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.

The Emergence of Time from Physical Existence and Events:

Time is the indefinite, continuous progression of existence and events encompassing the past, present, and future, collectively forming a unified whole. This progression occurs in an irreversible and uniform succession, often conceptualized as the fourth dimension, complementing the three spatial dimensions.

This definition suggests that 'existential events invoke cosmic time,' meaning that:

1. Existence is physical: The tangible reality forms the basis of all that exists.

2. Events are changes in the properties of physical existence: Alterations or transformations in the state of physical entities constitute events.

3. Time is an emergent concept arising from existential events: The perception of time stems from the occurrence and sequencing of events.

4. Both existence and events are necessary for the emergence of time: Without physical entities and their interactions, the concept of time would be meaningless.

5. Events cannot occur without existence: Changes presuppose the presence of entities to undergo transformation.

6. Time would not emerge without existential events: In the absence of events, there would be no framework to perceive or measure time.

Thus, when we utilize a clock, we are effectively invoking cosmic time. We reference the fundamental continuum of existence to justify our measurement of time intervals. The clock serves as a bridge, connecting the abstract concept of cosmic time with the practical act of time measurement.

This perspective aligns with the relational view of time, which posits that time is not an independent entity but is instead a system of relations among events.

Philosophers like Leibniz have argued that time is a construct that arises from the ordering of events, rather than an absolute entity existing independently of the physical world. 

In summary, time emerges from the dynamic interplay of physical existence and events. Our tools for measuring time, such as clocks, are practical manifestations that link this emergent concept to our daily experiences.

Re-evaluating the Interpretation of Light Bending in Gravitational Fields

Soumendra Nath Thakur 

February 15, 2025

The concept of "wrapping of space" is often interpreted as the wrapping of spacetime, forming the basis for the relativistic explanation of gravitational lensing and the Einstein Ring. This interpretation attributes the bending of light to spacetime curvature, yet an alternative perspective grounded in classical gravitational fields offers a more consistent explanation.

Observational evidence of light bending around massive objects is frequently cited as confirmation of relativistic spacetime curvature. However, gravitational fields themselves, as described in classical mechanics, inherently account for the deflection of light. If light bending were solely a consequence of spacetime curvature, the massive object generating the curvature should obstruct the bent light from reaching an observer. In contrast, considering light bending within a gravitational field avoids this inconsistency and remains aligned with empirical observations.

This raises a fundamental question: If a curved gravitational field around a massive body can provide a consistent and empirically supported explanation for the bending of light, why should these observations be interpreted as evidence of relativistic spacetime curvature? A reconsideration of the classical gravitational framework may offer a more precise understanding of light deflection phenomena, challenging the prevailing relativistic interpretation.

Contrast Between Philosophy and Science:

February 15, 2025

Consider the question: What if this philosophical construct (presented within an image, attached below) were plotted on a three-dimensional mathematical graph? Only then would the scientific facts behind it be fully justified.

Take, for example, the Penrose Triangle—an "impossible" figure first conceptualized 62by Swedish artist Oscar Reutersvärd in 1934 and later rediscovered in the 1950s by physicist Roger Penrose. Described as "impossibility in its purest form," this figure was popularized by Penrose and further explored in the works of M.C. Escher. It appears to be a solid structure composed of three straight sections of square beams, seamlessly joined at right angles.

However, its paradoxical nature cannot be conclusively analyzed through mere physical observation and philosophical interpretation. Instead, by mathematically plotting the enclosed three-dimensional image onto a precise three-dimensional graph, its inherent absurdity becomes evident. The deceptive illusion, which seems structurally feasible in a two-dimensional representation, is mathematically exposed as an impossible configuration in three-dimensional space.

Image 

Abstraction vs. Reality

Addressing the statement: "Abstract mathematics is based on logical principles rather than empirical validity. It does not rely solely on physical evidence."

When we add one apple to another, we perceive two apples. However, the concept of "two" itself is an abstract mathematical construct rather than a directly observable physical entity. The sum exists as a logical principle within mathematics, not as a tangible proof in itself.

All real numbers—1, 2, 3, and beyond—are fundamentally conceptual, created within the framework of mathematical reasoning rather than derived from physical evidence. While mathematical concepts often align with physical reality, their foundation is purely abstract, shaped by human perception and logical consistency rather than empirical observation.

Mathematics is not confined to the physical universe; its abstract principles hold universally, independent of space, time, or physical existence. It is the fundamental language of the cosmos—objective, unique, and uninfluenced by human divisions such as culture, religion, or race.

Physicists seek mathematical formulations to explain the origins, structure, and dynamics of the universe. In doing so, they attempt to decipher the underlying mathematical order that governs both the observable universe and any potential realities beyond it. Understanding the universe is, in essence, understanding its mathematical nature.

For philosophy to be scientifically meaningful, it must be grounded in abstract mathematical logic. Without mathematical rigor, philosophical reasoning remains speculative and cannot be accepted as a scientific discipline.

Conclusion

This distinction underscores a fundamental contrast between philosophy and science: while philosophy interprets illusions conceptually, science—through mathematical rigor—reveals their underlying reality.

Attachment: the image as stated in the above mentioned text.

February 21, 2025

Revisiting the Penrose Triangle :

Karl Pfeifer, Your statement, "Not quite so impossible if you know what you're doing. It's a matter of point of view," appears to distort the discussion. 

The three-dimensional construction of the object clearly represents its original structure, as shown in the image Penrose triangle.jpg. Meanwhile, the other image, Penrose Two-dimensional.jpg, illustrates an illusionary perception from a specific viewpoint where the object appears to have all its ends joined. In reality, only two ends are connected, while the third remains separate. 

This illusion results from a two-dimensional projection of a three-dimensional structure, making the impossible geometry seem plausible from a particular perspective. Additionally, the image enhances the illusion more prominently than what one would perceive when viewing the physical object up close.

Your comment suggests an unnecessary willingness to accept or entertain an absurdity as a real possibility. This tendency is often observed in individuals who prioritize appearing overly insightful rather than applying nuanced thinking to understand objective reality

Penrose Triangle 

Penrose Two-dimensional.

Clarifying the Concepts of Antigravity, Dark Energy, and Negative Apparent Mass in Extended Classical Mechanics (ECM)

Soumendra Nath Thakur

February 13, 2025

The assertion that "antigravity is an unlikely phenomenon" is inconsistent with established observations. The behaviour of photons provides direct evidence to the contrary. According to its energy, a photon possesses effective mass and is observed to escape gravitational wells, demonstrating a counteracting effect against gravity. Extended Classical Mechanics (ECM), a framework built upon classical mechanics principles, provides a clear formulation of this phenomenon. ECM reveals that photons exert an antigravitational force on massive bodies, accelerating at twice the speed of light within gravitational influence. As a photon leaves a gravitational well, it expends energy but retains its inherent energy, continuing to travel at the speed of light in free space. This indicates that antigravitational effects are an intrinsic feature of certain mass-energy interactions, contradicting the claim that antigravity is unlikely.

The notion that "dark energy is not real" is only partially correct. While dark energy is not a physical object with rest mass, its effects are observable. ECM equations establish dark energy as a form of potential energy with a dynamic nature, existing only as a consequence of gravitational and motion dynamics of massive bodies. Rather than being an independent entity, dark energy emerges from the interplay of gravity and motion at cosmic scales, reinforcing its role in large-scale universal dynamics.

Similarly, the claim that "negative mass lacks a physical description and remains unproven" overlooks key insights provided by ECM. Rather than considering negative mass as a standalone entity, ECM introduces the concept of negative apparent mass, which arises from motion and gravitational interactions. This phenomenon does not imply an intrinsic negative mass but rather an emergent property influenced by both baryonic matter and dark matter. ECM principles illustrate how apparent mass contributes to gravitational effects, expanding the understanding of mass-energy interactions beyond conventional classical mechanics.

These refinements in ECM extend classical mechanics while maintaining consistency with empirical observations, providing a structured approach to understanding gravitational repulsion, dark energy, and the role of apparent mass in astrophysical phenomena.