What question did this study set out to answer?

The research aims to derive a formula for Newton's gravitational constant using the fine-structure constant and Kaluza-Klein theory.

March 18, 2026Open Access

A formula for Newton's gravitational constant from the f ine-structure constant, motivated by Kaluza–Klein reduction on S2

Puntos clave

The research aims to derive a formula for Newton's gravitational constant using the fine-structure constant and Kaluza-Klein theory.
Developed a formula for Newton's gravitational constant derived from six-dimensional Kaluza-Klein reduction on S^2.
Implemented computational framework with 2130 unit tests and 45 modules to validate the formula.
Calculated deviation of predicted G from CODATA 2018 and 2022 values.
Predicted value for G is 6.674298 x 10^-11 m^3 kg^-1 s^-2, differing from CODATA values by -0.31 ppm.
The approach involves zero parameters fitted to G, using geometrically identified correction coefficients.

Resumen

A phenomenological formula for Newton's gravitational constant G in terms of the fine-structure constant alpha, motivated by six-dimensional Kaluza-Klein reduction on S². The formula G = (phi²/2) (1 + 3*alpha² + (phi/2) alpha³) * alpha²1 * hbarc/mₑ² predicts G = 6. 674298 x 10^-11 m³ kg^-1 s^-2, deviating from the CODATA 2018 value by -0. 31 ppm (-0. 33 ppm for CODATA 2022) with zero parameters fitted to G. The leading order (Brans-Dicke parameter omega=0, bridge exponent dD-3=21) follows from standard KK reduction. The bridge coefficient phi²/2 comes from a vacuum polynomial ansatz. The correction coefficients c₂=3 and c₃=phi/2 are geometrically identified but not yet derived from first principles. The dimensionality d=4, D=6 is selected by three constraints. Accompanying open-source computational framework (2130 unit tests, 45 modules): https: //github. com/rdnjm/Alpha-Ladder Interactive dashboard: https: //alphaladder. streamlit. app/

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