Layman Explanation: Rethinking Mass when Force is applied in Extended Classical Mechanics (ECM).

In everyday physics, we’re taught that if you push something (apply force), it accelerates, and how much it accelerates depends on its mass. This is Newton’s second law: more mass means less acceleration for the same push, and vice versa. This seems straightforward.

But Extended Classical Mechanics (ECM) looks more closely at what happens to mass when a force is actually applied. Traditionally, mass is treated as something fixed — a built-in resistance that doesn’t change, no matter how you push or move the object. ECM challenges this idea.

What ECM observes differently

ECM agrees that if a force isn’t zero (that is, if you’re pushing or pulling with some strength), then the relationship between the object’s mass and how it moves involves not just the mass itself, but something more subtle — the reciprocal of mass. This simply means one divided by mass.

Now, here’s where ECM makes a breakthrough. It points out that just because “one divided by mass” is a valid number, that doesn’t mean the mass itself stays unchanged. In fact, ECM says the moment this term becomes active in motion, the mass starts behaving differently.

Mass isn’t fixed when Force is involved

Instead of mass being a single constant value, ECM says it turns into a sort of effective mass — a combined quantity that depends on both the original mass and its reciprocal. That is, when something is moving because of a force, the mass acting in motion becomes more than just “mass” — it includes this new influence.

So, the result is simple but powerful: when something is pushed or pulled, its actual “mass in motion” is no longer just the mass it had at rest.

Why this matters

This is a major shift. In both classical and modern physics (like Einstein’s relativity), mass is usually assumed to stay the same while an object speeds up or slows down. ECM maintains this isn’t true — that the very act of applying force and creating motion changes how mass behaves.

In this way, ECM introduces a more dynamic and realistic view of mass — one that evolves as energy interacts with matter.

Explanation: ECM's view on Mass and Force

In regular physics (Newtonian mechanics), when you push something with a constant force, the way it speeds up (accelerates) depends on its mass. The bigger the mass, the slower it speeds up.

In math, that’s:

Force = mass × acceleration or,

Acceleration = force ÷ mass

So if the force is constant, then acceleration is controlled by 1/mass. If 1/mass stays the same, then the mass itself must also stay the same — simple.

ECM’s new insight

ECM agrees with this formula, but it goes deeper:

Even if 1/mass stays the same, that doesn't mean the actual mass isn’t changing— especially in systems where gravity or energy is involved.

That’s because ECM introduces a new way to look at mass in motion. It says the true “mass” that reacts to force is not just regular mass, but:

Effective Mass = mass ± (1/mass)

This extra piece, 1/mass, changes how things behave when they move — especially when they're gaining or losing energy, like in space or under gravity.

Key Takeaway:

Even if 1/mass seems constant when a force is applied, the real behaviour depends on this new “effective mass.” So the object might not behave as if it had constant mass — because it doesn’t, in ECM terms!

- Soumendra Nath Thakur
  May 24, 2025