The Original G
Title: The Original G: Exploration of the Gravitational Constant
Author: Orion Franklin, Syme Research Collective
Date: March 10, 2025
Abstract
The gravitational constant (G) has long been one of the most enigmatic and least precisely measured fundamental constants in physics. Unlike other constants, such as the speed of light (c) and Planck’s constant (h), which have been refined to extraordinary precision, G continues to exhibit inconsistencies across experimental measurements. In previous studies (More to C and Beyond Planck’s Limit), we explored the possibility that c and h are not truly fixed but instead emergent properties influenced by deeper physical structures. If this is the case, then G, which depends on these values, may also be subject to variability. This paper examines how recalculating G using micro-adjustments to c and h could lead to a more precise and potentially more accurate understanding of gravitational interactions. We conclude with recommendations on how AI-assisted analysis can be used to refine experimental methodologies and test the theoretical predictions that emerge from this approach.
1. Introduction: The Persistent Mystery of G
The gravitational constant is foundational to Newtonian and Einsteinian gravity, appearing in formulations ranging from Newton’s law of universal gravitation:
F = G (m₁m₂ / r²)
to Einstein’s general relativity:
Gμν + Λ gμν = (8πG / c⁴) Tμν
Despite its importance, G is notoriously difficult to measure. Its accepted value:
G ≈ 6.67430(15) × 10⁻¹¹ m³·kg⁻¹·s⁻²
has been challenged by numerous experimental discrepancies. Unlike the fine-structure constant, which is dimensionless and measured with extreme precision, G’s value remains uncertain at the 10⁻⁵ level, making it the least well-determined fundamental constant. The persistence of measurement inconsistencies raises fundamental questions:
Is G truly constant across time and space, or does it subtly vary?
Could inconsistencies in measuring G arise from our assumptions about the fixed nature of c and h?
If c and h are emergent rather than absolute, how would this affect the calculation of G?
To answer these questions, we must reassess the way G is traditionally derived and consider how modifications to c and h might refine our understanding.
2. Recalculating G: The Role of c and h
2.1 The Relationship Between G, c, and h
Traditionally, G is derived using known relationships between other physical constants, particularly c and h. The Planck units, which set natural scales for physics, are defined as:
ℓₚ = √(ħG / c³), tₚ = √(ħG / c⁵), mₚ = √(ħc / G)
These relationships imply that any change in c or h would necessarily influence G. If c and h are not truly fixed but instead emerge from deeper quantum-gravitational interactions, then G itself may be scale-dependent rather than universally constant.
2.2 Modifying c and h: How Would G Change?
If we introduce micro-adjustments to c and h as proposed in More to C and Beyond Planck’s Limit, then:
A slight increase in c would reduce the Planck length ℓₚ, potentially leading to a lower effective value of G in high-energy regimes.
A variation in h would alter the quantization of energy at small scales, modifying the effective gravitational interaction between quantum particles.
G may not be a single fixed value but instead take on slightly different values depending on the energy or curvature of spacetime in a given region.
To test this, we propose recalculating G under different scenarios where c and h are functions rather than constants. One approach involves defining a scale-dependent function for G based on variations in c and h:
G'(r) = G₀ [1 + f(c, h, r)]
where f(c, h, r) represents a function describing small perturbations in G as a function of c, h, and distance (r) in gravitational interactions.
This formulation suggests that in strong gravitational fields (e.g., near black holes), the value of G could shift slightly due to quantum fluctuations in c and h, providing a testable prediction for astrophysical observations.
3. Theoretical Implications of a Variable G
3.1 Black Holes and Event Horizons
The Schwarzschild radius of a black hole is given by rₛ = 2GM / c². If G is slightly modified due to a shifting c, then the event horizon of a black hole might be slightly different than predicted by classical general relativity.
Hawking radiation depends on G, h, and c. If h is emergent and varies at small scales, the energy output of evaporating black holes may need to be recalculated.
3.2 Early Universe Cosmology
The cosmic microwave background (CMB) is influenced by G. A scale-dependent G could provide an alternative explanation for anomalies in CMB temperature fluctuations.
If G was slightly different in the early universe due to variations in c and h, it may have influenced the rate of cosmic inflation, altering our understanding of primordial expansion.
3.3 Modifications to Dark Matter and Dark Energy Models
If G varies subtly in regions of high curvature, certain dark matter effects might be explained by a modified gravitational interaction rather than requiring unseen mass.
Dark energy, often attributed to a cosmological constant (Λ), could instead be related to small-scale variations in G arising from quantum gravitational effects.
4. Experimental and Observational Tests
To validate this framework, we propose several methods for testing the effects of a variable G:
Pulsar Timing Arrays – Precise measurements of binary pulsar orbits could reveal whether G is varying across interstellar distances.
Gravitational Wave Observations – Comparing waveforms from black hole mergers could test for deviations from classical predictions if G is slightly different in extreme gravity.
Lunar Laser Ranging – Reanalyzing Earth-Moon distance measurements over decades may uncover subtle variations in G.
Big Bang Nucleosynthesis – The early formation of elements depends on G; an adjusted value of G may offer a better fit for observed primordial abundances.
5. AI-Assisted Validation and Future Research
While the focus of this paper has been on recalculating G based on theoretical refinements to c and h, AI offers a powerful tool for analyzing the vast amounts of data required to validate these predictions. AI can assist in:
Pattern Recognition in Experimental Data – Detecting anomalies in past G measurements that may hint at systematic variations.
Astrophysical Data Processing – AI can automate the analysis of gravitational waveforms and CMB data for signatures of scale-dependent G.
Symbolic AI for Theoretical Model Refinement – AI can assist in testing whether an emergent G better fits cosmological models.
By integrating AI methodologies with theoretical physics, we can rigorously test whether G is truly a universal constant or instead emerges from deeper quantum-gravitational interactions.
Conclusion
By reconsidering the calculation of G through micro-adjustments to c and h, we open the door to new possibilities in gravitational physics. If G is indeed emergent and slightly variable, this could resolve longstanding measurement inconsistencies while providing new insights into quantum gravity, black hole physics, and cosmology. Future work should focus on refining these theoretical predictions and designing high-precision experiments to validate them. AI-assisted analysis could play a critical role in detecting subtle deviations in gravitational data, optimizing experimental methodologies, and discovering patterns that challenge our assumptions about fundamental constants.
Acknowledgments
We acknowledge the contributions of past researchers in gravitational physics, whose foundational work has informed our approach. Special thanks to those advancing experimental tests of G and to the developers of AI-driven methodologies that may soon help refine fundamental physics.
Special thanks to the Syme Papers initiative for providing a platform to explore advanced AI-driven theoretical physics.
References
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Webb, J. K., et al. (2011). Indications of a spatial variation of the fine-structure constant. Physical Review Letters, 107(19), 191101.
Williams, J. G., et al. (2004). Lunar laser ranging tests of the equivalence principle. Physical Review Letters, 93(26), 261101.
