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In Extended Classical Mechanics (ECM), curvature is not a geometric property of space but a physical manifestation of field distortions governed by variations in ΔMm, Mᵃᵖᵖ, and Δt under the unified influence of the extended classical force Fᴇᴄᴍ.
Conventional physics describes “curved magnetic,” “curved gravitational,” and “curved spacetime” as separate phenomena. ECM treats them as expressions of the same mass–energy transition process, described through variations of effective and apparent mass and corresponding time distortions:
| Curvature Type | Symbol | ECM Description | Underlying ECM Relation |
|---|---|---|---|
| Magnetic Curvature | ᴷᴮ | Spatial variation in Fᴇᴄᴍ arising from electromagnetic mass–energy differentials (ΔMm) within the field. | ᴷᴮ = (B×∇)B ÷ ∣B∣² ΔMm → Fᴇᴄᴍ → aᵉᶠᶠ |
| Gravitational Curvature | ᴷᴳ | Distortion of Mᵉᶠᶠ and Mᵃᵖᵖ within gravitational potential, accompanied by Δt variation in aᵉᶠᶠ = Fᴇᴄᴍ / Mᵉᶠᶠ. | ᴷᴳ ∝ ∇(−ΔMᵃᵖᵖ) / Mᵉᶠᶠ Δt ↔ gᴇᴄᴍ |
| Spacetime Curvature | ᴷˢᵗ | Macroscopic projection of energy–mass gradients (ΔMm, Δt); apparent geometry reflects mass–energy distortions rather than intrinsic curvature of space or time. | ᴷˢᵗ ∝ ∇(ΔMm, Δt) / Fᴇᴄᴍ gᵉᶠᶠ ↔ Mᵉᶠᶠc² |
In this reinterpretation, ECM restores classical consistency by maintaining space and time as non-physical, measurable frameworks, while identifying curvature as energetic and temporal distortion within Fᴇᴄᴍ. Curved spacetime thus becomes a coordinate expression of ΔMm–Δt interactions rather than a deformable geometry.
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