A Letter: On Mass, Displacement, and Negative Apparent Mass in Extended Classical Mechanics

 

Soumendra Nath Thakur

April 19, 2025

In response to Dr. Valentyn Nastasenko’s statement:

“Mass is the amount of substance in a unit volume. Everything else is impulses.”

I would like to offer a clarification that aligns with this classical understanding, while extending it through the lens of Extended Classical Mechanics (ECM).

Mass (m) is indeed the amount of substance confined within a unit volume. However, when any portion of that substance is displaced—either physically or dynamically—the measurable mass within that unit volume is no longer whole. This displacement can be denoted as a reduction of mass by an amount (mₐ), such that:

m_ʀᴇᴍᴀɪɴɪɴɢ = m − mₐ, where: 0 < mₐ ≤ m

In ECM, this reduction is not merely a subtraction but is interpreted dynamically as the emergence of a negative apparent mass, denoted as:

−Mᵃᵖᵖ ≡ −mₐ

This concept is analogous to Archimedes’ principle, where an object partially or fully submerged in a fluid displaces an amount of fluid equivalent to its volume, resulting in a buoyant force equal to the weight of the displaced fluid. Analogously, in ECM:

• The original mass m serves as the surrounding "field" or medium,
• The displaced portion mₐ represents a loss from the inertial configuration,
• And the resulting dynamics (e.g., force redirection, gravitational anomalies) emerge from this displacement.

In this framework, negative apparent mass does not imply the existence of exotic negative-mass particles. Rather, it is a phenomenological term to represent the dynamically displaced portion of mass-energy, which manifests in observations such as:

• The inertial response of massless particles like photons,
• The antigravitational effects attributed to dark energy in cosmology,
• And the effective force equations needed to reconcile Newtonian, relativistic, and quantum dynamics.

By distinguishing between intrinsic mass and apparent dynamic mass terms, ECM offers a refined interpretation without violating classical substance-based definitions. It bridges observed cosmological behaviour with energy-mass dynamics, while maintaining internal mathematical and physical consistency.

I hope this clarification contributes constructively to ongoing discussions on the nature of mass and the foundational structure of modern mechanics.

Sincerely,

Soumendra Nath Thakur