q₀ 作为广义相对论与量子场论之间的方法论桥梁 G₀ 极限下的自由能极小分片平直 Regge-cell 图像 - q₀ as a Methodological Bridge Between General Relativity and Quantum Field Theory A Free-Energy-Minimum Piecewise-Flat Regge-Cell Picture in the G₀ Limit

V3 Update: Utilize Regge Calcus for our q0 flat patches framework. V3 更新: 在我们的 q₀ 平直片元框架中引入 Regge Calculus。 摘要 广义相对论(GR)与量子场论(QFT)之间长期存在的困难,并不只是来自弯曲描述与量子化描述之间的差异。它还反映出一个共同物理层的缺失:这个物理层必须能够同时支撑 GR 的动力学几何以及普通 QFT 所要求的局部固定背景。本文并不声称已经给出 GR 与 QFT 的终极统一。相反,本文通过牛顿常数的内在结构,更准确地说,通过伴随结构涨落框架中引入的桥量 q₀,提出一种受限的桥接构造。 在该框架中,q₀ 由一个介观结构涨落子系统的自由能极小条件所固定,并取确定值 q₀ = α¹⁸。本文的核心主张是:由 q₀ 所固定的极小态,提供的不是预设光滑流形上的形式切平面,而是真实的局域闵氏物理单元。标准 QFT 被安置在每个 q₀-选定单元内部,而相邻单元之间的有向匹配承载 holonomy 与亏角。本文采用 Regge calculus 作为这一分片平直构造的现成几何骨架;本文新增的物理主张是:这些单元不是辅助三角剖分,而是由自由能极小规则固定的真实单元,其允许的有向元素由 nq₀ 量子化。 在无偏、各向同性、球对称的 G₀ 扇区中,这一单元拼接给出 Regge 型几何作用量;其连续粗粒化极限恢复 Einstein-Hilbert 形式,并且耦合强度由 G₀(q₀) 固定。定义在单元内部的 QFT 给出局域量子能动张量 ⟨T̂μν⟩q₀,而相邻单元之间的有向匹配给出由该张量作为源项参与决定的亏角几何。相应的桥接方程为 Gμν[g⁽q₀⁾cg] + Λ₀g⁽q₀⁾cg μν = 8πG₀(q₀)⟨T̂μν⟩q₀/c⁴。在弱场、慢速极限下,同一亏角几何给出带有 G₀(q₀) 的 Newton 方程。因此,本文的主张不应被理解为从 QFT alone 直接推出 GR,而应被理解为:q₀-cell 上的 QFT 与 q₀-固定的 Regge 几何共同构成一条最低阶恢复 GR 方程的路线。完整双体情形下的 Gth 推广留待后续工作。 Abstract The long-standing difficulty between general relativity (GR) and quantum field theory (QFT) does not arise only from the difference between curved and quantized descriptions. It also reflects the absence of a common physical layer that can simultaneously support the dynamical geometry of GR and the locally fixed background required by ordinary QFT. The present paper does not claim a final unification of GR and QFT. Instead, it proposes a restricted bridge construction through the internal structure of Newton’s constant, more precisely through the bridge quantity q₀ introduced in the companion structural-fluctuation framework. In that framework, q₀ is fixed by the free-energy-minimum condition of a mesoscopic structural-fluctuation subsystem and takes the determinate value q₀ = α¹⁸. The central proposal of the present paper is that the minimum state fixed by q₀ supplies physical locally Minkowskian cells rather than merely formal tangent-plane approximations. Standard QFT is then installed inside each q₀-selected cell, while the oriented matching of neighbouring cells carries holonomy and deficit angles. Regge calculus is used as the existing geometrical backbone for this piecewise-flat construction; the additional claim made here is that the cells are fixed by a physical free-energy-minimum rule, with admissible oriented elements quantized by nq₀, rather than by a merely auxiliary triangulation. In the unbiased, isotropic, spherically symmetric G₀ sector, the cell assembly gives a Regge-type geometric action whose continuum coarse-grained limit recovers the Einstein-Hilbert form with the coupling fixed by G₀(q₀). The QFT defined inside the cells supplies the local quantum stress tensor ⟨T̂μν⟩q₀, while the oriented matching between neighbouring cells supplies the deficit-angle geometry sourced by that tensor. The corresponding bridge equation is Gμν[g⁽q₀⁾cg] + Λ₀g⁽q₀⁾cg μν = 8πG₀(q₀)⟨T̂μν⟩q₀/c⁴. In the weak-field, slow-motion limit this same deficit-angle geometry gives the Newtonian equation with G₀(q₀). The proposal therefore should not be read as a derivation of GR from QFT alone, but as a q₀-cell QFT plus q₀-fixed Regge-geometry route through which the GR equation is recovered at lowest order. The full two-body Gth case is left for later extension.