The Foundations of Extended Classical Mechanics (ECM):

Soumendra Nath Thakur, Tagore's Electronic Lab, India.

February 07, 2025

Extended Classical Mechanics (ECM) builds upon the established principles of Newtonian, Lagrangian, and Hamiltonian mechanics, seeking to extend their applicability beyond the traditional boundaries of classical physics. ECM aims to address limitations encountered at quantum scales, relativistic speeds, and within complex astrophysical systems, such as those involving strong gravitational fields.

A central innovation of ECM is the introduction of apparent mass (Mᵃᵖᵖ) and effective mass (Mᵉᶠᶠ). These concepts provide a framework for incorporating the influence of phenomena like dark matter and dark energy into gravitational dynamics.  Apparent mass, derived from the fundamental relationship F=ma, is extended in ECM to account for observed cosmological effects, bridging classical mechanics with modern astrophysical observations.  Effective mass, related to apparent mass, further refines this description, offering a more nuanced understanding of gravitational interactions.

ECM also offers a novel perspective on photon dynamics. While respecting the classical principles of energy conservation, ECM considers the interaction of photons with gravitational fields.  It proposes that photons, while maintaining their intrinsic energy (E), dynamically exchange gravitational interactional energy (Eg) with the field during their trajectory. This approach suggests a deeper connection between classical mechanics and the behaviour of light in the cosmos.

By integrating classical mechanics with modern astrophysical observations through the concepts of apparent and effective mass, ECM offers a new lens through which to explore the universe.  This framework not only honours the foundations of classical physics but also embraces the complexities revealed by contemporary scientific inquiry, opening up new avenues for research.

Reference Papers:

Thakur,  S. N. (2024). A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. https://doi.org/10.20944/preprints202411.2325.v1

Thakur,  S. N. (2024). Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy. https://doi.org/10.20944/preprints202411.1797.v1

Thakur,  S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. https://doi.org/10.20944/preprints202409.1190.v3

Thakur,  S. N. (2024). A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields.  https://doi.org/10.20944/preprints202411.0956.v1

Thakur,  S. N. (2024). A supplementary resource to A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. https://www.researchgate.net/publication/385902096

Thakur,  S. N. (2024). Photon Interactions with External Gravitational Fields: True Cause of Gravitational Lensing. https://doi.org/10.20944/preprints202410.2121.v1

Thakur,  S. N. (2024). A Dual Framework for Rest and Motion States: Energy and Mass Dynamics in Extended Classical Mechanics. http://dx.doi.org/10.13140/RG.2.2.13901.14566

Thakur,  S. N. (2024). A Revised Framework for the Photon- to-Dark-Energy Transition: Refining Photon Gravitational Dynamics. http://dx.doi.org/10.13140/RG.2.2.10551.02723

Thakur,  S. N. (2024). Light's Distinct Redshifts under Gravitational and Anti-Gravitational Influences. http://dx.doi.org/10.13140/RG.2.2.26649.22889 

Thakur,  S. N. (2024). Photon Energy Interactions in Gravitational Fields: A Framework for Symmetry and Conservation. http://dx.doi.org/10.13140/RG.2.2.12403.34081 

Thakur,  S. N. (2024). Unified Study on Gravitational Dynamics: Extended Classical Mechanics -Vol-2. [ECM-2]. https://www.researchgate.net/publication/384501200

Thakur,  S. N. (2024). Dark Energy as a Consequence of Gravitational and Kinetic Interactions: The Dynamic Nature of the Universe. https://www.researchgate.net/publication/384198607