On the Possible Role of the Planck Length in Fitting the Neutron Lifetime

Despite decades of effort, expressing the Planck length and Newton’s gravitational constant in terms of elementary constants remains a challenge; in this work, we apply our 4G final-unification model to establish a relation tying the distance light travels during the neutron lifetime to nuclear parameters-namely the proton mass, nuclear volume, and neutron-proton mass difference-showing that slight variations in the nuclear charge radius influence neutron lifetime and resolve the beam and bottle method discrepancies (approximately 885 sec Vs 875 sec) through thermodynamic modulation of decay processes. This thermodynamic sensitivity, central to our framework, finds experimental validation in the recent J-PARC pulsed cold neutron beam study, which offers high-precision timing and statistical control, and strengthens the connection between nuclear structure and decay dynamics. We also derive a semi-empirical formula for Newton’s gravitational constant based on nuclear observables-such as Fermi’s weak coupling constant, which governs the strength of weak interactions in neutron beta decay, thus linking low-energy nuclear phenomena to quantum gravity. Extending the framework, we present a semi-empirical neutrino-mass model anchored on a benchmark electron-neutrino rest mass of 2.45 × 10⁻¹¹ eV / c², predicting the rest masses of about 3.3 × 10⁻⁴ eV / c² for the electron neutrino, 7.7 × 10⁻³ eV / c² for the muon neutrino, and 5.1 × 10⁻² eV / c² for the tau neutrino, with a combined ‘neutrino’ plus ‘antineutrino’ mass sum near (2 x 0.059) = 0.118 eV consistent with cosmological limits. These findings imply that laboratory-scale nuclear measurements contain signatures of Planck-scale physics, opening new avenues for experimental tests and theoretical developments in quantum gravity.