Abstract
This work presents a unified formulation of time, gravitation, and motion within the framework of Extended Classical Mechanics (ECM).
By identifying Negative Apparent Mass (NAM) as the physical carrier of potential energy and mass manifestation, relativistic time dilation, gravitational redshift, and length contraction are shown to arise from mass–energy redistribution rather than spacetime geometry.
A single ECM mass-conversion law is shown to reproduce both special and gravitational time-distortion effects while providing a physical basis for cosmic acceleration.
ECM Counter-Address to Minkowski Spacetime
Relativity claims that Minkowski spacetime replaces Euclidean geometry by redefining the interval.
ECM shows that this is a physical reinterpretation, not a mathematical necessity.
Cartesian geometry already operates on interval squared:
Δs² = Δx² + Δy² + Δz²
Minkowski spacetime merely introduces a sign change:
Δs² = c²Δt² − Δx² − Δy² − Δz²
ECM explains this sign not as geometry, but as mass–energy bookkeeping.
Motion and gravitation remove oscillatory mass from clocks, producing time distortion.
Thus, relativistic intervals are not fundamental spacetime geometry, but diagnostic expressions of:
−ΔPEecm ↔ ΔKEecm ↔ ΔMM
ECM therefore reproduces relativistic effects without abandoning Euclidean Cartesian space.
Geometry is preserved; physics is extended.
1. Fundamental ECM Identity
All physical processes in Extended Classical Mechanics arise from:
−ΔPEecm ↔ ΔKEecm ↔ ΔMM
Negative Apparent Mass (NAM) is defined as:
Mapp ≡ −ΔPEecm
2. Clocks in ECM
A clock tick is a NAM discharge event:
Mapp → ΔMM → oscillation
Clock frequency is proportional to available oscillatory mass:
f ∝ MM
3. Motion-Induced Time Distortion
Motion converts manifestable mass into kinetic mass:
Mapp → ΔMM(v) → KEecm
Remaining clock-driving mass:
MM,eff = MM,rest − ΔMM(v)
Time-rate distortion:
f(v)/f0 = MM,eff / MM,rest
4. Gravity-Induced Time Distortion
Gravitational binding is stored NAM:
Mappgrav = −ΔPEecm = GM MM / r
Effective oscillatory mass:
MM,eff = MM,rest − Mappgrav / c²
Gravitational time distortion:
f(r)/f∞ = 1 − Mappgrav / (MM c²)
5. Unified ECM Time Law
Motion and gravity both remove NAM-converted mass from clocks:
MM,eff =
MM,rest
− ΔMM(v)
− Mappgrav/c²
Unified ECM time-distortion equation:
f / f0 =
1 − ΔMM(v)/MM
− Mappgrav / (MM c²)
Conclusion
Extended Classical Mechanics provides a physically grounded alternative to spacetime-based relativity.
Time dilation, gravitational redshift, length contraction, and cosmic acceleration all originate from a single mass-energy conversion mechanism governed by Negative Apparent Mass.
Rather than geometry determining physics, ECM shows that physics determines the observed geometry of time and space.
