Time Dilation Reconsidered: Entropy's Insights:

Soumendra Nath Thakur
ORCiD:  0000-0003-1871-7803
26-02-2024

1. A Summary of Time, Entropy, and Consistency:

The connection between time and entropy highlights how entropy tends to increase over time according to the second law of thermodynamics, suggesting a directionality to time's passage. Additionally, they acknowledged that while entropy may vary depending on the system, the scale of time remains constant in measurements and observations, providing a consistent framework for understanding changes in entropy and other physical quantities.

2. The Inevitability of a Uniform Time Scale: Insights from Entropy

The reasons outlined in the summary statement, a consistent time scale is mathematically certain. It suggests that an enlargement of the time scale is not possible in principle, and a uniform time scale is inevitable unless there are errors in reading clock time.

3. Time Dilation Reconsidered: Entropy's Insights.

The scientific and mathematical understanding of time dilation implies a broadening of the time scale, as time dilation surpasses proper time, expressed as t' > t. However, insights from entropy underscore the certainty of a uniform time scale, indicating that enlarging the time scale is not theoretically feasible. Consequently, time dilation is deemed an erroneous concept in science.

#time #entropy #erronioustimedilation

Phase Shift and Infinitesimal Wave Energy Loss Equations. Longdom Publishing SL

Phase Shift and Infinitesimal Wave Energy Loss Equations. Longdom Publishing SL. Download

By Soumendra Nath Thakur.

The research paper provides a mathematical framework for understanding phase shift in wave phenomena, bridging theoretical foundations with real-world applications. It emphasizes the importance of phase shift in physics and engineering, particularly in fields like telecommunications and acoustics. Key equations are introduced to explain phase angle, time delay, frequency, and wavelength relationships. The study also introduces the concept of time distortion due to a 1° phase shift, crucial for precise time measurements in precision instruments. The research also addresses infinitesimal wave energy loss related to phase shift, enriching our understanding of wave behaviour and impacting scientific and engineering disciplines.

Keywords: Phase shift; Phase angle; Time distortion; Wave energy loss; Wave phenomena

https://www.longdom.org/open-access/phase-shift-and-infinitesimal-wave-energy-loss-equations-104719.html

Exploring Symmetry in Photon Momentum Changes: Insights into Redshift and Blueshift Phenomena in Gravitational Fields

Soumendra Nath Thakur *
ORCiD: 0000-0003-1871-7803
22^nd February, 2024

Abstract

This abstract provides a comprehensive overview of the intricate relationship between photon momentum changes and gravitational fields, as discussed in the context of the paper titled "Distinguishing Photon Interactions: Source Well vs. External Fields." The exploration delves into the fundamental symmetry observed in photon momentum changes, elucidating the principles of redshift and blueshift phenomena within gravitational fields. Through mathematical formulations and theoretical analyses, the abstract highlights how changes in photon momentum and wavelength are intricately linked, with the constant 'h' representing Planck's constant playing a crucial role. Furthermore, the abstract discusses the concept of symmetry in photon momentum changes, demonstrating how momentum exchanges in external gravitational fields ultimately lead to an equilibrium state. This enhanced understanding of photon interactions with gravitational fields contributes to the broader comprehension of astrophysical phenomena and energy conservation principles.

Keywords: Symmetry in Momentum, Energy Conservation, Photon Momentum Changes, External Gravitational Fields, Redshift and Blueshift Phenomena,

*Tagore’s Electronic Lab. India
Email: postmasterenator@gmail.com
The Author declares no conflict of interest.

Symmetry in Photon Momentum Changes:

The equation Δρ = −Δρ is possible due to the relationship Δρ = h/Δλ = h/-Δλ, indicating a fundamental symmetry between redshift and blueshift phenomena. These equations describe how changes in photon momentum (Δρ) correspond to changes in wavelength (Δλ). The constant 'h' represents Planck's constant, suggesting that the magnitude of the momentum change is inversely proportional to the magnitude of the wavelength change. Furthermore, when a photon traverses an external gravitational well, it follows an arc path. As a result, momentum exchanges gradually increase as the photon enters the influence of the massive object, leading to blueshift. Similarly, momentum exchanges gradually decrease as the photon exits the influence of the massive object, resulting in redshift equivalent to blueshift occurrences.

Mathematical Formulations:

These equations can be expressed as follows:

Equation for Photon Energy:

• E = hf = hc/λ

This equation relates the energy E of a photon to its frequency f and wavelength λ, where h is Planck's constant and c is the speed of light. It demonstrates how changes in wavelength correspond to changes in energy while maintaining the total energy constant.

Equation for Energy Change due to Frequency Change:

• ΔE = hΔf

This equation represents the change in energy ΔE of a photon due to a change in frequency Δf, where h is Planck's constant. It highlights how alterations in frequency lead to variations in energy.

Equation for Momentum Change due to Wavelength Change:

• Δρ = h/Δλ

This equation represents the change in momentum Δρ of a photon due to a change in wavelength Δλ, where h is Planck's constant. It illustrates the inverse relationship between changes in wavelength and momentum.

By considering these equations together, we observe that changes in energy and momentum are intricately linked in photon interactions with gravitational fields. The mathematical formulations provided in the paper demonstrate how variations in wavelength and frequency lead to compensatory changes in energy and momentum, ensuring consistency with energy conservation principles.

Conclusion:

The effective momentum changes of a photon in an external gravitational field can be described as zero (=0), as outlined in the concept of symmetry in photon momentum changes. This symmetry, represented by Δρ = -Δρ, illustrates how changes in photon momentum due to gravitational effects are symmetrically balanced, resulting in an overall equilibrium. As photons traverse through external gravitational fields, such as the gravitational well of a massive object, they experience momentum exchanges that lead to phenomena like blueshift and redshift. These exchanges occur as the photon follows an arc path, with momentum gradually increasing upon entering the influence of the massive object and gradually decreasing upon exiting it. Consequently, the net effect of these momentum exchanges is zero, ensuring conservation of momentum in the interaction between photons and external gravitational fields.

Reference:

[1] (PDF) Understanding Photon Interactions: Source Gravitational Wells vs. External Fields. (2024) ResearchGate https://doi.org/10.13140/RG.2.2.14433.48487

Enhanced Insights into Photon Interactions with External Gravitational Fields:

DOI: http://dx.doi.org/10.13140/RG.2.2.10173.64482

Soumendra Nath Thakur
22^nd February, 2024

Abstract:

This abstract provides an in-depth examination of photon interactions with external gravitational fields, building upon the principles discussed in the paper titled "Distinguishing Photon Interactions: Source Well vs. External Fields." The analysis elucidates how gravitational effects influence the properties of photons, including momentum and energy. Symmetry in the changes of photon momentum (Δρ) is explored, where Δρ = -Δρ signifies the equivalence between redshift and blueshift. Mathematical presentations demonstrate the conservation principles involved, highlighting how changes in wavelength affect photon energy while maintaining total energy constancy. The constancy of the speed of light (c) is emphasized, underscoring its fundamental nature amidst varying wavelengths. Through this abstract, a deeper understanding of the complexities of photon interactions with gravitational fields emerges, enriching the discourse on this intricate subject matter.

Keywords: Photon Interactions, Gravitational Fields, Momentum Symmetry, Energy Conservation, Speed of Light,

Tagore’s Electronic Lab, India

The author declared no conflict of Interest.

Introduction:

The interaction of photons with external gravitational fields constitutes a fundamental aspect of astrophysics and cosmology, shaping our understanding of the universe's dynamics. In the paper titled "Distinguishing Photon Interactions: Source Well vs. External Fields," the complexities of these interactions are explored, laying the groundwork for further investigation. This introduction provides a comprehensive overview of the additional insights presented herein, which offer a detailed examination of photon behaviour under the influence of gravitational forces. By delving into the symmetry of changes in photon momentum, the equivalence of redshift and blueshift, and the conservation principles governing photon energy, this analysis expands our comprehension of how photons respond to gravitational environments. Through mathematical formulations and conceptual discussions, this introduction sets the stage for a deeper exploration of the intricate relationship between photons and gravitational fields, enhancing our grasp of the underlying physics at play.

Mathematical Presentations:

Symmetry in Photon Momentum Changes:

Equation: Δρ = −Δρ

This equation represents the symmetry observed in the changes of photon momentum, where the change in momentum (Δρ) is equal in magnitude but opposite in direction for redshift and blueshift phenomena.

Relationship between Momentum Change and Wavelength Change:

Equation: Δρ = h/Δλ = h/-Δλ

These equations express the relationship between changes in photon momentum (Δρ) and changes in wavelength (Δλ). The constant 'h' represents Planck's constant, indicating that the magnitude of the momentum change is inversely proportional to the magnitude of the wavelength change.

Equation Relating Energy, Frequency, and Wavelength:

Equation: E = hf = h(c/λ)

This equation relates the energy (E) of a photon to its frequency (f) and wavelength (λ), where 'h' is Planck's constant and 'c' is the speed of light. It demonstrates how changes in wavelength correspond to changes in energy while maintaining the total energy constant.

Energy Conservation Equation for Redshift:

Equation: (E - ΔE) = hc/(λ+Δλ) = hc/(λ-Δλ) = (E + ΔE)

This equation represents energy conservation in the context of redshift, where there is a change (Δλ) in the photon's wavelength. It shows that the change in energy (ΔE) due to redshift is compensated by the corresponding change in wavelength, resulting in a total energy that remains constant.

Constancy of the Speed of Light Equation:

Equation: c = fλ

This equation represents the relationship between the speed of light (c), frequency (f), and wavelength (λ). It illustrates that even when the wavelength varies, the product of frequency and wavelength (fλ) remains constant, ensuring the constancy of the speed of light.

These mathematical presentations provide a quantitative framework for understanding the principles discussed in the quoted text, including symmetry in momentum changes, conservation of energy, and the constancy of the speed of light.

Discussion:

The discussion presented in the quoted text delves into the intricate interplay between photons and external gravitational fields, shedding light on several key concepts and their implications.

Firstly, the symmetry observed in the changes of photon momentum (Δρ) is highlighted, where Δρ = -Δρ signifies a fundamental symmetry between redshift and blueshift phenomena. This symmetry, rooted in the conservation principles of momentum, underscores the intricate balance at play in photon interactions with gravitational fields. By acknowledging this symmetry, researchers gain a deeper understanding of how photons respond to gravitational influences, whether they are experiencing redshift or blueshift.

Moreover, the mathematical presentation elucidates how changes in photon wavelength (Δλ) correspond to alterations in photon momentum and energy. The equations presented, such as E = hf = h(c/λ), provide a quantitative framework for understanding the relationship between photon energy, frequency, and wavelength. Through these equations, it becomes apparent that while changes in wavelength may result in shifts in photon energy, the total energy remains conserved, underscoring a fundamental principle of physics.

Furthermore, the discussion emphasizes the constancy of the speed of light (c) despite variations in wavelength. This constancy, rooted in the relationship c = fλ, elucidates how the interplay between frequency and wavelength maintains a consistent speed of light, even in the presence of gravitational influences. Understanding this fundamental property of light is crucial for interpreting observations in astrophysics and cosmology, where gravitational fields often play a significant role.

Overall, the discussion provides valuable insights into the complexities of photon interactions with external gravitational fields. By exploring concepts such as symmetry in momentum changes, conservation of energy, and the constancy of the speed of light, researchers can deepen their understanding of the fundamental principles governing the behaviour of photons in gravitational environments. These insights not only contribute to our theoretical understanding but also have practical implications for interpreting astronomical observations and phenomena.

Conclusion:

The discussion presented offers a comprehensive exploration of photon interactions with external gravitational fields, illuminating fundamental principles and their mathematical representations. By examining the symmetry in photon momentum changes, it becomes evident that redshift and blueshift phenomena exhibit a symmetric relationship, encapsulated by Δρ = -Δρ. This symmetry underscores the intricate balance in photon behaviour under gravitational influences.

Furthermore, the mathematical presentations elucidate the relationships between momentum changes, wavelength alterations, and energy conservation. Equations relating energy, frequency, and wavelength provide a quantitative understanding of how changes in photon properties manifest while preserving total energy. The analysis of energy conservation in the context of redshift highlights the compensatory nature of changes in energy and wavelength, maintaining a constant total energy.

Additionally, the constancy of the speed of light, emphasized through the relationship c = fλ, underscores a fundamental property of light unaffected by gravitational fields. This constancy serves as a cornerstone for interpreting observations in astrophysics and cosmology, facilitating our understanding of the universe's dynamics.

In conclusion, the insights provided deepen our understanding of the complexities of photon interactions with gravitational fields. By combining conceptual discussions with mathematical formulations, this discussion enriches our comprehension of fundamental principles governing photon behaviour and lays the groundwork for further exploration in astrophysics and cosmology.

References:

[1] (PDF) Understanding Photon Interactions: Source Gravitational Wells vs. External Fields. (2024) ResearchGate https://doi.org/10.13140/RG.2.2.14433.48487

[2] Thakur, S. N. (2023b). The dynamics of photon momentum exchange and curvature in gravitational fields Definitions https://doi.org/10.32388/r625zn

[3] Thakur, S. N. (2023a). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions https://doi.org/10.32388/81iiae

[4] Thakur, S. N. (2024c). Direct Influence of Gravitational Field on Object Motion invalidates Spacetime Distortion. Qeios.com. https://doi.org/10.32388/bfmiau

[5] Thakur, S. N., & Bhattacharjee, D. (2023b). Cosmic Speed beyond Light: Gravitational and Cosmic Redshift. Preprints.org. https://doi.org/10.20944/preprints202310.0153.v1

[6] Thakur, S. N., Bhattacharjee, D., & Frederick, O. (2023). Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects. Preprints.org. https://doi.org/10.20944/preprints202309.2086.v1

[7] Thakur, S. N. (2023d). Cosmic Speed beyond Light: Gravitational and Cosmic Redshift. ResearchGate https://doi.org/

Understanding Photon Interactions: Source Gravitational Wells vs. External Fields:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

20th February, 2024

This additional description provided here enhances the paper titled, 'Distinguishing Photon Interactions: Source Well vs. External Fields' by providing a more detailed explanation of the principles discussed. It expands upon the concepts of energy expenditure, gravitational redshift, and momentum exchange in a clear and concise manner. Additionally, the inclusion of mathematical formulations further strengthens the paper by providing quantitative insights into the phenomena under investigation.

This study delves into the intricate interactions of photons within gravitational fields, discerning between encounters with source gravitational wells and external gravitational fields. When photons escape source gravitational wells, such as those of stars or black holes, they expend energy, leading to gravitational redshift. Conversely, when traversing external gravitational fields, photons maintain their inherent energy while experiencing bending paths due to momentum exchange. Through mathematical formulations, we elucidate these principles, offering insights into astrophysical dynamics and gravitational physics.

When a photon or wave escapes a gravitational well, such as the gravitational field of a massive object like a star or a black hole, it expends energy in the process. This energy expenditure, resulting from a change in energy ΔE, follows the Planck equation:

• ΔE = hΔf

It's crucial to note that:

a. This alteration in photon frequency (Δf) corresponds to a change in photon wavelength (1/Δλ), leading to a redshift of the photon wavelength.

b. The change in photon wavelength (1/Δλ) is directly proportional to the photon's distance from its source gravitational well. This distance remains constant throughout the photon's journey, even when traversing through the gravitational field of external massive bodies like planets or galaxies. However, instead of experiencing energy variations in strong gravitational fields, the photons maintain their inherent energy (E = Eg) through the equation (Eg = E + ΔE = E − ΔE), while undergoing gravitational redshift due to (ΔE = hΔf).

c. In addition to undergoing gravitational redshift, photons also experience redshift due to cosmic expansion, but this occurs only when they enter dark energy-dominated intergalactic space.

Through these mathematical formulations, we elucidate the principles governing photon interactions in source gravitational wells versus external gravitational fields, thereby enhancing our understanding of gravitational physics in astrophysical contexts.