Trachenko Analysis Ties Fine-Structure Constant and Planck Scale to Viscosity Thresholds Blocking Cellular Diffusion

The work extends Trachenko's earlier 2020 result establishing a fundamental lower bound on liquid viscosity set by ħ, m_e and α. Here the bound is mapped onto biological transport: diffusion times for metabolites across a 10 µm cell rise exponentially once viscosity exceeds the observed cytoplasmic range of 1–10 mPa·s. The calculation uses only quantum-field and hydrodynamic scaling; no new parameters are introduced.

Because the same constants fix both nuclear reaction rates and intermolecular forces, the allowed window for life is narrower than standard anthropic arguments assume. A 4 % increase in α would render water tar-like while still permitting stellar nucleosynthesis, directly contradicting the common claim that only the cosmological constant requires fine-tuning.

The analysis remains purely theoretical; no molecular-dynamics simulation yet tests the predicted viscosity shift under altered constants. Future lattice QCD runs with varied α could falsify the bound within five years if they show no corresponding rise in hydrogen-bond lifetime.

Next steps require coupling the viscosity constraint to explicit metabolic network models to quantify the exact survival threshold for prokaryotic versus eukaryotic cells.