Extended Classical Mechanics and Photon Interactions in Gravitational Fields: A Unified Framework

Soumendra Nath Thakur

February 17, 2025

Extended Classical Mechanics (ECM) extends Newtonian dynamics by establishing force and energy equations for both massive and massless entities, naturally integrating with quantum mechanical principles.

In ECM, gravitational interactions are not limited to massive objects alone; instead, they incorporate apparent mass (Mᵃᵖᵖ) to describe how massless entities, such as photons, interact with gravitational fields. Unlike in Newtonian mechanics, where light is traditionally considered unaffected due to its lack of mass, ECM introduces effective mass (Mᵉᶠᶠ), which allows gravitational fields to influence photons through an apparent force.

For massless entities such as photons, the force equation is governed by apparent mass contributions, as there is no direct matter mass component. This leads to an alternative formulation:

Fₚₕₒₜₒₙ = −Mᵃᵖᵖaᵉᶠᶠ , since Mᴍ = 0

Fₚₕₒₜₒₙ = Mᵉᶠᶠaᵉᶠᶠ ,  since (Mᴍ −Mᵃᵖᵖ) = Mᵉᶠᶠ, Mᴍ = 0, Mᵉᶠᶠ < 0.

This formulation suggests that under negative effective mass conditions, repulsive gravitational effects emerge naturally, influencing photon trajectories. The result is a bending of light paths around massive objects, providing a classical mechanism for gravitational lensing without requiring the concept of spacetime curvature.

Furthermore, ECM provides a conservation framework for photon energy interactions in gravitational fields. The energy-momentum relation (p = hf/c) is extended to incorporate apparent mass (Mᵃᵖᵖ) and negative inertia, revealing that a photon undergoing gravitational lensing experiences a symmetrical energy exchange: a blueshift as it approaches a gravitational well and a redshift as it recedes. This process maintains the photon's intrinsic energy (E) while explaining observed light bending.

In summary, ECM presents a refined classical explanation for light deflection in gravitational fields by extending Newtonian mechanics to account for apparent mass effects. This approach provides an empirically consistent alternative to relativistic spacetime curvature and invites further examination of fundamental gravitational interactions.

QM Description of Photon Interaction in External Gravitational Field:

A photon, representing light, carries inherent energy denoted as E. A photon emitted from a gravitational well experiences a redshift (Δλ>0) as it moves outward, losing energy due to gravitational interaction. However, the photon’s behaviour changes significantly when it encounters a strong external gravitational field. As the photon approaches a strong external gravitational body, it undergoes a blueshift (Δλ < 0) due to its interaction with the external gravitational field. This shift occurs as a result of electromagnetic-gravitational interaction, causing the photon to follow an arc-shaped trajectory. During this process, the photon’s momentum increases, described by the relation Δρ=h/Δλ, where h is Planck’s constant. This momentum gain reflects the gravitational influence on the photon's trajectory.

As the photon completes the first half of its curved trajectory around the gravitational body, the blueshift transitions into a redshift (Δλ>0). At this point, the photon begins to lose momentum, following the relation Δρ=h/Δλ. This process indicates a symmetrical momentum exchange, where the photon experiences a balanced gain and loss of external energy (Eg), preserving symmetry in its overall energy behaviour. Importantly, while the photon undergoes these external changes in wavelength, momentum, and energy during its trajectory around the gravitational body, it retains its inherent energy (E). The only exception occurs when the photon loses energy (ΔE) while escaping the gravitational well of its source. Thus, despite these external interactions, the photon’s inherent energy remains conserved, except for the loss associated with its initial emission. After bypassing the gravitational field, the photon resumes its original trajectory, maintaining its inherent energy (E) and continuing unaffected by further gravitational influences.

Conclusion:

The observed symmetry, where photons gain energy as they approach an external gravitational well and lose energy as they recede, could provide critical insights into refining our understanding of spacetime and gravity. These findings highlight a fundamental discrepancy between observed photon behaviour and the predictions of general relativity, suggesting that GR may be incomplete. By reconsidering gravitational interactions through ECM and QM principles, we open new pathways toward a more unified understanding of gravity and light propagation. By engaging with alternative models like quantum gravity and flat spacetime theories, we can advance our understanding of the universe’s underlying principles, contributing to a more complete and unified description of reality.