This short paragraph is misleading and wrong? A confusing and incorrect reiteration:

Reiteration, ''Consistency of Total Photon Energy: We reiterate the core principle that in strong gravitationalfields, the total energy of a photon remains constant, as expressed by the equation Eg = E. The equation underscores that the total energy of a photon Eg remains unchanged despite the influence of a strong gravitational field. This constancy of energy is a fundamental property of photons in such environments, emphasizing their resilience to external forces (4) (PDF) Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects. Available from: 

www.researchgate.net/publication/374264333 [accessed Oct 12 2023]. (Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects)

This short paragraph is misleading and wrong. What happens to a photon in a gravitational field is the following:

• h∆f=hf/c²g∆H.

h is Planck’s action constant. f is the photon frequency, ∆f is the change of the photonfrequency, c is the speed of light, g is the gravitational field strength, H is the height in the gravitational field, h∆f is the energy gain or loss of the photon according of changing its height in the gravitational field by ∆H.

We get ∆f/f=g∆H/c². g is the mean value between H and H+∆H.''

The Author Answers:

I see your pointing out, 'this short paragraph is misleading and wrong';

So let me explain the basic difference between the equation I provided, Eg = E and your equation h∆f (= ∆E).

It's evident that "Eg = E" and "hΔf = hf/c²gΔH" address different aspects of a photon's interaction with gravitational fields. Wherewas, my explanations highlights that "Eg = E" focuses on the conservation of the total energy of a photon within an external gravitational field, while "hΔf = hf/c²gΔH" pertains to local energy changes within a single gravitational well. Additionally, the mention of "Δλ/λ" as a representation of intrinsic energy changes helps differentiate these concepts further.

1. Your explanation, 'what happens to a photon in a gravitational field is the following:

h∆f=hf/c²g∆H.

where "h∆f" represents the energy gain or loss of a photon as it changes its height in a gravitational field by ∆H. It quantifies the energy change of the photon due to its change in height within the gravitational field. This aligns with the concept that a photon loses energy as it moves away from a massive object (the source of gravity) or "escapes a gravitational well."

The equation "∆f/f = g∆H/c²" in the quoted text is a simplified form that shows the relative change in photon frequency (and hence energy) as a function of the gravitational field strength (g) and the change in height (∆H) within the gravitational field. It is consistent with the idea that a photon loses energy (or experiences a change in frequency) while moving within a gravitational well.

However, the inconsistency arises when one equation focuses on local energy changes within a single gravitational well, while the other equation takes into account the cumulative effect of multiple gravitational fields:

(A1) what is incosnsistent in your presentation is that, the change in height (∆H) mentioned in the previous comment is specific to the source gravitational well that the photon is escaping. It represents the change in altitude or position within that particular gravitational field. It does not directly take into account other gravitational fields that the photon may encounter in its transit path.

The equation "hΔf = hf/c²gΔH" and the equation "0 = Δρ - Δρ" describe different aspects of a photon's interaction with gravity.

(a) "Eg" represents the energy state of a photon within an external gravitational field, and "Eg = E" signifies the conservation of energy, meaning that a photon's total energy within a gravitational field remains the same as its initial intrinsic energy "E." Despite any local changes in energy or frequency that might occur as a photon moves through gravitational fields (as represented by ΔE), the total energy of the photon remains constant, with respect to (Eg). The idea that within a gravitational field, even though there may be local variations or changes, the overall energy of the photon does not change, and the equation ΔEg = 0 is a reflection of this conservation of energy. This is consistent with the broader principles of physics, where the conservation of energy is a fundamental concept.

(b) Your equation: "hΔf = hf/c²gΔH" focuses on how the energy (and frequency) of a photon changes due to the specific gravitational well it is within. In this context, ΔH represents the change in height or position within a particular gravitational field, which indeed influences the photon's energy. This equation primarily pertains to the effects of a single gravitational field.

Whereas, my equation presented, "0 = Δρ - Δρ" refers to the concept of effective deviation, emphasizing how photons respond to multiple gravitational fields along their path. It suggests that even though photons may experience local changes in momentum as they move through different gravitational fields, the net change in momentum over the entire journey equals zero. This principle aligns with the concept of geodesics in general relativity, where particles, including photons, follow curved paths determined by the combined gravitational influences of all massive objects in their vicinity.

The inconsistency arises when your equation focuses on local energy changes within a single gravitational well, while the other equation takes into account the cumulative effect of multiple gravitational fields.

To provide a more comprehensive and consistent description of a photon's journey, it's important to consider both the local changes in energy within specific gravitational wells (as in "hΔf = hf/c²gΔH") and the overall path and effective deviation that accounts for all gravitational fields encountered (as in "0 = Δρ - Δρ").

(A2) It is well established fact that the photon expends energy while escaping a gravitational well (its source)," is a fundamental concept in general relativity. In this context, a photon is considered to lose energy as it climbs out of a gravitational well. The relevant equation that describes this phenomenon is known as the gravitational redshift equation, which is derived from Einstein's theory of general relativity.

The gravitational redshift equation is as follows:

Δλ/λ = GM/(rc²)
Where:
Δλ/λ is the relative change in the wavelength of light emitted by the photon.
G is the gravitational constant.
M is the mass of the object creating the gravitational well (the source of gravity).
r is the radial distance from the center of the gravitational well to the location of the photon.
c is the speed of light in a vacuum.

This equation shows that as a photon moves away from a massive object (the source of gravity), its wavelength increases. In other words, the photon loses energy as it escapes the gravitational well. This effect is commonly referred to as gravitational redshift or gravitational blueshift, depending on the direction of the photon's motion.

So, when the photon escapes a gravitational well (such as the gravitational field of a massive celestial body), it does so with less energy than when it was closer to the source of gravity. This concept is a key prediction of general relativity and has been experimentally confirmed.

The equation "Δλ/λ = GM/(rc²)" focuses on the local change in energy within a single gravitational well and how this affects the photon's wavelength and energy. This equation takes into account the gravitational field produced by a single massive object.

On the other hand, "0 = Δρ - Δρ" considers the overall path and effective deviation of the photon as it encounters multiple gravitational fields along its journey. It accounts for the cumulative effects of these fields on the photon's trajectory.

The inconsistency arises when your equation focuses on local energy changes within a single gravitational well, while the other equation takes into account the cumulative effect of multiple gravitational fields. To provide a more comprehensive and consistent description of a photon's journey, it's important to consider both the local changes in energy within specific gravitational wells (as in "Δλ/λ = GM/(rc²)") and the overall path and effective deviation that accounts for all gravitational fields encountered (as in "0 = Δρ - Δρ"). 

"Eg" represent the total energy of a photon within an external gravitational field and I am not focusing on changes in the photon's intrinsic energy represented by "Δλ/λ," then the context and interpretation of your equations would be specific to the total energy state of the photon as it encounters external gravitational fields. (Eg) does not represent (Δλ/λ) which is inherent to photons intirnsic energy (E - ΔE).

Definition of Relativistic Time:

ORCiD: 0000-0003-1871-7803 Link: Research Gate DOI: http://dx.doi.org/10.32388/UJKHUB

Abstract: 

Relativistic time encompasses a range of intriguing phenomena, including time distortion, error in time, time delay, and time shift. It emerges from the intricate interplay of relative frequencies influenced by relativistic effects, such as motion and variations in gravitational potential. This abstract concept can be understood as a phase shift in relative frequencies, driven by two fundamental mechanisms. The first mechanism involves the infinitesimal loss of wave energy in oscillators with mass, resulting in time distortion or error in time measurement. This effect arises from the impact of motion on time measurement, manifesting as a phase shift or an error in the perception of time. The second mechanism centers on the infinitesimal loss of energy in propagating waves, leading to time delay or time shift. This phenomenon extends beyond motion and encompasses variations in gravitational potential. As a result, it introduces variations in the passage of time. Together, these mechanisms highlight the dynamic and interconnected relationship between relative frequencies, energy, and the perception of time in the context of relativistic effects. This abstract illuminates the multifaceted nature of relativistic time and the critical role it plays in our understanding of the fundamental principles governing the universe.

Definition:

Relativistic time encompasses phenomena of time distortion, error in time, time delay, and time shift.

Description:

Relativistic time emerges from the interplay of relative frequencies under the influence of relativistic effects, such as motion or gravitational potential difference. It can be understood as a phase shift in relative frequencies due to two primary mechanisms:

Infinitesimal Loss of Wave Energy in Oscillators with Mass (Time Distortion/Error in Time): This aspect of relativistic time arises from the influence of motion on time measurement. It manifests as a phase shift or error in time measurement due to the loss of wave energy in systems with mass.

Infinitesimal Loss of Energy of Propagating Waves (Time Delay/Time Shift): Another facet of relativistic time relates to the loss of energy in propagating waves, resulting in a time delay or time shift. 

Both of these effects are not limited to motion but also encompass gravitational potential differences, leading to variations in the passage of time. The associated phase shift in relative frequencies reflects the relative energy loss experienced by these waves.

Citation:

Thakur, Soumendra Nath; Samal, Priyanka; Bhattacharjee, Deep (2023). Relativistic Effects on Phaseshift in Frequencies Invalidate Time Dilation II. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.22492066.v2

Summary: Time Interval in Degrees and Phase Shift Analysis for Physical Phenomena:

Date: 10-10-2023 Author ORCiD: 0000-0003-1871-7803

Abstract:

This summary research paper delves into the intricate relationship between Time Interval in Degrees T(deg) and Phase Shift (ϕ) in various physical phenomena. It explores the applicability of T(deg) to different scenarios, including relative frequencies, wavelength changes, time delays, and distortions in oscillations. This paper aims to deepen our understanding of how phase shifts and time intervals are interconnected across different physical contexts. Furthermore, it sheds light on their implications for time distortion and emphasizes that it should not be confused with time dilation.

Introduction:

Time Interval in Degrees T(deg) and Phase Shift (ϕ) are fundamental concepts in the study of waves and oscillations in diverse physical phenomena. This paper explores the relationship between T(deg) and ϕ in various contexts and their implications for time distortion. Drawing inspiration from equations and examples outlined in the referenced research paper [1], this work emphasizes the connection between wave properties, particularly frequency and phase shift, and their role in shaping temporal variations. Importantly, it seeks to clarify that time distortion is distinct from the concept of time dilation, often misconstrued in scientific discourse.

Method:

In this research, we derive and examine a series of equations related to Time Interval in Degrees T(deg) and Phase Shift (ϕ) across different physical scenarios. Each equation represents a specific phenomenon and its impact on T(deg) and ϕ. We utilize these equations to calculate T(deg) and ϕ in various situations, providing concrete examples for clarity and illustration.

A few equations:

(1) Time Interval in Degrees T(deg) applicable to relative frequencies (f₀, f):

• T(deg) = (1/f₀ - 1/f) / 360 = Δt

ϕ = 360 × f₀ × T(deg)

(2) Time Interval in Degrees T(deg) applicable to change (Δλ₀) in relative wavelengths (λ₀, λ):

• T(deg) = (Δλ₀ / λ₀) / 360 = Δt

ϕ = 360 × f₀ × T(deg)

Discussion:

The analysis of the equations and examples presented in this paper highlights the versatility of Time Interval in Degrees T(deg) and its direct relationship with Phase Shift (ϕ) in various physical phenomena. These equations provide a fundamental understanding of how changes in frequency and wavelength influence T(deg) and subsequently affect ϕ. Furthermore, the discussion emphasizes the practical significance of these relationships in different scientific contexts. Importantly, it clarifies the distinction between time distortion and time dilation.

Conclusion:

In conclusion, this research paper explores the intricate connections between Time Interval in Degrees T(deg) and Phase Shift (ϕ) in diverse physical scenarios. By examining a range of equations and practical examples, we have elucidated how changes in wave properties, specifically frequency and wavelength, impact phase shifts and temporal variations. These findings enhance our comprehension of time distortion effects and their implications for relativistic phenomena. Understanding the interplay between T(deg) and ϕ contributes to the broader understanding of time-related concepts in physics and engineering.

Reference:

[1] Thakur, Soumendra Nath; Samal, Priyanka; Bhattacharjee, Deep (2023). Relativistic effects on phase shift in frequencies invalidate time dilation II. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.22492066.v2

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