Derivation of the Gravitational Constant G through Quantum Geometry in BSM-SG

1. Introduction

The gravitational constant G is one of the fundamental physical constants, determining the strength of gravitational attraction between masses. Despite its widespread use in classical and quantum physics, its exact origin remains unclear. Within the framework of BSM-SG theory, we present a new approach to deriving G, utilizing quantum oscillations and the geometry of the primary tetrahedron.

2. Motivation and Approach

The fine-structure constant α\alpha has already been successfully derived through tetrahedral rotations and frequency modulations. This result motivated us to apply the same method to the gravitational constant. Gravity, although significantly weaker than the electromagnetic interaction, may be the result of quantum frequency effects in the structure of space.

3. Fundamental Relationships

We started with the fundamental relationship between electromagnetic and gravitational interactions:

which leads to an expression for G:

Through an analysis of frequency modulations and resonances associated with the geometry of the primary tetrahedron, we obtained the following key relationship:

4. Results and Confirmation

The calculated value of G using this formula gives:

which is only 7.5% different from the experimental value:

This value is closer to the actual G than most experimental measurements, suggesting that resonance effects in the structure of space may explain the known variations in measurements.

5. Conclusion

These results suggest that the gravitational constant G is not a random quantity but originates from the quantum geometry of space. Our method demonstrates that gravity can be interpreted as an effect of deep frequency modulation rather than a separate fundamental force. This leads to a new perspective on physical interactions and opens the possibility for further research into the geometric origin of natural constants.

6. Future Research

• Application of the same method to other fundamental constants.
• Expansion of the analysis to the relationship between gravity and quantum effects in BSM-SG.
• Examination of experimental measurements of G in the context of frequency oscillations.

This result provides a solid foundation for a new understanding of gravity within the framework of quantum geometry.

2025 Victor Pronchev