BCT Letter 9: The Planck Mass and Newton's Constant from BCT Lattice Geometry — Why Gravity Is Weak

The hierarchy between the electroweak scale (v = 246 GeV) and the Planck scale (mP = 1.22 × 1019 GeV)—a ratio of ∼ 1017—is the central fine-tuning problem of fundamental physics. Within the Body-Centred Tetragonal (BCT) Superfluid Lattice Model, this hierarchy is derived geometrically, not assumed. The Planck mass is mP = MR/α2 0, where MR = 6.695 × 1014 GeV is the tripleunification (seesaw) scale and α0 = 0.0074081 is the BCT crystal coupling. This gives mP = 1.220× 1022 MeV (−0.08% error). Newton's gravitational constant GN = c 4 /(8πKBCT) is determined by the bulk modulus KBCT of the vacuum condensate. The physical reason gravity is weak is geometric: the graviton, being spin-2, requires two void-to-void couplings, each contributing a factor of α0, making the gravitational coupling ∝ α 4 0 ∼ 10−9 times weaker than the strong force. No fine-tuning, no supersymmetry, and no extra dimensions are required—the hierarchy is a consequence of the vacuum lattice structure.