Abstract Aiming at the long-standing cognitive misconception of "higher-dimensional physical space" in theoretical physics, this paper reconstructs the physical image of the critical dimension formulas and compactification models in string theory, based on the mathematical theorem of three-dimensional spatial rigidity and the cross-scale hierarchical framework of Real-Virtual Dual Field Theory (RVDT). The study first distinguishes three core concepts: physical spatial dimension, mathematical parameter dimension, and cosmic scale hierarchy, and proves that three dimensions are the only physical spatial dimension with objective reality. Secondly, by decomposing the critical dimension constraint equations of bosonic string, superstring and M-theory, as well as the Calabi-Yau manifold metric, it is pointed out that all "extra dimensions" are essentially algebraic markers of independent physical variables, not new spatial coordinate axes. Furthermore, based on the virtual field medium model of RVDT, higher-dimensional parameters are divided into three sources: longitudinal hierarchical perturbation, transversal peer perturbation, and microscopic intrinsic degree of freedom, and their real physical mechanisms are restored. The study shows that the 11-dimensional/10-dimensional/26-dimensional settings of string theory are mathematical products of the mixed packaging of three types of perturbation parameters. Its "dimensional compactification" corresponds to the steady-state encapsulation of perturbation parameters at the macroscopic scale, and the "string landscape" corresponds to the differences of parameter combinations under different cosmic hierarchies and environments. Without denying the mathematical self-consistency of string theory, this study corrects the conceptual dislocation between parameter dimensions and physical space, provides a physical ontological interpretation of higher-dimensional theories that conforms to three-dimensional spatial rigidity and falsifiability, and also provides mathematical evidence for the cross-scale unified framework of RVDT. Key words: String Theory; Higher-Dimensional Space; Parameter Dimension; Scale Hierarchy; Real-Virtual Dual Field Theory; Three-Dimensional Spatial Rigidity 摘要 针对理论物理领域长期存在的 “物理空间高维” 认知误区,本文以三维空间刚性的数学定理为基础,结合实虚二元场论(Real-Virtual Dual Field Theory, RVDT)的跨尺度层级框架,对弦论体系的临界维度公式与紧致化模型进行物理图像重构。研究首先明确区分物理空间维度、数学参数维度与宇宙尺度层级三类核心概念,证明三维是唯一具备客观实在性的物理空间维度;其次通过拆解玻色弦、超弦、M 理论的临界维度约束方程与卡拉比 - 丘流形度规,指出所有 “额外维度” 本质是独立物理变量的代数标记,并非新增的空间坐标轴;进一步基于实虚二元场论的虚场介质模型,将高维参量划分为纵向层级扰动、横向同级扰动、微观内禀自由度三类来源,还原其真实物理机制。研究表明,弦论的 11 维 / 10 维 / 26 维设定,是三类扰动参量混合打包的数学产物,其 “维度紧致化” 对应宏观尺度下扰动参数的稳态封装,“弦景观” 对应不同宇宙层级与环境下的参量组合差异。本研究在不否定弦论数学自洽性的前提下,纠正了参数维度与物理空间的概念错位,为高维理论提供了符合三维空间刚性、具备可证伪性的物理本体论诠释,也为实虚二元场论的跨尺度统一框架提供了数学佐证。 关键词:弦论;高维空间;参数维度;尺度层级;实虚二元场论;三维空间刚性
Zhongqiang Liu (Sat,) studied this question.