Quantum Gravity and String Theory

    

A Dimensionless Gravitational State Parameter from a Planck-Scale U(1) Lattice

Authors: Wenhao Xiong

We derive a dimensionless gravitational state parameter R from a discrete U(1) lattice with Planck spacing. From H=J[sum][1−cos(Δφ)] with J=ℏc/ℓP, point defects interact via the 3D Coulomb potential, yielding Newton’s law with n=m/mP. The parameter R≡Fr2/FP(FP=c4/G) decomposes into a defect rigidity term Rm=n2r/ℓP and the lowest-order compact U(1) vacuum contribution 2πℓP/r: R={[m/(m^P)]^2}r/(ℓ^P)−2π(ℓ^P)/r.(1) [for] R larger than 0: classical attraction. R smaller than 0: repulsion. R=0 defines a critical line mr=2πℏ/c. The effective force F=FPR/r2 acquires a mass-independent r−4 correction. At laboratory scales this effective correction is estimated to be [about 10^(130) N.

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[v1] 2026-07-25 02:07:10

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