Part 8/9:
Importantly, Mach's perspective introduces the idea that the gravitational influence of distant masses shapes local inertial frames. This means the effect of global mass distribution should not be viewed simply as linear. Instead, the non-linear nature of curvature in general relativity suggests a more complex interplay, where inertia is not merely the sum of local and global effects.
Theories could indicate that inertia depends on the inherent strength of these gravitational fields, suggesting a non-linear relationship between inertial mass and the gravitational influence of both local and distant masses. This leads to potential reformulations of Newton’s second law, reflecting corrections based on nearby and far-off accelerations and field intensities.