AI 中文总结
本文基于连续介质力学，证明洛伦兹与规范对称性可从弹性介质波包的动力学约束同构涌现，为相对论与标准模型的数学结构提供了统一的物理起源解释。
AI 中文摘要
洛伦兹对称性和规范对称性构成了现代物理学的数学基石，但它们的终极物理起源仍难以捉摸。从构造性解释的角度出发，本文证明这两种对称结构可从统一的经典源——连续弹性基底介质（SM）中波包激发的动力学约束同构涌现，二者均不被视为基本假设，其涌现也不依赖于量子化。本文确立三项核心结果：第一，在约定论同步方案下，取均匀各向同性SM的横波速度为基准，闵可夫斯基型时空同构涌现，洛伦兹变换为惯性系间的有效坐标变换，这重新解释了迈克尔逊-莫雷零结果：观测者是复合波包激发，介质诱导的运动学修正被编码在其测量框架中；第二，对于具有SU(N)内禀对称性的波包，同一性不变性要求驱动SM自发产生规范场，这要求传播过程中内禀态的不变等价类，产生同构于杨-米尔斯理论的规范结构，规范群SU(N)由介质支持的稳定简正模数量唯一确定；第三，通过相同的约定论测量协议，SM的非均匀分布同构涌现为弯曲时空几何，由介质形变自由能变分极值得到的爱因斯坦型场方程支配。本文为相对论与标准模型数学结构背后的物理起源提供了统一的解释性说明。
英文摘要
Lorentz symmetry and gauge symmetry constitute the mathematical cornerstones of modern physics, yet their ultimate physical origins remain elusive. From the standpoint of a constructive interpretation, this paper demonstrates that both symmetry structures can emerge isomorphically from a unified classical source: dynamical constraints on wave-packet excitations in a continuous elastic substrate medium (SM). Neither symmetry is posited as fundamental, nor does their emergence rely on quantization. Three core results are established. First, taking the transverse wave speed of a homogeneous, isotropic SM as the benchmark under a conventionalist synchronization scheme, Minkowski-type spacetime arises isomorphically, with Lorentz transformations as effective coordinate transformations between inertial frames. This reinterprets the Michelson--Morley null result: observers are composite wave-packet excitations, and medium-induced kinematic corrections are encoded in their measurement frameworks. Second, for wave packets endowed with $SU(N)$ intrinsic symmetry, the requirement of identity invariance drives the SM to spontaneously generate gauge fields. This requires invariant equivalence classes of intrinsic states under propagation, yielding gauge structures isomorphic to Yang-Mills theory. The gauge group $SU(N)$ is uniquely determined by the number of stable normal modes supported by the medium. Third, through the same conventionalist measurement protocols, inhomogeneous distributions of the SM emerge isomorphically as curved spacetime geometry, governed by Einstein-type field equations from variational extremization of the medium's deformation free energy. This paper advances a unified interpretive account of the physical origin underlying the mathematical structures of both Relativity and the Standard Model.
Comments26 pages, 1 table,0 figures
