Investigating Resistance in ECM: The Interplay of Inertia, Apparent Mass, and Gravitational Potential

Soumendra Nath Thakur

February, 08, 2025

In classical mechanics, resistance to acceleration is attributed to inertia—an object's inherent tendency to resist changes in motion, which is directly proportional to its mass. This principle remains fundamental in Extended Classical Mechanics (ECM); however, ECM extends the classical notion by introducing the concept of negative apparent mass (-Mᵃᵖᵖ) in motion or gravitational potential differences. Observationally, this concept finds support in the study by Chernin et al. (2013) on the Coma cluster of galaxies, which demonstrates the large-scale influence of dark energy as a repulsive gravitational effect. Their research suggests that in certain cosmic environments, gravitationally repulsive behaviour emerges, aligning with ECM’s framework where negative apparent mass modifies the classical understanding of resistance and acceleration.

In ECM, an object's resistance to acceleration is not solely determined by its classical inertial mass but also by the interaction between inertial mass and negative apparent mass. This interaction gives rise to an effective mass (Mᵉᶠᶠ) that can transition between positive and negative values, depending on the influence of motion or gravitational potential differences:

At low velocities or in weak gravitational fields, the system behaves classically, with a positive effective mass.

In high-motion regimes or strong gravitational potential differences, negative apparent mass introduces a repulsive effect, modifying the system's resistance to acceleration.

This interplay between inertial mass, apparent mass, and gravitational potential leads to a broader understanding of resistance in ECM. Rather than solely relying on classical inertia, ECM incorporates dynamic influences that may provide deeper insights into gravitational interactions, repulsive forces, and potential connections to dark matter and cosmic-scale phenomena.