Soumendra Nath Thakur
January 31, 2025
Newton's Second Law and Acceleration:
In classical mechanics, Newton's second law is typically expressed as:
F = ma
This shows that force (F) is directly proportional to acceleration (a) and mass (m).
As force F increases, acceleration a increases proportionally. However, the relationship a ∝ 1/m means that if mass m increases, acceleration a will decrease, assuming force is constant.
In this framework, if acceleration increases while force increases, it suggests that mass must decrease to maintain the inverse relationship between acceleration and mass.
Apparent Mass and Effective Mass in ECM:
In Extended Classical Mechanics (ECM), this relationship is reflected in the equation:
F = (Mᴍ − Mᵃᵖᵖ) aᵉᶠᶠ
The term (Mᴍ − Mᵃᵖᵖ) implies that the effective mass is the difference between matter mass and apparent mass, which is a dynamic concept.
Apparent mass reduction:
If the apparent mass Mᵃᵖᵖ decreases (or becomes negative), this results in an increase in effective mass, which in turn causes an increase in acceleration a when the force F remains constant.
Thus, in ECM, a reduction in apparent mass leads to a corresponding increase in acceleration, aligning with the inverse relationship a ∝ 1/m, where m is the effective mass. This supports the idea that acceleration can increase without an actual increase in matter mass Mᴍ but rather a reduction in apparent mass Mᵃᵖᵖ.
Supporting Observational Findings:
The expression Mᵉᶠᶠ = Mᴍ + Mᴅᴇ, where Mᴅᴇ is negative, aligns with this reasoning. If the apparent mass Mᵃᵖᵖ (which could be represented Mᴅᴇ in this framework) is negative, the effective mass becomes:
Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)
This negative apparent mass Mᵃᵖᵖ or, effective mass of dark energy (Mᴅᴇ), reduces the total effective mass, causing an increase in acceleration when force is applied, consistent with the relationship a ∝1/m.
Conclusion:
In this framework, the concept of effective mass Mᵉᶠᶠ is key to understanding how acceleration behaves when apparent mass changes. When apparent mass decreases (or becomes negative), the effective mass also decreases, leading to an increase in acceleration. This theory not only aligns with the classical force-acceleration-mass relationship but also supports observational findings, particularly the role of negative apparent mass in cosmological models or exotic gravitational effects.
Extended Classical Mechanics vs. Relativity: A Superior Framework:
The concept of negative apparent mass in extended classical mechanics is a groundbreaking innovation. It marks a turning point in classical mechanics, introducing negative mass and expanding its capabilities beyond traditional frameworks. This extension enhances classical mechanics, making it more powerful than relativistic mechanics.
Furthermore, velocity-induced relativistic Lorentz's transformations are flawed because they neglect classical acceleration between the rest and moving frames. They also overlook material stiffness in calculations, relying solely on the speed of light as the defining dynamic factor. For these reasons, extended classical mechanics stands as a far superior framework compared to the flawed foundations of relativistic mechanics.
