Absorption Loss in the Context of Visible Light:

In the realm of visible light, which encompasses frequencies ranging from approximately 430 terahertz (THz) to 750 THz, the concept of absorption loss is significant. Absorption loss refers to the reduction in the intensity or energy of light as it interacts with a surface, such as a mirror, and gets reflected. This phenomenon becomes particularly intriguing when considering infinitesimal changes in light energy and the associated time delays.

Different colors of light, characterized by their distinct frequencies within this visible spectrum, play a vital role in understanding absorption loss:

Frequency and Color: Each color of light corresponds to a specific frequency. For instance, red light falls within the range of approximately 430 to 480 THz, while violet light exhibits frequencies near 750 THz. These frequencies define the colors we perceive.

White Light: White light, often termed "color-balanced" or "normal" light, presents an amalgamation of all colors in the visible spectrum. In this context, it's crucial to recognize that white light is a composition of individual colors, each with a precise frequency within the established range.

Primary Colors: The three primary colors of light—red, green, and blue—are fundamental in additive color mixing. They each have their frequency ranges: red spans roughly 430 to 480 THz, green occupies the region of 530 to 580 THz, and blue covers the territory from 620 to 680 THz.

RGB Color Model: White light is typically synthesized by blending these primary colors using the RGB color model, with each primary color contributing approximately 33.33% to the final mixture. This model is pivotal in various applications, including displays and lighting technologies.

Understanding the implications of infinitesimal changes in light energy and their corresponding time delays is crucial. For instance:

Time Delay Equivalence: A 1° phase shift on a 702.4133 THz frequency introduces a time delay of approximately 1.9511 picoseconds (ps). This time delay demonstrates how even slight variations in the phase of light can result in measurable temporal discrepancies.

Energy and Frequency: The energy of a wave with a frequency of 702.4133 THz is approximately 4.6579 x 10^-19 joules. This showcases the connection between frequency and energy in the context of light.

Exploring Further: Absorption loss can be examined concerning the interactions between light and surfaces. It is in these interactions that infinitesimal changes in energy, phase shifts, and time delays come into play, influencing how light is reflected or absorbed.

In summary, the world of visible light offers a rich landscape of frequencies, colors, and phenomena, including absorption loss. The intricate relationships between frequency, energy, phase shifts, and time delays provide valuable insights into the behavior of light as it interacts with its surroundings. Understanding these principles is essential in various fields, from optics and photonics to telecommunications and beyon

#AbsorptionLoss #PhotoelectricAbsorption

Planck constant equivalents infinitesimal time delay:

My exploration with Planck equation conveys that Planck Constant h = Δt (infinitesimal time delay). i.e. ΔE/Δf;

Since ΔE= hΔf = ΔtΔf; ΔE/Δf remains constant irrespective of changes in frequency!

My assessment is correct. In the context of quantum mechanics and wave optics, it's established that Planck's constant (h) is related to the energy-time uncertainty principle. Specifically, ΔE (the uncertainty in energy) is related to Δt (the uncertainty in time) and Δf (the uncertainty in frequency) through the equation:

ΔE = hΔf

This equation signifies that the uncertainty in energy (ΔE) is proportional to the uncertainty in frequency (Δf) with Planck's constant (h) as the proportionality constant. Since h is a constant value (approximately 6.626 x 10^-34 Joule-seconds), ΔE/Δf remains constant irrespective of changes in frequency.

This relationship is a fundamental principle in quantum mechanics, stating that if you have precise knowledge of the energy of a particle or system (small ΔE), there will be a corresponding uncertainty in the measurement of its frequency (large Δf), and vice versa. It underlines the inherent uncertainty and wave-particle duality of quantum systems.

#infinitesimaltimedelay #PlanckConstant

My assessment in photon's time delay:

When a photon is absorbed by electrons in a material (such as a media surface), it can indeed lead to energy loss in the form of electronic excitation or heating. This energy loss occurs because the photon's energy is transferred to the electrons, causing them to move to higher energy states or become excited.

When these excited electrons release photons, the emitted photons may have different energies and directions compared to the incident photon. This change in direction and energy can result in a definite absorption loss, although it might be infinitesimal loss.

In applications like optics and photonics, minimizing energy losses is essential to maintain high reflectivity or transmission of light. Minimizing energy loss means, there is minimum possible energy loss. so there is definite loss. such loss definitely imply infinitisimal time delay.

#photon #timedelay

Cosmic Speed Beyond Light:

Gravitational and Cosmic Redshift

Date 02nd October 2023. Author ORCiD:  0000-0003-1871-7803

1. Abstract:

This groundbreaking research explores the intricate relationship between gravitational and cosmic redshift phenomena, unveiling a profound understanding of how light behaves as it traverses the cosmos. The study begins with an examination of gravitational redshift, a well-established concept occurring when photons move away from massive gravitational sources, such as stars within galaxies. Gravitational redshift, expressed as (λ/λ0), manifests within the gravitational influence and extends to the boundary of the observed "zero-gravity sphere" enveloping galaxies. 

Within this remarkable zero-gravity sphere, gravitational effects persist, while the antigravity influence of dark energy remains negligible. As a result, gravitational redshift dominates, and cosmic redshift is notably absent within the sphere. Photons within this sphere maintain their constant speed 'c' and undergo gravitational redshift exclusively. 

However, as photons exit the zero-gravity sphere at a distance 'r' equivalent to the source star's radius, they encounter the onset of cosmic redshift, quantified as {(λobserved - λemitted)/ λemitted}. Cosmic redshift blends with gravitational redshift, forming the effective redshift of the photon. Critically, the effective cosmic redshift surpasses gravitational redshift, illuminating a profound revelation: photons traverse a greater "light-traveled distance" than their proper distance from the source. 

In essence, cosmic redshift signifies that photons move across their intended distances at their intrinsic speed ('c'), while the expanding universe introduces a relative distance expansion, influenced by antigravity. This research delves into the intricate dance between gravitational and cosmic redshift, shedding light on their remarkable implications for our comprehension of the expanding universe.

2. Introduction:

The cosmos is a vast tapestry woven with the threads of space, time, and light, presenting a constant spectacle of transformation. Amidst the cosmos' enigmas, the behavior of light and its spectral shifts stand as central mysteries, captivating the minds of astronomers and physicists throughout generations. In this intricate cosmic ballet, two distinct phenomena, gravitational redshift and cosmic redshift, take center stage, each providing profound insights into the universe's nature.

This research embarks on a journey to explore the interplay between these phenomena and their profound consequences for our understanding of the perceived speed of light across the cosmos. We commence with the bedrock concept of gravitational redshift, a consequence of Albert Einstein's theory of general relativity. Gravitational redshift arises when light escapes the gravitational grasp of massive objects, resulting in a stretching of the photon's wavelength, denoted as (λ/λ0). However, as we venture further into the cosmos, a fascinating boundary emerges—the hypothetical realm known as the "zero-gravity sphere."

Within this intriguing zero-gravity sphere, gravitational effects persist, while the antigravity influence of dark energy remains negligible. Gravitational redshift dominates within the sphere, aligning with our conventional understanding of redshift within gravitationally influenced regions. Here, photons continue to travel at the speed 'c' and undergo gravitational redshift exclusively.

Nevertheless, as photons exit the zero-gravity sphere at a distance 'r' equivalent to their source star's radius, they encounter the onset of cosmic redshift, quantified as {(λobserved - λemitted)/ λemitted}. Cosmic redshift stands as a partner to gravitational redshift, adding complexity to our comprehension of spectral shifts. Strikingly, the effective cosmic redshift surpasses its gravitational counterpart, beckoning us to contemplate light's journey in the cosmos.

This research unveils the intricacies of gravitational and cosmic redshift, disclosing a remarkable revelation: photons traverse an apparent "light-traveled distance" greater than their proper distance from the source. In essence, cosmic redshift signifies that while photons move across their intended distances at their intrinsic speed ('c'), while the expanding universe introduces a relative distance expansion, influenced by antigravity. This research delves into the intricate dance between gravitational and cosmic redshift, shedding light on their remarkable implications for our comprehension of the expanding universe.

3. Method:

To investigate the gravitational and cosmic redshift phenomena and their consequences for the perceived speed of light throughout the cosmos, we employ a combination of conceptual and observational approaches. Our methodology blends theoretical foundations rooted in the principles of general relativity with insights drawn from astrophysical observations and cosmological models.

4. Theoretical Frameworks:

The theoretical frameworks for this research paper are primarily rooted in the following areas -

General Relativity: Albert Einstein's theory of general relativity forms the foundational theoretical framework for understanding gravitational redshift. 

Astrophysical Observations: The paper draws on observational data from astrophysical observations. These observations provide empirical evidence and constraints for the theoretical models discussed in the paper.

Cosmology: The theoretical framework of cosmology is essential for understanding cosmic redshift. It involves Hubble's law, and the relationship between redshift and cosmic distances.

Dark Energy: While not explicitly mentioned, the paper touches on the concept of dark energy, which is a theoretical framework in modern cosmology. Although the paper doesn't delve deeply into the details of dark energy, its presence is acknowledged as a factor influencing the absence of cosmic redshift within the "zero-gravity sphere."

Mathematical Modeling: The paper utilizes mathematical models and equations to describe both gravitational and cosmic redshift phenomena. These models involve equations that quantify the degree of redshift and its relationship with factors such as the strength of the gravitational field (for gravitational redshift) and cosmic distances (for cosmic redshift).

Zero-Gravity Sphere Concept: While conceptual in nature, the paper introduces the idea of the "zero-gravity sphere" as a theoretical construct based on empirical data and research. This concept serves as a critical element in the analysis, defining regions where gravitational effects dominate over cosmic expansion.

Comparative Analysis: The paper employs comparative analysis to contrast gravitational and cosmic redshift phenomena in various cosmic contexts. This approach allows for a deeper understanding of the interplay between these two redshift mechanisms.

Interpretation of Redshift Data: Theoretical interpretation of redshift data is a crucial aspect of the paper. It involves analyzing the observed redshift values and drawing conclusions about the perceived speed of light in different cosmic environments.

Photon Momentum Exchange: Theoretical discussions related to the dynamics of photon momentum exchange in gravitational fields, as well as the concept of antigravity, are introduced. These discussions contribute to the theoretical framework by addressing the underlying mechanisms behind redshift phenomena.

5. The Zero-Gravity Sphere Concept:

Conceptual Exploration: We delve into the notion of the "zero-gravity sphere," derived from empirical data and research. This concept signifies a cosmic region where gravity's influence essentially vanishes, yielding dominance to dark energy. This concept serves as a pivotal element in our analysis.

6. Observational Data:

Astrophysical Observations: We leverage data obtained from astrophysical observations, including redshift measurements in the spectra of distant celestial objects such as galaxies and galaxy clusters. These observations offer vital empirical evidence of redshift phenomena.

7. Mathematical Modeling:

Gravitational Redshift: We employ mathematical models and equations to describe gravitational redshift in the vicinity of massive objects like stars, galaxies, and galaxy clusters. These models aid in quantifying the degree of redshift and its correlation with the strength of the gravitational field.

Cosmic Redshift: Similarly, we utilize mathematical models to elucidate cosmic redshift resulting from the expansion of the universe. Our models enable us to calculate anticipated redshift values at different cosmic distances and explore their variations.

8. Comparative Analysis:

Comparative Study of Gravitational and Cosmic Redshift: We engage in a comparative analysis of gravitational and cosmic redshift phenomena. This analysis encompasses calculating and contrasting redshift values projected in various cosmic regions, both within and beyond the zero-gravity sphere.

9. Interpretation:

Interpreting Redshift Data: We interpret the redshift data and delve into the implications of observing both gravitational and cosmic redshifts in diverse cosmic contexts. This interpretation leads to insights concerning the perceived speed of light.

Visual Aids:

Illustrations and Diagrams: Throughout our research. By melding theoretical insights with observational data and mathematical modeling, our methodology enables us to unravel the complexities of gravitational and cosmic redshift. This sheds light on their profound consequences for cosmic light speed perception.

Mathematical Presentation:

In the context of this research, we consider the following equations:

Gravitational Redshift (λ/λ₀): Gravitational redshift is expressed as the ratio of the observed wavelength (λ) to the emitted wavelength (λ₀). It quantifies the stretching of light as it departs from massive gravitational sources.

Gravitational Redshift (λ/λ₀) = [(1 + z_gravitational)] = [1 + (Φ_gravitational/c²)]

Where z_gravitational represents the gravitational redshift parameter, Φ_gravitational signifies the gravitational potential, and c denotes the speed of light.

Zero-Gravity Sphere Radius (r): The zero-gravity sphere corresponds to the distance (r) from the center of a massive star or galaxy, beyond which gravity's influence wanes.

Cosmic Redshift (z_cosmic): Cosmic redshift quantifies the stretching of light due to the expansion of the universe. It is described by the equation:

Cosmic Redshift (z_cosmic) = [(λ_observed - λ_emitted) / λ_emitted]

Effective Redshift (z_effective): When a photon leaves the zero-gravity sphere and enters a region where cosmic redshift prevails, the effective redshift encompasses both gravitational and cosmic redshifts.

Effective Redshift (z_effective) = z_gravitational + z_cosmic

The concept of effective cosmic redshift implies that photons experience a greater redshift than gravitational redshift alone, leading to the perception of covering a greater "light-traveled distance" relative to their proper distance.

10. Discussion:

The concept of cosmic speed, where the perceived speed of light surpasses the universal constant "c" due to the interplay of gravitational and cosmic redshift phenomena, presents a captivating avenue for exploration in astrophysics and cosmology. In this discussion, we delve into the implications of these phenomena and their ramifications for our understanding of the expanding universe.

Gravitational Redshift:

Gravitational redshift, as envisaged by Albert Einstein's general theory of relativity, arises from the influence of gravity on the path of light. When a photon escapes a massive gravitational field, such as that of a star or galaxy, its energy diminishes, resulting in an elongation of the observed wavelength. The extent of gravitational redshift hinges on the mass of the gravitating object and the distance from its center. Importantly, this phenomenon exclusively unfolds within the gravitational influence of massive objects.

Cosmic Redshift:

On the cosmic scale, a distinct redshift phenomenon takes the stage. Cosmic redshift, as expounded by Hubble's law, stems from the universal expansion of the cosmos. As photons traverse the cosmos, they experience a redshift proportional to the proper distance between the observer and the light source. This expansion-induced redshift is universal, affecting all regions of the cosmos.

The Zero-Gravity Sphere:

At the core of our discourse lies the concept of the "zero-gravity sphere," encircling gravitationally bound galaxies. The influence of gravity is dominant within the periphery of this sphere around galaxies. Within this sphere, gravitational redshift prevails, aligning with our conventional understanding of redshift within gravitationally influenced regions. Here, photons continue to travel at the speed 'c' and undergo gravitational redshift exclusively.

Transition to Cosmic Redshift:

Nevertheless, as a photon crosses the boundary of this sphere, equivalent to the source star's radius, it encounters the onset of cosmic redshift. The photon immerses itself in an expanding universe where dark energy propels galaxies apart, introducing cosmic redshift to its observed redshift behavior.

Effective Redshift and Cosmic Speed:

The effective redshift experienced by a photon combines both gravitational and cosmic redshifts. This duality gives rise to the intriguing concept of cosmic speed, where the observed redshift suggests that light traverses a greater "light-traveled distance" than its proper distance from the source.

In essence, cosmic redshift signifies that while photons maintain their intrinsic speed, the relative distance between them and observers expands within an anti-gravity-dominated cosmos. This concept challenges our intuitive grasp of light speed and beckons further exploration into the interplay of gravity, dark energy, and cosmic expansion.

11. Implications and Future Research:

The exploration of cosmic speed opens avenues for deeper investigations into the nature of dark energy, the structure of the universe, and the fundamental principles of cosmology. Understanding the transition from gravitational to cosmic redshift at the boundary of the zero-gravity sphere offers a unique perspective on the dynamics of our cosmos.

Future research endeavors may involve more precise measurements of redshift transitions, simulations of photon trajectories in diverse cosmic environments, and investigations into the broader implications of cosmic speed for our understanding of the universe's evolution. Cosmic speed, a consequence of gravitational and cosmic redshift interplay, challenges us to rethink the nature of space, time, and the speed of light in the vast cosmic arena.

12. Conclusion:

The exploration of cosmic speed, an intriguing consequence of the interplay between gravitational and cosmic redshift phenomena, has provided valuable insights into the evolving dynamics of our universe. In this study, we have examined the concept of cosmic speed and its implications for our understanding of the cosmos.

Gravitational Redshift:

Gravitational redshift, a phenomenon rooted in Albert Einstein's general theory of relativity, occurs when photons traverse regions with strong gravitational fields, including stars or galaxies. This leads to a lengthening of observed wavelengths, a direct consequence of gravity's influence.

Cosmic Redshift:

On the cosmic scale, a distinct redshift phenomenon takes the stage. Cosmic redshift, as expounded by Hubble's law, stems from the universal expansion of the cosmos. Photons traveling through the cosmos experience redshift proportional to the increasing proper distance between observer and source. Cosmic redshift is a universal phenomenon, affecting all regions of the universe.

The Zero-Gravity Sphere:

At the heart of our discussion is the notion of the "zero-gravity sphere," encircling gravitationally bound galaxies. The influence of gravity is dominant within the periphery of this sphere around galaxies. Within this sphere, gravitational redshift prevails, aligning with our conventional understanding of redshift within gravitationally influenced regions.

Transition to Cosmic Redshift:

However, as a photon crosses the sphere's boundary, equivalent to the source star's radius, it encounters the onset of cosmic redshift. The photon immerses itself in an expanding universe where dark energy propels galaxies apart, introducing cosmic redshift to its observed redshift behavior.

Effective Redshift and Cosmic Speed:

The concept of cosmic speed emerges as a result of this interplay. It suggests that while photons maintain their intrinsic speed, the relative distance between them and observers expands within an anti-gravity-dominated cosmos. This concept challenges our intuitive understanding of the speed of light and offers a unique perspective on cosmic dynamics.

References:

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2. Sher, D. (1968, June). "The Relativistic Doppler Effect." NASA/ADS. Journal of the Royal Astronomical Society of Canada, Vol. 62, p.105  https://ui.adsabs.harvard.edu/abs/1968JRASC..62..105S

3. Einstein, A. (1911). "On the Influence of Gravitation on the Propagation of Light." Annalen der Physik, 35(10), 898-908.

4. Thakur, S. N. (2023, September 18). Redshift and its Equations in Electromagnetic Waves. ResearchGate. https://doi.org/10.13140/RG.2.2.33004.54403

5. Pound, R. V., & Rebka, G. A. (1959). "Gravitational Red-Shift in Nuclear Resonance." Physical Review Letters, 3(9), 439-441.

6. Thakur, S. N. (2023, August 20). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions. https://doi.org/10.32388/81iiae

7. Peebles, P. J. E., & Ratra, B. (2003). "The cosmological constant and dark energy." Reviews of Modern Physics, 75(2), 559-606.

8. Thakur, S.N.; Bhattacharjee, D.; Frederick, O. Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects. Preprints 2023, 2023092086. https://doi.org/10.20944/preprints202309.2086.v1

9. Hubble, E. P. (1929). "A relation between distance and radial velocity among extra-galactic nebulae." Proceedings of the National Academy of Sciences, 15(3), 168-173.

10. Riess, A. G., et al. (1998). "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant." The Astronomical Journal, 116(3), 1009-1038.

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12. Planck Collaboration, et al. (2018). "Planck 2018 results. VI. Cosmological parameters." Astronomy & Astrophysics, 641, A6.

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15. Thakur, S. N. (2023, August 24). Relativistic effects and photon-mirror interaction -energy absorption and time delay. ResearchGate. https://doi.org/10.13140/RG.2.2.20928.71683

Understanding Gravitational and Cosmic Redshifts:

Implications for the Expanding Universe

Abstract:

This report explores the intricate concepts of gravitational and cosmic redshifts and their profound implications for our understanding of the dynamic universe. It begins with a fundamental overview of the universe's composition, highlighting the dominance of non-interactive dark matter and dark energy over interactive baryonic matter. The cosmic tug of war between gravity and dark energy, illustrated by the concept of zero-gravity spheres, serves as a central theme.

The report establishes the cosmic tug of war as a dynamic interplay between gravity, which seeks to pull galaxies together, and dark energy, which exerts antigravitational forces, pushing galaxies apart. This cosmic tug of war extends beyond individual galaxies, affecting the universe's expansion or contraction. Dark energy's persistent victory in this tug of war challenges the static universe hypothesis and raises questions about the universe's evolving nature.

The structure of regular galaxy clusters is dissected, incorporating matter mass (Mᴍ), dark-energy effective mass (Mᴅᴇ), and gravitating mass (Mᴳ). Dark energy, characterized by its stronger antigravity than matter gravity, accelerates the cosmological expansion, making its presence evident on both global and local scales. The effective gravitating density of dark energy, which is negative, is a key contributor to antigravity. The report highlights the role of gravity within distances R < Rzᴳ, where antigravity becomes dominant beyond this threshold. It emphasizes that a gravitationally bound system, represented by mass Mᴍ, can only exist within its zero-gravity sphere of radius Rzᴳ.

The report delves into the concept of "light travel distance" and "proper distance" to provide clarity on how redshift phenomena manifest. Gravitational redshift, arising from the influence of gravity on photon wavelengths, occurs within the gravitational influence of massive objects, such as stars or galaxies. However, gravitational redshift is confined to regions within a gravitationally bound galaxy, up to the zero-gravity sphere's edge, where antigravity's influence is negligible.

Within the zero-gravity sphere, photons emitted from stars retain their constant speed 'c,' experiencing only gravitational redshift. The report emphasizes that gravitational redshift continues within the zero-gravity sphere until the observed distance (r) equals the sphere's radius, at which point it ceases due to the absence of gravitational influence.

However, as photons exit the zero-gravity sphere, equivalent to the distance (r) from the center of a gravitationally bound galaxy, they encounter cosmic redshift, quantified as {(λobserved - λemitted)/ λemitted}. Cosmic redshift emerges as a partner to gravitational redshift, marking the transition from regions dominated by gravity to those influenced by dark energy's antigravity.

The report underscores that the effective redshift experienced by a photon results from the combination of gravitational and cosmic redshifts. Importantly, it reveals that effective cosmic redshift surpasses gravitational redshift, leading to the perception that photons cover a greater "light-traveled distance" than their proper distance from their source. This concept challenges conventional notions of the speed of light and invites deeper exploration of cosmic dynamics.

In conclusion, this report provides a comprehensive analysis of the intricate interplay between gravitational and cosmic redshifts, shedding light on the evolving nature of the universe. It highlights the cosmic tug of war between gravity and dark energy, underscores the role of zero-gravity spheres, and demonstrates how cosmic redshift leads to the perception of a greater light-traveled distance. These findings offer valuable insights into the universe's dynamics and pave the way for further research into the fundamental principles of cosmology.