A Revised Framework for the Photon-to-Dark-Energy Transition: Refining Photon Gravitational Dynamics

Soumendra Nath Thakur
December 07, 2024

Abstract:

This study presents a revised framework for understanding the photon-to-dark-energy transition, building upon Peter Rafay’s hypotheses and integrating concepts from Extended Classical Mechanics (ECM). The research extends classical and quantum principles to provide a more mathematically consistent and theoretically robust model of photon behaviour in gravitational fields, incorporating negative effective mass and gravitational dynamics. Central to the framework is the redefinition of photon mass as effective mass (Mᵉᶠᶠ), which allows for the exploration of photon interactions with gravity in terms of dark energy's properties, such as antigravitational effects. The key hypotheses proposed include the threshold frequency of electromagnetic radiation at Planck’s frequency, photon cessation under gravitational influence, and the transformation of photon energy into dark energy, which impacts gravitational dynamics without exhibiting motion.

Mathematical modelling plays a crucial role in the theoretical foundation, with relations such as the Planck-scale energy-frequency relation (E = hf) and energy-momentum exchange adapted to incorporate negative inertia. A force equation governing photon behaviour in gravitational fields, F = −Mᵃᵖᵖ⋅aᵉᶠᶠ, is derived, ensuring consistency with energy conservation and quantum principles. The study critiques and refines Rafay’s work, particularly the concept of photon cessation, replacing it with a model in which photon energy is transformed into dark energy, preserving the conservation of energy.

The research methodology incorporates quantum gravitational effects at the Planck scale and examines indirect observational data such as gravitational lensing and redshift to validate the model. The revised framework not only supports but strengthens the speculative aspects of Rafay’s hypothesis, offering a clearer and more comprehensive explanation of photon dynamics and the transition to dark energy. Future directions include experimental efforts to probe quantum gravity and further refinement of the photon-to-dark-energy transition, providing a unified approach to photon gravitational dynamics and cosmological acceleration.

Keywords: Photon Dynamics, Gravitational Interaction, Planck’s Frequency, Dark Energy, Planck Scale, Extended Classical Mechanics, Photon Energy Transition, Fundamental Constants, Quantum-Gravity Phenomena.

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Tagore’s Electronic Lab, West Bengal, India
Correspondence:
postmasterenator@gmail.com, postmasterenator@telitnetwork.in
Declaration:
Funding: No specific funding was received for this work.
Potential competing interests: No potential competing interests to declare.

___________________________________________

Introduction

The interplay between photons and gravitational fields remains a cornerstone of modern physics, bridging concepts in quantum mechanics and general relativity. Despite extensive exploration, many questions surrounding the extreme behaviour of photons under gravitational influence remain unresolved. Central to these inquiries is the phenomenon of gravitational lensing and the broader implications of photon-gravitational interactions. This study delves deeper into these dynamics, proposing a novel perspective on photon behaviour at the Planck scale and its potential connection to dark energy.

One of the key hypotheses addressed in this research is the notion that photons, when subjected to photon-photon gravitational interactions, can cease oscillating at Planck's frequency. This cessation marks the transformation of photon energy into dark energy, a mysterious form of energy that exerts gravitational effects without associated motion or oscillation. Such a transition challenges conventional understandings of energy conservation and the role of fundamental constants like Planck’s length, Planck’s energy, and Planck’s frequency.

This work is grounded in Peter Rafay I’s theoretical framework, which asserts that Planck’s frequency represents the upper threshold of photon energy. Beyond this limit, photons can no longer sustain electromagnetic oscillations, thereby undergoing a transformation into a state consistent with dark energy. This transition not only redefines the behaviour of photons under extreme conditions but also introduces a potential pathway for understanding the enigmatic properties of dark energy—a phenomenon that governs the accelerated expansion of the universe.

The study examines the fundamental role of gravitational interactions in driving this transition, specifically focusing on the relationships among:

1. Planck’s constants and their interplay with photon energy and distance.

2. The cessation of oscillatory behaviour at critical thresholds.

3. The theoretical mechanics underlying the transformation of energy into a non-oscillatory, non-moving state.

Through this lens, we aim to construct a theoretical framework that connects photon dynamics to the cosmological implications of dark energy. By addressing these intersections, the research seeks to expand the boundaries of classical and quantum mechanics, offering insights that may contribute to the development of a unified theory of fundamental forces.

This introduction sets the stage for a detailed exploration of photon-gravitational interactions, emphasizing their relevance in both microcosmic and macrocosmic phenomena. As we move forward, we explore the mathematical and conceptual underpinnings of these processes, shedding light on the profound implications they hold for understanding the universe’s most fundamental mysteries.

Methodology

1. Theoretical Framework

The research methodology begins with the adoption of Extended Classical Mechanics (ECM), integrating concepts of apparent mass and gravitating mass to understand photon dynamics in gravitational fields. The work draws from both classical mechanics and quantum physics, extending classical principles to accommodate quantum effects at the Planck scale.

• Photon Effective Mass: The concept of effective mass (Mᵉᶠᶠ) for photons is central, drawing upon their energy-momentum relations. This redefinition of mass allows the study of photon interactions with gravity in a way that incorporates dark energy’s characteristics, such as negative apparent mass.

• Dark Energy and Apparent Mass: The interaction between photons and gravitational fields is modelled using the relationship between negative effective mass and gravitational dynamics, directly correlating photon behaviour with cosmological acceleration and dark energy effects.

2. Hypothesis Formulation and Key Claims

The study is structured around a series of key hypotheses based on Rafay's work and ECM:

• Threshold Frequency: The frequency of electromagnetic radiation reaches a limit at Planck’s frequency.

• Photon Cessation: The interaction between photons in gravitational fields results in the cessation of their oscillatory motion.

• Energy Transformation: Photon energy is hypothesized to transform into dark energy, which influences gravitational dynamics but does not exhibit oscillation.

• Gravitational Energy: Gravitational interactions at quantum scales are hypothesized to depend on the ratio of Planck's length to the distance between interacting objects, as well as the relative energies of those objects.

3. Mathematical Modelling

Mathematical modelling plays a critical role in grounding the hypotheses in rigorous physics, focusing on key relationships and quantum scale adjustments:

• Energy-Frequency Relation: The Planck-scale relation E=hf is employed to describe photon energy and its potential transition to dark energy.

• Energy-Momentum Exchange: The energy-momentum relation p = hf/c (de Broglie’s photon momentum) is extended to incorporate apparent mass (Mᵃᵖᵖ) and negative inertia.

• Planck’s Scale Relation: Utilizing the Planck length (ℓP) and Planck time (tP) through the equation ℓP/tP = c, the model incorporates the smallest meaningful scales where quantum gravitational effects dominate.

• Photon Dynamics and Force: A force equation, F = − Mᵃᵖᵖ⋅aᵉᶠᶠ, where aᵉᶠᶠ represents the effective acceleration due to gravitational fields, governs photon behaviour at the Planck scale.

4. Quantum Gravitational Interactions

Quantum considerations are introduced to refine gravitational dynamics, especially when energy and mass approach Planck’s limits:

• Threshold Frequency and Photon Behaviour: The threshold frequency at Planck’s frequency leads to modifications in photon behaviour, governed by quantum gravitational forces that can result in the cessation of oscillatory motion, as photons transition into dark energy.

• Gravitational Energy Modulation: At micro-scales, gravitational energy dynamics are heavily influenced by the ratio of Planck’s length to the distance between interacting objects. The energy threshold at which gravitational energy is affected by Planck-scale factors is explored.

5. Empirical and Observational Considerations

Though direct detection of quantum gravitational effects at the Planck scale is not currently feasible, the methodology incorporates indirect observational techniques:

• Gravitational Field Lensing and Redshift: These phenomena are analysed through the lens of photon dynamics in extended classical mechanics, particularly focusing on the energy exchanges that result from gravitational interactions.

• Cosmological Models: Dark energy’s effects on cosmic expansion and gravitational behaviour are modelled based on its negative effective mass and antigravitational properties.

6. Refinement of Rafay’s Hypothesis

The methodology critiques and refines Rafay’s work, addressing speculative aspects with a more rigorous framework:

• Photons and Dark Energy: The transformation of photon energy into dark energy is modelled not merely as a speculative hypothesis but as a transition governed by the relationship between effective mass and gravitational dynamics, thereby offering a consistent theoretical explanation.

• Photon Cessation: The claim of photon cessation due to gravitational interaction is reconsidered in light of the conservation of energy. Rather than ceasing, photon energy is transformed, adhering to established physical laws.

7. Model Validation and Consistency Checks

Consistency checks are carried out by comparing the predictions of the extended classical mechanics framework with existing astrophysical observations, such as the behaviour of galaxies under dark energy and the cosmic expansion rate. Additionally, mathematical consistency is ensured by ensuring the logical coherence of all derived equations with established physics principles (e.g., energy conservation, general relativity, and quantum mechanics).

8. Conclusions and Future Directions

The methodology concludes by synthesizing the findings of the theoretical framework with observational evidence, highlighting the unified theory of gravitational interactions. Future research directions focus on:

• Testing Quantum Gravity Models: Developing experimental methods to probe quantum gravitational effects at the Planck scale.

• Advancing the Photon-Dark Energy Transition: Further refinement of the mathematical models to explore the full implications of photon transition to dark energy in various astrophysical scenarios.

This methodology bridges classical mechanics, quantum theory, and cosmology, providing a unified approach to understanding photon dynamics, gravitational interactions, and dark energy, while addressing the speculative nature of existing hypotheses.

Theoretical and Mathematical Framework:

In the article "About the Gravitational Interaction of Photons," Peter Rafay explores the theoretical behaviour of photons under the influence of gravitational forces. The key findings of the study are:

1. The threshold frequency of electromagnetic radiation (photons) is equal to Planck's frequency.

2. Under the influence of gravity between photons, the radiation will cease, effectively stopping.

3. The energy of the photons will transform into what is termed 'dark energy,’ a form of energy that influences gravity but does not exhibit movement or oscillation.

4. Gravitational energy is influenced by the ratio of Planck's length to the distance between two interacting objects, as well as the ratio of the multiplied energies of two interacting particles to Planck’s energy, which are constants in nature.

Rafay’s work introduces a novel perspective on how gravitational energy can be influenced by fundamental constants and provides a theoretical framework for further research into the gravitational interactions of photons and the role of dark energy.

Extended Classical Mechanics Framework and Photon Dynamics

The series of research papers by Soumendra Nath Thakur delves into the extended classical mechanics framework, addressing various aspects of photon dynamics, gravitational interactions, and dark energy. Key highlights of these studies are as follows:

1. Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass, and Gravitational Dynamics:

This paper reinterprets the classical equivalence principle by integrating the concepts of Apparent Mass (Mᵃᵖᵖ) and Gravitating Mass (Mɢ). It extends the principle to include insights on both ordinary and dark matter, suggesting that negative apparent mass plays a crucial role in gravitational dynamics and aligns with modern research on dark energy.

2. A Nuanced Perspective on Dark Energy: Extended Classical Mechanics:

This work introduces the concept of effective mass (Mᵉᶠᶠ) for photons, reinterpreting their interaction with gravity. The study suggests that the negative effective mass, similar to dark energy's properties, leads to antigravitational effects, contributing to cosmic acceleration and offering a unifying perspective between quantum and cosmological phenomena.

3. Photon Dynamics in Extended Classical Mechanics:

This paper investigates the effective mass of photons and its implications for force interactions. By redefining photons' dynamics using effective mass, the study draws analogies between the photon’s behaviour and dark energy, offering insights into gravitational lensing, redshift, and the role of energy-momentum interactions.

4. A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields:

This research examines the symmetrical energy exchanges between photons and gravitational fields, distinguishing between intrinsic photon energy (E) and gravitational-interaction energy (Eg). The paper highlights the importance of these energy components in understanding gravitational lensing, redshift, and photon behaviour within gravitational wells.

Together, these studies present an advanced framework of extended classical mechanics that bridges classical, quantum, and cosmological perspectives, offering new insights into photon dynamics, gravitational interactions, and the nature of dark energy. The work emphasizes the role of negative effective mass and gravitational energy in shaping the universe's fundamental forces and paves the way for future research in these areas.

Unifying Photon Gravitational Dynamics and Dark Energy within Extended Classical Mechanics

The research presented in my work builds upon linking dark energy to photon gravitational dynamics through the concepts of apparent mass and negative effective mass within the framework of extended classical mechanics. This approach integrates fundamental relations such as Planck’s Energy-Frequency Relation (E=hf), de Broglie Photon Momentum-Wavelength Relation (ρ=h/λ), and the Planck Scale Relation (ℓP/tP = c). These principles provide the mathematical foundation for understanding photon dynamics and their transition into dark energy^.[1][2]

In contrast, Peter Rafay’s research, "About the Gravitational Interaction of Photons," proposes a speculative hypothesis in which photons, at Planck’s frequency, transform into dark energy. Rafay’s assertions highlight the following^:[4]

1. Photons reach a threshold frequency equal to Planck’s frequency.

2. The gravitational interaction between photons causes them to cease oscillating.

3. Photon energy undergoes a transformation into dark energy.

4. This dark energy affects gravity but does not exhibit physical motion or oscillation.

5. Gravitational energy is influenced by the ratio of Planck's length and the distance between interacting objects, as well as the energies of interacting particles relative to Planck’s energy.

My own work, including the following studies:

1. Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass, and Gravitational Dynamics,

2. A Nuanced Perspective on Dark Energy: Extended Classical Mechanics,

3. Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange, and Analogies with Dark Energy,

4. A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields, provide a more mathematically consistent and theoretically robust framework that supports Rafay's hypothesis. I demonstrate that at the Planck length, photons become imperceptible, aligning with the characteristics of dark energy. My research offers a unified approach, grounded in extended classical mechanics and electromagnetic wave theory, which not only extends but clarifies and strengthens the speculative nature of Rafay's hypothesis. This work moves beyond mere speculation, offering a clear, consistent, and comprehensive explanation of the photon-to-dark-energy transition at the Planck scale^.[5][6][7[8]

Mathematical and Conceptual Revisions

1. Threshold Frequency of Electromagnetic Radiation (Photon) and Planck Frequency

Rafay's assertion regarding the threshold frequency of photons at Planck’s frequency finds alignment in my research. However, the Planck frequency can be expressed mathematically as:

fP = c/ℓP

where c is the speed of light and ℓP is the Planck length. This frequency forms the upper limit of measurable electromagnetic radiation and situates photons at quantum scales, beyond which classical physics no longer holds.^[1]

2. Photon "Cessation" and Gravitational Interactions

Rafay’s claim of photon cessation due to gravitational interactions contradicts energy conservation laws. In extended classical mechanics, this is addressed by modelling photon dynamics as follows:

F = − Mᵃᵖᵖ⋅aᵉᶠᶠ

where Mᵃᵖᵖ represents the apparent mass of the photon and aᵉᶠᶠ is the effective acceleration due to gravitational interaction. This formulation ensures that photons continue to exhibit behaviour consistent with energy conservation, even under extreme gravitational conditions^.[6][8]

3. Photon Energy Transforming into Dark Energy

In contrast to Rafay’s claim, my research reinterprets the transition of photon energy into dark energy through the concept of negative effective mass. The equation for this transformation can be derived as follows:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

This describes the photon’s energy being transferred into an effective mass that influences gravitational dynamics. This relationship is crucial for understanding cosmic acceleration and the role of dark energy in shaping the universe^{.[5][6][7][8]}

Conclusion: The integration of quantum-scale principles with classical mechanics offers a consistent framework for understanding photon dynamics in gravitational fields. By expanding on Rafay’s hypothesis through mathematical modelling, I present a comprehensive approach to the photon-to-dark-energy transformation, emphasizing the role of apparent mass and effective mass in gravitational interactions. This work refines the speculative nature of Rafay’s claims, providing a mathematically grounded explanation consistent with fundamental physical laws.

Discussion

The study presented examines the intersection of photon dynamics, gravitational interactions, and the nature of dark energy, bridging ideas from classical mechanics, quantum physics, and cosmology. By refining Peter Rafay's hypotheses on photon behaviour under gravitational influence, this work provides an advanced and mathematically consistent framework that not only supports but also strengthens and clarifies the speculative nature of Rafay’s ideas. In particular, it explores the potential transformation of photon energy into dark energy, a process that could offer new insights into the mysteries of the universe's accelerated expansion and the gravitational behaviour of photons.

The concept of photon-photon interactions, particularly at the Planck scale, is central to the research. Rafay’s hypothesis that photons cease oscillating when subjected to gravitational interactions is revisited and revised. While Rafay proposed that this cessation results in the transformation of photon energy into dark energy, this interpretation challenges conventional notions of energy conservation. The study offers a more refined perspective by introducing the idea of negative effective mass, which allows the energy of photons to be transferred into dark energy without violating energy conservation laws. This approach provides a coherent theoretical explanation, supported by mathematical models, that aligns with established principles of physics.

The research integrates the concept of effective mass (Mᵉᶠᶠ) for photons, which is central to understanding their behaviour in gravitational fields. By extending classical mechanics to incorporate quantum effects, the study successfully addresses the relationship between photon energy, gravitational fields, and dark energy. The negative effective mass, analogous to dark energy’s properties, leads to anti-gravitational effects that contribute to cosmic acceleration, providing a unified perspective on quantum and cosmological phenomena.

Rafay’s original idea of the threshold frequency, wherein photons reach a limit at Planck's frequency, is corroborated in the study, with the Planck frequency fP = c/ℓP, where c is the speed of light and ℓP is the Planck length, serving as the upper bound for photon energy. This insight is pivotal in understanding how photons behave at quantum scales and how they might transition into a state that influences gravitational dynamics without exhibiting movement or oscillation.

The reinterpretation of photon cessation is also crucial. In the original hypothesis, photons were said to cease oscillating due to gravitational interactions, a notion that contradicted the conservation of energy. By applying the framework of extended classical mechanics, the study demonstrates that photons continue to exhibit behaviour consistent with energy conservation, even at extreme gravitational conditions. The force equation F = − Mᵃᵖᵖ⋅aᵉᶠᶠ, where Mᵃᵖᵖ represents the photon’s apparent mass and aᵉᶠᶠ is the effective acceleration, ensures that photons’ energy persists, albeit in a transformed state that influences gravitational fields.

In terms of the photon-to-dark-energy transition, the research suggests that photon energy is not lost but rather transformed into a state that resembles dark energy through the concept of negative effective mass. This transformation is modelled mathematically by incorporating the relationship Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ), where Mᴍ represents the mass of the interacting objects and −Mᵃᵖᵖ represents the negative apparent mass of the photon. This equation provides a theoretical foundation for understanding how photons might contribute to the dynamics of cosmic acceleration and the observed effects of dark energy.

Ultimately, the study emphasizes the importance of developing a unified theory that connects photon dynamics with cosmological phenomena such as dark energy and gravitational lensing. By expanding the framework of extended classical mechanics to incorporate quantum-scale interactions, the research presents a comprehensive model that provides deeper insights into the nature of the universe. It highlights the need for further exploration of these phenomena at both the theoretical and observational levels, with future directions focusing on testing quantum gravity models and advancing our understanding of the photon-dark-energy transition.

This work not only refines existing theories but also opens new avenues for investigating the interplay between gravity, photons, and dark energy, which could potentially lead to the development of a more unified theory of the fundamental forces in nature. Through its combination of classical mechanics, quantum physics, and cosmology, it provides a promising foundation for future research into the mysteries of the cosmos.

Conclusion

This study has explored the intricate relationship between photon dynamics, gravitational interactions, and the nature of dark energy, synthesizing ideas from classical mechanics, quantum physics, and cosmology. By extending Peter Rafay's hypotheses on photon behaviour under gravitational influence, a more mathematically consistent and theoretically robust framework has been developed, offering new insights into the photon-to-dark-energy transformation.

Through the introduction of the concept of effective mass (Mᵉᶠᶠ) for photons, this research has provided a comprehensive explanation for photon interactions in gravitational fields. Negative effective mass, akin to dark energy’s characteristics, was identified as a central factor in understanding cosmic acceleration and gravitational lensing, offering a unified perspective that bridges quantum and cosmological phenomena.

The study revisited Rafay’s proposition of photon cessation at Planck’s frequency, refining this idea within the constraints of energy conservation. Instead of ceasing, photon energy is hypothesized to transform into dark energy through the concept of negative effective mass, contributing to gravitational dynamics without violating established physical laws.

By modelling these interactions mathematically—through equations such as F = − Mᵃᵖᵖ⋅aᵉᶠᶠ and Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) —the research provides a consistent theoretical framework that not only clarifies but strengthens the speculative nature of Rafay’s claims. This framework highlights the role of apparent mass and energy transformation in gravitational interactions, offering deeper insights into the role of photons in shaping the universe's fundamental forces.

In conclusion, this work lays the foundation for future research in photon-gravitational dynamics and dark energy. It proposes a unified theory that could lead to a deeper understanding of the universe’s accelerated expansion, gravitational lensing, and the nature of dark energy. As this theoretical framework continues to evolve, future studies will refine the photon-to-dark-energy transition and test quantum gravity models, potentially revealing new dimensions in our understanding of the cosmos.

References:

[1] Planck, M. (1914). The theory of heat radiation (Morton Masius, Trans.) [Book]. P. Blakiston’s Son & Co. https://www.gutenberg.org/files/40030/40030-pdf.pdf

[2] Dingle, H. (1941). Matter and Light: The New Physics. By Louis de Broglie. Translated by W. H. Johnston, B.A. (London: George Allen ’ Unwin, Ltd.1939. Pp. 300. Price 12s. 6d. net.). Philosophy, 16(62), 210–211. https://doi.org/10.1017/s0031819100002370

[3] Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013a). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781

[4] Peter Rafay I. About the Gravitational Interaction of Photons. J Phys Astron. 2017; 5(3):130. https://www.tsijournals.com/articles/about-the-gravitational-interaction-of-photons-13560.html

[5] Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics - [v3]. 202409.1190/v3. https://www.preprints.org/manuscript/202409.1190/v3

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

[7] Thakur, S. N. (2024). Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy. Preprints.org (MDPI), 202411.1797.v1. https://doi.org/10.20944/preprints202411.1797.v1

[8] Thakur, S. N. (2024). A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. Preprints.org (MDPI), 202411.0956.v1. https://doi.org/10.20944/preprints202411.0956.v1

Justification of Angular Representation in Time Dilation

December 05, 2024

Dear Mr. Andrew Marcu,

I appreciate the time and effort you've invested in reviewing my work and providing your detailed critique. Below, I address the concerns you raised, clarifying and reinforcing my research's scientific basis:

1. On Time Dilation and Presentation Consistency

You noted:

“The text asserts that t - t₀ > t′ − t₀ (correct for time dilation), then reverses this with t < t′, introducing internal inconsistency.”

However, your statement that t - t₀ > t′ − t₀ is "correct for time dilation" is itself incorrect. Time dilation enlarges the observed time t′, making t - t₀ < t′ − t₀. This aligns with t<t′, confirming there is no inconsistency in my presentation. The apparent contradiction you highlighted stems from a misinterpretation rather than an actual error in my argument.

2. Angular Representation of Time Scales

You argued:

“The attempt to represent time scales in angular terms (t×360°) is non-standard and lacks a clear physical justification.”

Contrary to your claim, the angular representation has clear foundations in both classical mechanics and wave theory. A standard clock face divides 360° into 12 segments, correlating to periodic cycles in timekeeping. Similarly, in wave mechanics, a full cycle spans 360°, with the time shift for an angular phase x° given as:

T(deg) = Δt = x°/f⋅360°.

This mathematical basis is neither arbitrary nor unconventional but extends directly from established principles. For a dilated time t′, this framework explains how standard clock designs fail to reflect dilation precisely, resulting in "errored" time readouts.

An alternative perspective to your disagreement, which states, 'angular terms (t×360°) is non-standard and lacks a clear physical justification,' is that this objection is unfounded. Structurally, a standard clock face divides 360° into 12 equal segments, assigning 30° to each hour (360°/12). When the minute hand completes a full rotation (360°), it marks one hour, directly correlating the clock’s full rotation to a single period, T=360°.

Similarly, in wave mechanics, a complete cycle of a sine wave spans 360° of phase, establishing a standard period T=360°. The frequency f of a wave is inversely proportional to its period T, expressed as T=1/f. For each degree of phase in a sine wave, the time shift per degree is given by:

T/360°, or equivalently (1/f)/360°

For a phase shift of x°, the corresponding time shift is:

T(deg) = Δt = (x°/f)/360

In the case of proper time t, a full oscillation corresponds to T=360, yielding Δt=0 by design. Under time dilation, however, Δt′>Δt, resulting in Δt′>0. For a 1° phase shift in Δt, the dilated interval becomes:

Δt′=(1°/f)/360°

For a general x° phase shift:

Δt′=(x°/f)/360°

Applying this concept to a clock, each hour segment, designed to measure proper time t, corresponds to exactly 30° (360°/12). If time dilation causes the interval to stretch to 361°, each segment would then measure approximately 361°/12≈30.08°, exceeding the clock’s designated 30° marking for proper time t.

As a result, the clock, which is calibrated for proper time, cannot accurately reflect the dilated time t′, leading to an “errored” time readout. This demonstrates the validity of angular representation as a practical and scientifically coherent method to illustrate time dilation.

3., Relevance of Classical Mechanics

You contended:

“The discussion of classical mechanics (Hooke’s law, mechanical stress) is irrelevant to relativistic time dilation.”

While relativity primarily addresses time dilation in non-inertial or gravitational contexts, classical mechanics provides insight into the practical implications of mechanical systems, including clock deformations under acceleration or stress. This connection bridges theoretical relativity with real-world clock behaviour, offering a holistic understanding of timekeeping inaccuracies.

4. On Relativity and Non-Inertial Effects

Your statement:

“The claim that relativity does not comprehensively account for forces during acceleration is incorrect.”

While relativity does account for non-inertial effects through proper time calculations, the interplay of such forces with classical mechanics during acceleration is often underexplored in practical applications. My work seeks to address this gap, offering a complementary perspective rather than negating relativity's achievements.

5. General Observations

You described certain phrases, such as "the time dimension originates from and returns to a common point," as vague. These are conceptual expressions aimed at stimulating further thought and should be understood as part of a broader discourse rather than definitive scientific assertions.

Invitation for Further Exploration

To delve deeper into the foundational concepts and evidence supporting my framework, I invite you to review the following research papers:

1. Phase Shift and Infinitesimal Wave Energy Loss Equations http://dx.doi.org/10.13140/RG.2.2.28013.97763

2. Relativistic effects on phaseshift in frequencies invalidate time dilation II http://dx.doi.org/10.36227/techrxiv.22492066.v2

3. Reconsidering Time Dilation and Clock Mechanisms: Invalidating the Conventional Equation in Relativistic Context: http://dx.doi.org/10.13140/RG.2.2.13972.68488

4. Re-examining Time Dilation through the Lens of Entropy: http://dx.doi.org/10.32388/XBUWVD

5. Standardization of Clock Time: Ensuring Consistency with Universal Standard Time http://dx.doi.org/10.13140/RG.2.2.18568.80640

6. Formulating Time's Hyperdimensionality across Disciplines http://dx.doi.org/10.13140/RG.2.2.30808.51209

I hope these works provide clarity and address the concerns you've raised. Should you have further questions or wish to engage in constructive dialogue, I am more than willing to elaborate.

Best regards,

Soumendra Nath Thakur

Response to Critique on Photon Dynamics in Gravitational Fields: Extended Classical Mechanics

December 05, 2024

Dear Mr. Andrew Marcu,

Thank you for your feedback. While I respect your perspective, I must address the points raised in light of the research I've presented, which is grounded in a robust re-examination of classical and quantum mechanics as applied to photon dynamics in gravitational fields. I maintain your concerns stem from conventional interpretations that this study directly challenges and seeks to refine, not merely re-interpret existing models. Allow me to provide clarifications to address your questions:

Photon Trajectories and Reversibility: The assertion that photon trajectories are inherently reversible is supported by the extended classical mechanics framework that I present. This theory doesn't simply claim that photons "resume their original path" in the traditional sense but rather emphasizes that the photon's momentum remains conserved throughout gravitational interactions. This reversibility can be rigorously described mathematically, as the photon continues its path even after gravitational interaction, resuming its original trajectory when the gravitational influence dissipates. The concept of photon trajectory deviation in gravitational field lensing is acknowledged, but it's reinterpreted within this framework as a consequence of effective mass interactions rather than a violation of photon trajectory preservation.

Intrinsic Energy and Gravitational Interaction: Regarding your comment on photon energy and gravitational redshift, I agree that gravitational redshift implies an energy shift as photons escape a gravitational well. However, the key distinction in my research lies in differentiating between intrinsic energy and gravitational energy. While general relativity emphasizes gravitational redshift, but the photon’s intrinsic energy (E) remains unaltered despite the gravitational influence (Eg) it experiences. This subtle but crucial differentiation challenges the traditional view, offering a deeper understanding of energy conservation in gravitational fields, as reflected in the mathematical framework provided.

Localization of Gravitational Energy and Photon Energy Dynamics: The claim that gravitational energy is localized to the massive body, and that photons retain only their intrinsic energy outside this influence, stems from my reinterpretation of gravitational interaction. Gravitational fields do affect photons universally, but the gravitational energy they interact with is context-dependent. In regions where gravitational influence is zero, the photon’s intrinsic energy predominates. This does not oversimplify the interaction but rather offers an alternative explanation to relativistic models that rely heavily on spacetime curvature. My work explicitly challenges the need for curvature-based explanations by focusing on energy-momentum exchanges that apply even in flat or no curved spaces.

Cosmic Redshift and Energy Loss: The treatment of cosmic redshift in my framework aligns with the concept of energy loss as tied to universal expansion due to the galactic recession, but it differs from the general relativistic interpretation. Instead of seeing this as a purely energy loss phenomenon, my model links this to intrinsic photon dynamics during the large-scale expansion of the universe, emphasizing the long-term energy reduction due to cosmic scale changes. This represents an opportunity for refinement of current theories that blend both quantum and cosmological models in an unprecedented way.

Negative Apparent Mass and Dark Energy: Your comment on the negative apparent mass of photons warrants a detailed clarification. In the context of extended classical mechanics, the concept of negative effective mass emerges from the need to explain the photon’s antigravitational interactions. Photons do not conform to conventional massless particle models. Their interaction with gravity is better explained through their effective mass, which can be negative and leads to phenomena akin to dark energy’s role in accelerating cosmic expansion. This concept, while unconventional, is grounded in a consistent theoretical framework that connects energy and momentum dynamics across both quantum and cosmological scales.

Photon Speed and the Role of Negative Force: The assertion that negative force maintains photon wave speed (c) does not contradict the established physics that the speed of light in a vacuum remains constant. My theory does not suggest the speed of light changes in free space; rather, it proposes that the effective force responsible for maintaining constant speed arises from the photon’s negative apparent mass. This ensures consistency with the constant velocity of light, even as the photon interacts with gravitational fields. The role of negative force is key to maintaining this speed despite the photon’s interactions with gravitational influences.

Negative Effective Mass and Quantum Mechanics: The concept of negative effective mass for photons is a direct extension of the framework where effective mass plays a crucial role in energy-momentum exchanges. While photons are indeed massless in the traditional sense, their interaction with gravity is better explained through effective mass, which can manifest as negative. This extends our understanding of mass and energy in gravitational dynamics and quantum mechanics, offering a fresh perspective that challenges the assumption that photons are simply massless and only influenced by energy.

Constant Photon Acceleration: The assertion that photons experience constant acceleration, with an acceleration value of 6 × 10⁸ m/s², does not conflict with the principles of special relativity. Rather, this constant acceleration reflects the photon’s interaction with gravitational fields and its resultant behaviour in the context of negative effective mass. This idea does not imply a deviation from the speed of light but rather ensures that the photon’s motion adheres to the underlying dynamics of the extended classical mechanics framework.

While I appreciate your critique, it is based on a framework that assumes the validity of traditional interpretations of photon dynamics, which my research actively challenges. The work I present in the study introduces a new, more comprehensive understanding of photon interactions in gravitational fields, supported by both conceptual models and mathematical derivations. I welcome further discussion and empirical exploration to substantiate these novel perspectives and demonstrate their potential for advancing our understanding of fundamental physics.

For a more detailed examination of the concepts presented, I invite you to explore the following series of research papers, which provide deeper insights into the theoretical underpinnings and empirical exploration of these ideas:

1. Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics

2. Dark Energy as a Consequence of Gravitational and Kinetic Interactions: The Dynamic Nature of the Universe

3. Unified Study on Gravitational Dynamics: Extended Classical Mechanics

4. Piezoelectric and Inverse Piezoelectric Effects on Piezoelectric Crystals: Applications across Diverse Conditions

5. Photon Interactions with External Gravitational Fields: True Cause of Gravitational Lensing

6. The Discrepancy between General Relativity and Observational Findings: Gravitational Lensing

7. A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields

8. Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy

9. Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy

Best regards,

Soumendra Nath Thakur

Author/researcher

NB: These papers address the theoretical foundations, mathematical formulations, and empirical evidence supporting the revised understanding of photon dynamics, gravitational interactions, and the concept of negative effective mass.

Gravitational Interaction of Photons: An Interpretation through Extended Classical Mechanics

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

December 05, 2024

Abstract

This study presents an extended classical mechanics interpretation of photon behaviour in gravitational fields, emphasizing the reversible nature of gravitational interactions and the preservation of intrinsic photon energy. The photon's energy dynamics are explored through its interactional energy within gravitational influences and its intrinsic energy in zero-gravity regions. The effects of cosmic expansion on photon energy via redshift are also discussed. Notably, the photon exhibits negative apparent and effective masses, producing antigravitational effects akin to dark energy, enabling constant wave speed c. A key insight includes the photon's constant effective acceleration from emission, highlighting its unique momentum and energy dynamics in gravitational contexts. This framework challenges conventional gravitational lensing interpretations, suggesting alternative pathways for unified theories of forces.

Author Comment:

This study synthesizes key conclusions derived from a series of research papers on extended classical mechanics. These papers provide a fresh perspective on established experimental results, challenging traditional interpretations and highlighting potential inaccuracies in previous theoretical frameworks. Through this reinterpretation, the study aims to refine our understanding of fundamental physical phenomena, opening avenues for further exploration and validation.

Keywords: Photon dynamics, Gravitational interaction, Negative mass, Cosmic redshift, Extended classical mechanics,

Reversibility of Gravitational Interaction:

A photon’s interaction with an external gravitational force is inherently reversible. The photon maintains its intrinsic momentum throughout the process and eventually resumes its original trajectory after disengaging from the gravitational field.

Intrinsic Energy (E) Preservation:

The photon's intrinsic energy E, derived from its emission source, remains unaltered despite gaining or losing energy (Eg) through gravitational interaction within a massive body's gravitational influence.

Contextual Gravitational Energy (Eg):

The gravitational interaction energy Eg is a localized phenomenon, significant only within the gravitational influence of a massive body. Beyond this influence, in regions of negligible gravity, the photon retains only its intrinsic energy E.

Cosmic Redshift and Energy Loss (ΔE):

In the context of cosmic expansion, the recession of galaxies causes a permanent loss of a photon's intrinsic energy ΔE due to the cosmological redshift. This energy loss is independent of local gravitational interactions and reflects the large-scale dynamics of the expanding universe.

Negative Apparent Mass and Antigravitational Effects:

The photon's negative apparent mass Mᵃᵖᵖ,ₚₕₒₜₒₙ generates a constant negative force −F, which manifests as an antigravitational effect. This behaviour parallels the characteristics attributed to dark energy in its capacity to resist gravitational attraction.

Wave Speed Consistency (c):

The constant negative force −F, arising from the photon's energy dynamics, ensures the photon’s ability to maintain a constant wave propagation speed c, irrespective of gravitational influences.

Negative Effective Mass:

The photon’s negative effective mass Mᵉᶠᶠ,ₚₕₒₜₒₙ allows it to exhibit properties akin to those of a negative particle. This feature contributes to its unique interaction dynamics within gravitational fields and reinforces its role in antigravitational phenomena.

Constant Effective Acceleration:

From the moment of its emission at an initial velocity of 0m/s, the photon experiences a constant effective acceleration, quantified as aᵉᶠᶠ,ₚₕₒₜₒₙ = 6 × 10⁸ m/s². This acceleration underpins the photon’s ability to achieve and sustain its characteristic speed of light (c), reinforcing its intrinsic energy and momentum dynamics.

#Photondynamics, #Gravitationalinteraction, #Negativemass, #Cosmicredshift, #Extendedclassicalmechanics,

Redshift, Blueshift, and Phase Shifts: A Unified Framework for Time Deviations in Oscillatory Systems Under Motion and Gravitational Effects.

Soumendra Nath Thakur

December 04, 2024

Following reasoning highlights an essential relationship between frequency, wavelength, and period in oscillatory systems, particularly under the influence of redshift (energy loss) or blueshift (energy gain). Here's a formalized explanation:

Key Relationship:

The proportionality (1/f) ∝ λ ∝ T establishes that frequency (f), wavelength (λ), and period (T) are intrinsically linked. Any change in frequency due to a phase shift (Δf) directly affects both wavelength and period, as follows:

• Redshift (Energy Loss):

If a phase shift reduces the frequency (f₀-Δf) = f₂, then: 

λ↑ and T↑

This corresponds to an elongation of the wavelength and an increase in the period (time for one cycle).

• Blueshift (Energy Gain):

If a phase shift increases the frequency (f₀+Δf) = f₃, then:

λ↓ and T↓

This corresponds to a compression of the wavelength and a decrease in the period.

Effect on Clock Time:

Since clock time (T) is derived from the oscillatory system's period, a change in frequency due to energy shifts (redshift or blueshift) will directly influence clock time. Specifically:

1. Redshift/Energy loss:

• Energy is lost (e.g., due to gravitational potential differences or relative velocity).

• Wavelength enlarges (λ↑), and the period lengthens (T↑).

• The clock runs slower compared to a reference frame.

2. Blueshift/Energy gain:

• Energy is gained (e.g., approaching a gravitational source or moving towards the observer).

• Wavelength shortens (λ↓), and the period shortens (T↓).

• The clock runs faster compared to a reference frame.

The relative frequency shift (Δf) resulting from these effects leads to phase shifts, which manifest as errors in time synchronization between clocks. These shifts are governed by:

ΔT = 360°/(f+Δf) − 360°/f.

This discrepancy affects the oscillatory synchronization, causing an observable error in clock readings.

Conclusion:

The phase shift in frequency (f₀ ±Δf) resulting from energy changes unequivocally affects both wavelength and period. This causal relationship ensures that any change in wavelength due to frequency shifts directly impacts clock time. Consequently, oscillatory dynamics influenced by redshift (energy loss) or blueshift (energy gain) manifest as measurable time deviations in clocks under conditions of motion or gravitational influence. A single phase-shift formula for frequency (f₀ ±Δf) can effectively account for these variations across both scenarios, providing a unified approach to analysing time deviations.

By emphasizing the direct and observable relationship between frequency shifts, wavelength changes, and clock time deviations, my approach effectively sidesteps the need for relativistic formulas that rely on abstract interpretations like spacetime curvature. This streamlined framework rooted in physical causality offers a more intuitive and consistent explanation for phenomena like redshift and blueshift, making it a powerful alternative to traditional relativistic models.

"Abstract: Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time; which is wrongly presented as time dilation."

This abstract of the research titled, "Relativistic effects on phaseshift in frequencies invalidate time dilation II" by Soumendra Nath Thakur et al, presents clear and meaningful in its presentation, effectively summarizing the core idea of the research. It encapsulates the relationship between relative frequencies, phase shifts, wave energy loss, and wavelength changes, highlighting their roles in creating errors in clock time readings. Moreover, it challenges the conventional interpretation of these phenomena as time dilation, instead presenting them as measurable and quantifiable effects of oscillatory dynamics under relativistic influences or gravitational potential differences.

For the research by Soumendra Nath Thakur et al., this abstract is appropriate and aligns well with the study's focus on reframing time dilation through a more physically grounded explanation. It clearly conveys the intent to debunk the conventional time dilation narrative while proposing an alternative mechanism rooted in phase shifts and frequency dynamics.