How Force, Mass, and Energy Interact in Extended Classical Mechanics (ECM): A Layman Explanation Without Relativity:

Soumendra Nath Thakur 
May 27, 2025

Extended Classical Mechanics (ECM) supports classical mass-energy equivalence but without relying on relativity. The main question it explores is: how does matter behave internally when a force is applied to it?

In ordinary materials, this internal response isn't always visible — we just see the object move, fall, or accelerate. But in materials like piezoelectrics, the internal effect is quite obvious: when mechanical or gravitational force is applied, these materials generate electrical energy. This is a clear example of force being converted into energy.

But how does this conversion happen? It happens because the force causes the material to deform — its internal atomic or molecular structure shifts. This rearrangement releases energy, and in doing so, the material loses a small amount of its rest mass. This is written as:

          (Mm − ∆Mm)

where Mm is the original mass of matter and ∆Mm is the portion lost due to this internal shift, converted into kinetic energy (KE).

In ECM, this lost mass appears as a temporary apparent mass, denoted −M^app, derived from the internal matter itself. So, the effective mass of the object under motion or deformation becomes:

          M^eff = (Mm − M^app)

This process reverses when the force is removed — the material returns to its rest state, regaining its mass and structure.

The kinetic energy is expressed classically as:

          KE = (1/2)M^eff v² = ∆Mm

So, ECM interprets kinetic energy as an expression of mass loss — i.e., mass-energy equivalence in classical terms.

For particles like photons (which are massless in conventional physics but treated differently in ECM), the equation adjusts because they carry negative apparent mass. For example, a pair of such particles would have:

          −M^app + (−M^app) = −2M^app

And since photons move at the speed of light v = c, the energy equation becomes:

          KE = (1/2)(−2M^app)c² = M^eff c²

This matches the energy-frequency relation:

          E = KE = M^eff c² = hf

So the famous Planck relation E = hf emerges here without using relativity.

In ECM, this means that moving mass loses energy in the form of internal mass displacement, and adding or removing energy changes its internal mass configuration.

Hence, a strong gravitational field can affect the mass of objects within its range — not because of spacetime curvature (as in relativity), but because it displaces the internal mass structure of the object through interaction