无法从第一性原理给出其物理起源,由此衍生出测量坍缩、量子非局域性等一系列理论疑难;现有场论框架下的自发对称破缺理论,也未建立破缺场与量子波函数的内在关联。本文以含戈德斯通模的朱山林方程为唯一第一性公理,严格划定基础公理与推论的层级边界,通过复场极分解、协变导数展开与方程拆分,完成本源场自发对称破缺的动力学推导,最终从基础方程直接导出量子波函数的显式场论形式。研究表明:波函数是全域本源场经自发对称破缺后形成的局域稳定凝聚态,其振幅对应局域破缺度场,相位对应戈德斯通模与引力几何效应的真实激发;薛定谔方程是朱山林方程在弱场、非相对论极限下的自然推论。本文从统一场公理出发完成了波函数的第一性原理溯源,为量子力学的实在性诠释提供了严格的场论支撑。

DOI
10.5281/zenodo.20912608

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Science in China Series A-Mathematics (in Chinese)•Apr 1, 2002•0 citations
量子力学创立百余年,波函数的物理实在性始终是基础物理的核心争议。哥本哈根诠释将波函数视为抽象概率计算工具,无法从第一性原理给出其物理起源,由此衍生出测量坍缩、量子非局域性等一系列理论疑难;现有场论框架下的自发对称破缺理论,也未建立破缺场与量子波函数的内在关联。本文以含戈德斯通模的朱山林方程为唯一第一性公理,严格划定基础公理与推论的层级边界,通过复场极分解、协变导数展开与方程拆分,完成本源场自发对称破缺的动力学推导,最终从基础方程直接导出量子波函数的显式场论形式。研究表明:波函数是全域本源场经自发对称破缺后形成的局域稳定凝聚态,其振幅对应局域破缺度场,相位对应戈德斯通模与引力几何效应的真实激发;薛定谔方程是朱山林方程在弱场、非相对论极限下的自然推论。本文从统一场公理出发完成了波函数的第一性原理溯源,为量子力学的实在性诠释提供了严格的场论支撑。
基于量子统计方法,通过考虑单粒子能谱的相对论修正且引入无自旋自由费米子的非相对论自由能,导出弱磁场中弱相互作用费米气体的自由能,给出各种温度条件下系统热力学量的解析式,详细具体地展示相对论修正对热力学性质的影响,并分析其影响机理.研究表明,与非相对论比较,相对论修正总是降低化学势,在低温下也降低总能及热容量,而在高温下增加总能及热容量;除低温下的热容量外,总能及热容量的改变比例于磁场的平方.
基于里德堡原子的微波测量方法具有突破传统电子学测量系统热噪声极限的潜力,已成为最具潜力的微波量子测量技术之一。然而,原子系统中存在的各种噪声限制了测量灵敏度的提升。本文主要对基于里德堡原子超外差测量系统中存在的原子渡越噪声进行了研究。首先介绍了基于里德堡原子超外差技术的微波测量原理;然后,详细研究了原子热运动产生的渡越噪声对基于原子微波测量的影响。研究表明,渡越噪声的频率影响范围与激发光腰斑的大小成反比,且噪声强度随探测光强度的增加具有先增大后趋于饱和的现象。最后,我们展示了原子渡越噪声对测量灵敏度的影响。此工作对提升里德堡原子微波测量系统的灵敏度具有重要意义。
核方法在机器学习中有广泛的应用。量子计算与核方法结合,可以有效解决经典核方法中当特征空间变大时计算成本随之增加的问题。研究表明,基于核方法构建的最小化量子电路可以可靠地在含噪声的中型量子设备上执行。目前已提出的一些基于量子核方法的分类器在充分映射数据以及电路架构等方面仍存在一定的缺陷。因此,提出了一种基于多项式核函数的紧凑型量子分类器。首先通过引入多项式核函数,提升了非线性数据的分类迭代速率,从而提升了分类效率;在此基础上进一步提出紧凑型振幅编码,将量子态相对应相位的数据标签编码。相比于已有的量子核方法分类器,所提模型的量子电路的编码位数可以从5个量子比特减少到3个量子比特,而且,所提模型将已有方法中的双量子位测量简化为单量子位测量。此外,该模型在测量阶段的量子电路参数达到了最优方差,可以有效节省计算资源开销。实验仿真表明,所提分类器模型中的期望值更接近理论值,且获得了更高的分类精度,同时该模型具有较低的纠缠度,有效降低了整个准备工作的开销。
中文摘要传统量子力学与经典电磁学长期依赖点粒子模型解释电子行为,由此产生原子稳定性悖论、电磁辐射判定局限、物质波物理本源模糊、电子云概率诠释反直觉等一系列理论矛盾。本文提出电子带电涡旋流体拓扑模型,摒弃点状粒子假设,将电子定义为具有甜甜圈闭环拓扑、双旋耦合结构的可形变连续带电流体。本模型完成三项核心自洽修正:第一,明确麦克斯韦电磁辐射公式仅适用于时变加速点电荷,面包圈形态的闭环涡旋电子环整体绕核公转时满足经典向心力与库仑引力平衡,电荷全域均匀分布无时间起伏,不会向外辐射电磁波,从底层解决轨道原子坍缩难题,并依靠环路驻波闭合几何条件形成分立量子化轨道与能级;第二,以丝状自转 + 环状公转双旋手性拓扑结构匹配狄拉克四分量旋量与矩阵体系,依靠镜像手性构型区分电子与正电子,利用经典旋转动力学解释正反粒子等质量特性与湮灭机理;第三,重新定义薛定谔方程物理内涵,证明原子轨道轮廓并非粒子随机出现的概率云,而是带电涡旋流体在外场作用下的真实弹性形变,替换哥本哈根概率解读。本研究依靠单一拓扑结构搭建理论框架,无额外补丁与特设假说,以经典物理体系统一兼容电磁规律、相对论效应、波动特征与轨道形态,完成电子底层结构逻辑自洽重构。AbstractTraditional quantum mechanics and classical electromagnetism rely fundamentally on the point-particle assumption for describing electrons, which inevitably leads to theoretical paradoxes, including the atomic stability crisis, misapplication of electromagnetic radiation rules, ambiguous physical origin of matter waves, and the counter-intuitive probabilistic interpretation of electron clouds. This paper proposes a topological vortex fluid model of the electron, abandoning the point-charge hypothesis and describing the electron as a continuously distributed, deformable, closed toroidal electromagnetic fluid with dual rotational degrees of freedom. Three core physical conclusions are established. First, Maxwell’s radiation criterion only applies to time-varying accelerating point charges. The toroidal vortex electron ring revolves around the atomic nucleus while keeping balance between classical centripetal force and Coulomb attraction. Uniform charge distribution avoids time-domain fluctuation and electromagnetic radiation, solving the atomic collapse problem fundamentally. The closed standing wave geometric constraint of the loop forms discrete quantized orbits and energy levels. Second, the dual rotation structure consisting of filamentary spin and toroidal revolution exactly corresponds to the four-component Dirac spinor and matrix formalism. Chiral mirror symmetry defines electron and positron states, explaining matter–antimatter duality, identical mass, and annihilation dynamics purely through classical topological rotation mechanics. Third, all orbital shapes solved by the Schrödinger equation represent real, deformed morphological states of the charged fluid under external potential constraints, rather than probabilistic particle distributions. This model completely replaces the Copenhagen probabilistic interpretation with deterministic structural deformation physics. The proposed framework reconstructs the fundamental electronic structure with full logical self-consistency, unifying classical electromagnetism, relativistic quantum structure, wave behavior and atomic orbital morphology without artificial theoretical patches.
标准物理体系中,微观量子效应的本体论困惑与宏观不可逆的表观矛盾长期并存,其共同认知根源在于 “粒子为承载属性的本原实体” 这一默认预设。本文在朱山林等提出的独立自由度框架基础上进行理论延伸,将位置、自旋、动量、内禀状态等定义为相互独立的宇宙底层本体,而非依附于客体的属性,进而对叠加态、不确定性原理、量子纠缠、无规则热运动四类典型物理现象进行统一的本体论重构与逻辑推导。研究表明:在独立自由度框架内,独立自由度是四类现象的共同本体论根源 —— 叠加态源于单个自由度自身的取值弥散性,不确定性源于共轭自由度的本体论独立与测量显现,量子纠缠源于内态自由度的非定域整体性与位置自由度的空间可分性,无规则运动源于自由度演化次序的天然不同步与耦合 - 脱耦的随机性。在此基础上进一步阐明:宏观稳定组态的 “不可拆分性” 与 “属性捆绑” 本质是海量自由度形成强耦合约束网络后的集体表观效应,底层自由度的独立性并未消失,仅被耦合作用压制与粗粒化观测掩盖。该框架实现了微观量子行为与宏观经典物性的本体论连续,为消解 EPR 悖论、统一微观可逆与宏观表观不可逆提供了新的理论路径。 Within the standard physical framework, ontological puzzles concerning microscopic quantum effects and the apparent contradiction of macroscopic irreversibility have long co‑existed. Their shared cognitive origin lies in the default presupposition that “particles are primitive entities bearing physical properties”. Extending the theory built upon the Framework of Independent Degrees of Freedom proposed by Zhu Shanlin et al., this paper defines position, spin, momentum, intrinsic states and other quantities as mutually independent underlying cosmic ontological entities, rather than properties attached to objects. Unified ontological reconstruction and logical derivation are then carried out for four typical physical phenomena: superposition, the uncertainty principle, quantum entanglement, and random thermal motion. This study demonstrates that, within the Framework of Independent Degrees of Freedom, independent degrees of freedom constitute the common ontological source of the four phenomena. Superposition originates from the value dispersion intrinsic to a single degree of freedom; uncertainty arises from the ontological independence of conjugate degrees of freedom as revealed by measurement; quantum entanglement stems from the non‑local holism of internal‑state degrees of freedom together with the spatial separability of position degrees of freedom; random motion results from the inherent asynchronism in the evolutionary sequence of degrees of freedom and the randomness of coupling‑decoupling processes. It is further clarified that the “indivisibility” and “property‑binding” of stable macroscopic configurations are essentially collective apparent effects produced when massive degrees of freedom form a strongly‑coupled constraint network. The independence of underlying degrees of freedom does not vanish; it is merely suppressed by coupling interactions and concealed under coarse‑grained observations. This framework achieves ontological continuity between microscopic quantum behaviours and macroscopic classical physical properties, and provides a new theoretical route for resolving the EPR paradox and unifying microscopic reversibility with the apparent irreversibility at macroscopic scales.
将复数折射率介质的Helmholtz方程化为具有复数势能的Schrödinger方程的形式, 用进化算子的逆算子代替相应的共轭算子, 定义了新的左矢、力学量的新平均值和推广的Heisenberg图像, 利用量子力学方法讨论了力学量的新平均值表示的复数光束传输参数、复数ABCD定律和复数ABCD系统的Huygens积分. 研究表明, 复数光束传输参数的进化方程与实数折射率系统的相应方程相同. 对于复数光束质量因子守恒系统的研究表明, 复数ABCD定律成立, 位置算子和动量算子的进化方程是线性的, Huygens积分可以写成ABCD形式.