In Extended Classical Mechanics (ECM), the total energy is redefined by incorporating real mass redistribution into the kinetic and potential energy relationships. ECM proposes that kinetic energy arises from physically displaced matter mass (ΔMᴍ), while gravitational potential remains a function of effective matter mass, leading to a revised total energy formula. [1, 2]
Here's a more detailed breakdown:
Traditional Classical Mechanics: Total energy (Eₜₒₜₐₗ) is the sum of potential energy (PE) and kinetic energy (KE): Eₜₒₜₐₗ = PE + KE. [1, 3]
ECM's Reinterpretation: ECM modifies this by considering the variation in potential energy due to apparent mass effects. The total energy is expressed as: Eₜₒₜₐₗ = (PE - ΔPE) + ΔPE, where PE - ΔPE represents the potential energy associated with matter mass (Mᴍ), and ΔPE represents the kinetic energy associated with displaced matter mass (ΔMᴍ). [1]
Apparent Mass: ECM introduces the concept of apparent mass (Mᵃᵖᵖ), which is related to kinetic energy and is negative in sign. [4]
Effective Mass: The effective mass (Mᵉᶠᶠ) is the sum of matter mass (Mᴍ) and the negative apparent mass (-Mᵃᵖᵖ): Mᵉᶠᶠ = Mᴍ - Mᵃᵖᵖ. [4]
Total Energy in ECM: The total energy in ECM can be expressed as: Eₜₒₜₐₗ = PE - ΔPE + KE, which is equivalent to (PE - ΔPE of Mᴍ) + (KE of ΔPE) or (Mᴍ - 1/Mᴍ) + (-Mᵃᵖᵖ). [1, 4]
Key Features of ECM's Total Energy:
Redistribution of Energy: ECM proposes that energy is not just transformed but also redistributed within a system, with kinetic energy arising from the displacement of matter. [2, 2]
Negative Dynamic Mass: ECM assigns a negative mass to kinetic energy, represented by -Mᵃᵖᵖ, which is crucial for understanding its role in gravitational interactions. [4, 4]
Effective Mass: The effective mass, which is a combination of matter mass and apparent mass, plays a crucial role in determining gravitational interactions and the behavior of objects, including photons. [4, 4, 5, 5]
Unified Approach: ECM aims to provide a unified framework for understanding force, inertia, and motion, encompassing both massive and massless particles. [5, 5]
Cosmological Implications: The principles of ECM have potential applications in cosmology, particularly in understanding the behavior of large-scale structures and the role of dark energy. [6, 6, 7]
In essence, ECM reinterprets the total energy as a dynamic quantity that depends on the redistribution of matter mass, leading to a more nuanced understanding of force, inertia, and motion in both classical and relativistic regimes. [2, 5]
References:
[1]https://www.researchgate.net/post/Energy_and_Mass_Considerations_in_Extended_Classical_Mechanics_Vol-2
[2]https://www.researchgate.net/publication/392232034_Appendix_B_Alignment_with_Physical_Dimensions_and_Interpretations_of_Standard_Categorization_of_Energy_Types_in_Extended_Classical_Mechanics_ECM
[3]https://www.preprints.org/manuscript/202409.1190
[4]https://www.preprints.org/manuscript/202504.1501/v1
[5]https://www.researchgate.net/publication/390845447_Foundational_Formulation_of_Extended_Classical_Mechanics_From_Classical_Force_Laws_to_Relativistic_Dynamics
[6]https://www.researchgate.net/publication/391704357_Restoring_Dynamic_Mass_in_Classical_Mechanics_-The_Foundation_of_Extended_Classical_Mechanics_ECM
[7]https://www.researchgate.net/post/Analysis_of_Concepts_within_the_Extended_Classical_Mechanics_ECM_Framework
[8]https://www.researchgate.net/publication/392232034_Appendix_B_Alignment_with_Physical_Dimensions_and_Interpretations_of_Standard_Categorization_of_Energy_Types_in_Extended_Classical_Mechanics_ECM
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