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This work investigates the relationship between the inverse fine structure constant and Planck mass in conjunction with Newton's gravitational constant.

April 12, 2026

The inverse fine structure constant, Planck mass, and Newton’s gravitational constant

Key Points

This work investigates the relationship between the inverse fine structure constant and Planck mass in conjunction with Newton's gravitational constant.
Calculated Planck mass using the inverse fine structure constant and masses of protons, neutrons, and electrons.
Utilized various combinations of fundamental constants and theoretical calculations.
Compared results with recent experimental and statistical data for validation.
Calculated Planck mass is approximately 2.176 x 10^-8 kg.
Found consistent results with the recent experimental value for gravitational constant.
Results align closely with 2024 experimental data confirming gravitational constant values.

Abstract

The exponent of the inverse fine structure constant, exp α − 1 , used in conjunction with various combinations of the neutron, proton, and electron masses, permits the calculation of Planck mass as m P L = c / G = 2.176 433 6 ( 52 ) × 10 − 8 kg , where Newton’s gravitational constant is G = 6.674 305 ( 32 ) × 10 − 11 m 3 kg − 1 s − 2 , in excellent agreement with the 2024 experimental and statistical data which give G = 6.674 30 ( 15 ) × 10 − 11 m 3 kg − 1 s − 2 .

The inverse fine structure constant, Planck mass, and Newton’s gravitational constant

Key Points

Abstract

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