Mass Redefined in Extended Classical Mechanics: Beyond Baryonic (Mᴏʀᴅ), Inertial (m), and Relativistic Rest Mass (m₀).

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803

March 27, 2026

Within the Extended Classical Mechanics (ECM) framework, the traditional identification of mass—whether classical inertial mass (m), relativistic rest mass (m₀), or ordinary baryonic mass (Mᴏʀᴅ)—is revealed to be fundamentally incomplete. These conventional definitions account only for visible matter and therefore fail to represent the full gravitational reality of the universe.

ECM resolves this limitation by redefining total matter mass as:

Mᴍ = Mᴏʀᴅ + Mᴅᴍ,

thereby incorporating both visible and dark matter contributions. However, this total mass alone remains insufficient to account for gravitational behaviour. The crucial advancement of ECM lies in recognizing that gravitational mass is not determined by Mᴍ alone, but by an emergent quantity—the effective mass (Mᵉᶠᶠ).

This effective mass includes the influence of negative apparent mass (Mᵃᵖᵖ < 0), identified with dark energy, leading to the defining relation:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ

Thus, gravity in ECM is not governed solely by matter content, but by the net outcome of a scale-dependent interplay between:

• Ordinary baryonic mass (Mᴏʀᴅ)

• Dark matter mass (Mᴅᴍ)

• Negative effective mass of dark energy (Mᵃᵖᵖ = Mᴅᴇ < 0)

This establishes a profound shift in understanding:

Gravitation is an emergent phenomenon arising from the balance of positive and negative mass contributions, not merely an intrinsic property of matter.

In essence, ECM elevates Mᵉᶠᶠ as the physically meaningful quantity, unifying dark matter and dark energy within a single coherent structure. As a result, gravitational mass (Mɢ) is no longer a simple reflection of matter, but the net manifestation of the universe’s mass–energy architecture across scales.