6.1. Effective Acceleration Generates Apparent Mass:

In extended classical mechanics, effective acceleration (aᵉᶠᶠ) is inversely proportional to effective mass (Mᵉᶠᶠ). This relationship can be mathematically expressed as:

aᵉᶠᶠ ∝ 1/Mᵉᶠᶠ

​This means that as effective acceleration increases, there is a corresponding decrease in effective mass. This dynamic interaction leads to the generation of negative apparent mass (-Mᵃᵖᵖ). As effective acceleration increases, the effect of apparent mass becomes more pronounced, creating a unique and significant relationship between acceleration and mass within this framework.

The notion of apparent mass, particularly when it takes on a negative value, introduces a novel perspective on the behaviour of objects under acceleration. In this context, as an object's effective acceleration increases—potentially due to external forces or influences—the effective mass must decrease in order to maintain the equality described in the proportionality. Consequently, this decrease in effective mass manifests as a more pronounced negative apparent mass.

This relationship underscores a crucial aspect of extended classical mechanics, suggesting that the dynamics of motion and mass are interlinked in ways that deviate from classical interpretations. The generation of negative apparent mass illustrates how accelerated systems can exhibit behaviours that challenge traditional notions of mass and inertia. It reflects a deeper understanding of how effective forces interact with mass in a non-linear fashion, leading to counterintuitive outcomes, such as reduced resistance to acceleration or even increased responsiveness to applied forces.

In summary, the interplay between effective acceleration and apparent mass in extended classical mechanics reveals a complex relationship that enriches our understanding of mechanical systems. As effective acceleration increases, the resultant behaviour of apparent mass not only emphasizes the significance of acceleration in determining mass properties but also challenges established principles, paving the way for further exploration into the mechanics of motion.