Conceptual and Equation-Level Comparison
| Aspect |
Classical Mechanics (Newtonian) |
Relativity (Einstein) |
Extended Classical Mechanics (ECM) |
| Ontology |
Absolute space and time; point masses |
4-D manifold governed by energy–momentum tensor |
Same 4-D manifold, but introduces a signed debit term −Mᵃᵖᵖ to track displaced energy within the mass–field system |
| Mass Symbol |
m = constant scalar |
m = invariant rest-scalar |
Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ — dynamic, field- and frequency-dependent effective mass |
| Gravitational Source |
ρₘ (matter density only) |
T₀₀ = ρₘ c² (matter term only) |
T₀₀ = (Mᴍ − Mᵃᵖᵖ)c² = Mᵉᶠᶠ c² — instantaneous field–frequency balance |
| Equation Novelty |
F = m a ; ∇²Φ = 4πGρₘ |
Field equation Gμν = 8πG Tμν |
All classical and relativistic forms recast via ρ → ρₑ𝒻𝒻 = (ρₘ − ρₐₚₚ) |
| Dynamical Law |
F = m a (static) |
Geodesic motion in curved spacetime |
Fᴇᴄᴍ = Mᵉᶠᶠ aᵉᶠᶠ — a mutually adaptive triplet (F, Mᵉᶠᶠ, aᵉᶠᶠ) |
| New Free Constant? |
G (introduced by Newton) |
None (c and G known) |
None (h, c, G retained) |
| Role of G |
Couples constant masses |
Couples invariant rest-masses |
Couples dynamic effective mass balance (Mᵉᶠᶠ ↔ field) |
| Role of −Mᵃᵖᵖ |
— |
— |
Universal negative gravitational charge; records energy displaced from the real-mass field, dynamically reducing or inverting Mᵉᶠᶠ to represent field-mediated loss or reversal of gravitational influence |
| Unique Physical Effect |
— |
— |
Local g < 0 inside bound systems when Mᵃᵖᵖ > Mᴍ |
| Legacy Limit |
v ≪ c, Φ ≪ c² → Newtonian domain |
Mᵃᵖᵖ ≪ Mᴍ → reduces to Newton + Einstein limits |
— |
| Conceptual Leap |
Force causes acceleration |
Geometry causes acceleration |
Mass-energy bookkeeping causes acceleration change |
| Anomaly Addressed |
Terrestrial orbits |
Mercury perihelion shift, light bending |
Coma repulsion, flat rotation curves, lab weight dip without Λ |
| Novelty Verdict |
New physics (introduces G) |
Re-interpretation (no new constant) |
New physics variable −Mᵃᵖᵖ — energy coins pre-exist, debit column formalized |
