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,