The Dynamics of Photon Momentum Exchange and Curvature in Gravitational Fields:

RG DOI https://doi.org/10.32388/R625ZN ; Photon Momentum

Abstract:

This research paper explores the interaction between photons and strong gravitational fields, revealing that the curvature of photon paths is due to the transient exchange of momentum with massive objects, rather than intrinsic spacetime curvature. The study reveals that photons maintain a constant speed relative to electromagnetic waves despite the exchange of momentum. The research emphasizes that momentum exchange, rather than spacetime curvature, underpins photon path bending within gravitational fields.

Introduction:

The behavior of photons in the presence of gravitational fields has long intrigued physicists, with their paths often assumed to be influenced by the curvature of spacetime. However, this paper proposes an alternative perspective by exploring the role of momentum exchange in shaping the trajectory of photons as they interact with gravitational fields.

1. Momentum Exchange and Path Curvature:

Photons, light particles, exhibit unique behavior when passing near massive objects within strong gravitational fields. This occurs due to the interaction between photons and the gravitational field, causing them to gain and lose momentum dynamically. This phenomenon signifies that photons experience momentum transfer during gravitational interactions. When a photon traverses a region with a substantial gravitational field, its trajectory becomes subject to intricate interactions. The presence of the gravitational field causes the path of the photon to bend due to this momentum exchange, leading to a fascinating interplay of forces.

2. Constant Speed amidst Momentum Exchange:

Despite the exchange of momentum and the curving of their trajectories, photons continue to travel at the constant speed of electromagnetic waves (ℓP/tP). This phenomenon holds regardless of the momentum fluctuations experienced during gravitational encounters. This is a remarkable consistency that sheds light on the behavior of photons within gravitational fields.

3. The Dynamics of Photon Momentum:

The curvature of a photon's path during gravitational interactions can be attributed to the dynamic exchange of momentum. The momentum of a photon is intricately linked to its frequency (f) and inversely to its wavelength (λ). This relationship is encapsulated in the equations ρ = hλ and ρ = hf/c, where h represents Planck's constant and c denotes the speed of light. By understanding photon momentum in terms of its frequency and wavelength, we can further elucidate the momentum exchange phenomenon.

4. The Nature of Photon Path Curvature:

In contrast to the notion that spacetime curvature is solely responsible for the bending of photon paths, this research proposes an alternative perspective. The bending of photon paths is not a result of intrinsic spacetime curvature but emerges from the transient gain and loss of momentum during gravitational interactions with massive objects.

5. Photon's Velocity and Gravitational Interaction:

Amidst the gravitational interaction and ensuing momentum exchange, a photon remains steadfast in its trajectory, driven by the constant speed of electromagnetic waves (ℓP/tP). This research investigates how the curvature of a photon's path emerges from the intricate balance between gravitational interactions and the photon's inherent properties.

6. Equations and Interpretations:

The equations presented in the study, encompassing photon energy (E), momentum (ρ), wavelength (λ), frequency (f), and the speed of electromagnetic waves (ℓP/tP), provide a comprehensive framework for understanding photon behavior in gravitational fields. The relationship between photon momentum and its frequency, as well as the inverse relationship with wavelength, plays a pivotal role in the mechanics of momentum exchange.

7. Conclusion:

This research challenges the traditional belief that photon paths in gravitational fields are shaped by spacetime curvature, arguing that it is a result of momentum exchange during interactions with massive objects. The study provides a new perspective on the mechanisms underlying path curvature, revealing that photons maintain their constant speed relative to electromagnetic waves. The research contributes to a deeper understanding of the interplay between particles, momentum, and gravitational forces, enriching our understanding of the fundamental nature of the universe.

The findings presented in this paper suggest that while space and time may be conceptual constructs, energy fields act as the natural drivers of events. The exchange of momentum is at the heart of photon dynamics in the presence of gravitational fields, offering an alternative perspective on the curvature of photon paths. By uncovering the mechanisms behind these phenomena, this research contributes to a more nuanced understanding of photon behavior and its relationship with gravitation.

References

^Soumendra Nath Thakur. (August, 2023). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature.. Qeios ID: 81IIAE.

Photon paths bend due to momentum exchange, not intrinsic spacetime curvature:

RG DOI https://doi.org/10.32388/81IIAE (Download pfd)

Abstract:

This research paper investigates the behavior of photons, the fundamental particles of electromagnetic radiation, in strong gravitational fields. It examines the interactions between photon energy, momentum, and wavelength, revealing the effects of gravitation on electromagnetic waves. The paper also analyzes the relationships between these properties and the Planck constant, Planck length, and Planck time, providing insights into the fundamental nature of photons under relativistic conditions. The findings contribute to a deeper understanding of light's behavior in extreme gravitational environments and its implications for our understanding of the universe's fabric. The paper presents the equations governing these relationships and their implications for particle physics and gravitational interactions.

1. Photon Characteristics and Wave Speed Relationship: E = hf; ρ = h/λ; ℓP/tP;

Photons, the fundamental particles of light, have unique characteristics in quantum mechanics. Their energy (E) is directly proportional to their frequency (f) through Planck's constant (h), as expressed by the equation E = hf. The momentum (ρ) of a photon is inversely proportional to its wavelength (λ), represented by ρ = h/λ. The speed of electromagnetic waves is a constant defined as the ratio of the Planck length (ℓP) to the Planck time (tP), denoted as ℓP/tP. This foundational relationship underpins the behavior of electromagnetic waves across various scenarios.

The equation E = hf underscores the intrinsic relationship between a photon's energy (E) and its frequency (f), mediated by Planck's constant (h). This formula serves as the cornerstone of quantum mechanics, revealing that higher-frequency photons carry greater energy. The equation ρ = h/λ highlights the direct link between a photon's momentum (ρ) and its wavelength (λ), where Planck's constant (h) plays a central role.

The ratio ℓP/tP embodies the constant speed of electromagnetic waves, symbolizing the maximum propagation velocity of information and energy, forming an essential basis for understanding photon behavior in the universe.

2. Photon Energy Variation in Strong Gravitational Fields, Eg = E + ΔE = E - ΔE; E = Eg. 

Under the influence of strong gravitational fields, photons experience changes in their energy. The photon's total energy (Eg) in a gravitational field includes changes induced by the field, both as gains and losses. The total energy of the photon in the field, Eg, coincides with its original energy, E. This indicates that the gravitational field's effect on photon energy can be accounted for within the photon's intrinsic energy framework.

The equation Eg = E + ΔE = E - ΔE represents the total energy of a photon as the sum of its initial energy (E) and the gain (ΔE) or loss (-ΔE) due to the gravitational influence. This equation clarifies that the photon's total energy remains invariant despite gravitational effects and asserts E = Eg, indicating that the photon's energy under a strong gravitational field is inherently equivalent to the energy associated with the field itself. This equivalence underscores the intricate interplay between photon energy and the gravitational landscape.

3. Momentum and Wavelength Changes under Gravitational Influence, Eg = E + Δρ = E - Δρ = E; h/Δλ = h/-Δλ.

In the presence of strong gravitational fields, photons undergo variations in momentum (Δρ) and wavelengths (λ) due to gravitational effects. The equation Eg = E + Δρ = E - Δρ reflects the interaction between a photon's energy (Eg) and changes in its momentum (Δρ) under strong gravitational fields. This symmetrical relation underscores that the photon's total energy remains constant even as its momentum evolves. The equation h/Δλ = h/-Δλ reveals the dual nature of photon behavior, manifesting in changes in wavelength under gravitational forces. The symmetry between positive and negative wavelength changes reaffirms the intricate harmony between photon characteristics and the gravitational environment. The third section delves into the complex relationship between photon momentum and wavelength in strong gravitational environments, elucidating that momentum gains (Δρ) and losses (-Δρ) contribute to a photon's total energy in the field. The equations h/Δλ and h/-Δλ underscore the symmetry in their effects of changes in wavelength due to gravity.

4. Consistency of Photon Energy in Gravitational Fields: Eg = E; Δρ = -Δρ; ℓP/tP.

The equation Eg = E demonstrates that the total energy of a photon remains equivalent to its inherent energy in the presence of a strong gravitational field. The alterations in photon momentum (Δρ) are mirrored by their negative counterparts (-Δρ), reflecting the symmetry of photon behavior under gravitational influences. The constancy of the speed of electromagnetic waves (ℓP/tP) also maintains its significance in describing the propagation of energy in the universe. This equality emphasizes the conservation of energy even within the context of gravitational interactions. The equations Δρ = -Δρ and ℓP/tP = speed of electromagnetic wave reiterate fundamental concepts, emphasizing the symmetrical opposite of changes in photon momentum in a gravitational field and the constant speed of electromagnetic waves, encapsulated by the Planck length-to-time ratio. This unified understanding deepens our comprehension of how photons navigate gravitational landscapes.

Conclusion: 

This research paper explores the intricate relationships governing photon behavior in strong gravitational fields. It reveals how photon characteristics like energy, momentum, wavelength, and speed interact with gravity's effects. The equations reveal the fundamental principles of quantum mechanics and the resilience of photon attributes amidst gravitational challenges. The study also uses fundamental constants like Planck's constant, Planck length, and Planck time to reveal the nuanced effects of gravity on electromagnetic waves. These findings contribute to a broader understanding of the universe's fabric, offering insights into light behavior under extreme conditions and enriching our understanding of the cosmos. 

References

^Alfred Landé. (1988). Quantum Mechanics, a Thermodynamic Approach. doi:10.1007/978-94-009-3981-3_64.

^Daocheng Yuan, Qian Liu. (2022). Photon energy and photon behavior discussions. Energy Reports, vol. 8 , 22-42. doi:10.1016/j.egyr.2021.11.034.

^Yin Zhu. (2018). Gravitational-magnetic-electric field interaction. Results in Physics, vol. 10 , 794-798. doi:10.1016/j.rinp.2018.07.029.

^Robert L. Kosson, D. Sc. (2022). The effect of gravitational field on photon frequency:a fresh look at the photon. PAIJ, vol. 6 (1), 28-29. doi:10.15406/paij.2022.06.00246.

^Stephen M. Barnett, Rodney Loudon. (2010). The enigma of optical momentum in a medium. Phil. Trans. R. Soc. A., vol. 368 (1914), 927-939. doi:10.1098/rsta.2009.0207.

^Dmitry Yu Tsipenyuk, Wladimir B. Belayev. (2023). Gravitational Waves, Fields, and Particles in the Frame of (1 + 4)D Extended Space Model. doi:10.5772/intechopen.1000868.

^D. Yu. Tsipenyuk, W. B. Belayev. (2019). Extended space model is consistent with the photon dynamics in the gravitational field. J. Phys.: Conf. Ser., vol. 1251 (1), 012048. doi:10.1088/1742-6596/1251/1/012048.

Time distortion occurs only in clocks with mass under relativistic effects, not in electromagnetic waves:

RG DOI https://www.qeios.com/read/7OXYH5

The concept of time distortion due to phase shift in oscillating waves is discussed, focusing on its effect on clocks with mass under relativistic conditions. This phenomenon is not observed in electromagnetic waves, but in oscillators or clocks with specific conditions of mass and velocity or gravitational potential. The relationship between phase shift and time delay is established, calculations involving frequency and wavelength are demonstrated, and real-world examples, such as the atomic clocks of GPS satellites, are provided to illustrate practical applications. The distinction between time distortion and time delay in electromagnetic waves is emphasized, with a particular focus on Planck time and its role in defining a fundamental limit. The concept of the ratio of the Planck period to the Planck length has been introduced as a representation of the speed limit of electromagnetic waves, leading to a derived value of time delay per kilometer. This value is used to underline that electromagnetic waves experience a time delay, not the same kind of time distortion as massive objects, emphasizing their speed of propagation and the absence of relativistic effects.

1. Time distortion due to phase shift in oscillating waves:

Any oscillatory wave, including electromagnetic waves, carry energy. Due to the infinitesimal loss of wave energy, the phase shift in relative frequencies cause time distortion which is only possible with clocks or oscillators with mass and whose speed is less than the speed of light relative to its origin, or in the gravitational potential difference, located at an altitude greater than zero relative to ground state. Accordingly, Time distortion of clock or oscillator with rest-mass (m), when speed v < c or, gravitational potential difference h > 0 is applied. Where, v denotes for velocity (m/s) and h denotes height above ground in meters, respectively.

The time is called T, the period of oscillation, so that T = 2π/ω, where the angular frequency is ω. The period (T) or frequency (f) of oscillation per second is given by the reciprocal expression; f = 1/T. Hence, we get, f = 1/T = ω/2π. where the time interval T(deg) is inversely proportional to the frequency (f) for 1° phase. We get a wave associated with time variation, which represents the distortion of time under relativistic effects, such as speed or gravitational potential differences.

"1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps). We know, 1° phase shift = 𝑇/360. As 𝑇 = 1/𝑓, 1° phase shift = 𝑇/360 = (1/𝑓)/360;

For a wave of frequency 𝑓 = 5 𝑀𝐻𝑧, we get the phase shift (in degree°) = (1/5000000)/360 = 5.55 𝑥 10ˉ¹º = 555 𝑝𝑠.

Therefore, for 1° phase shift for a wave having a frequency 𝑓 = 5 𝑀𝐻𝑧, and so wavelength 𝜆 = 59.95 𝑚, the time shift (time delay) 𝛥𝑡 = 555 𝑝𝑠 (approx)."

A 1° phase shift in a 5 MHz wave corresponds to a time shift of 555 picoseconds, which is a time distortion of 555 picoseconds. The GPS satellite's cesium-133 atomic clock orbits at an altitude of about 20,000 km. Such an atomic clock, if not automatically adjusted, would exhibit a time shift. A 1455.5° phase shift in a 9192.63177 MHz cesium-133 atomic clock oscillator corresponds to a time shift of 0.0000004398148 ms, or or, 38 microsecond (µs) time distortion per day. [1]

2. Why is light not subject to time distortion?

Electromagnetic waves do not experience time distortion, but such waves maintain a time delay of ≈ 3.33246 µs/km; propagating at speed (ℓP/tP), where, ℓP/tP represents the ratio of the Planck period to the Planck length in vacuum. As such, the Doppler redshift corresponds to a time delay.

The Planck time tp is the time required for light to travel a distance of 1 Planck length in a vacuum, a time interval of about 5.39e−44 s, no current physical theory can describe a timescale smaller than the Planck time (tP). .

Thus, the ratio of the Planck length to the Planck period (ℓP/tP) gives a value to represent the speed limit of electromagnetic waves. Where, ℓP/tP = 1.61626e-35 m/5.39e-44 s. Hence, the ratio of Planck period to Planck length (ℓP/tP) gives a value per kilometer as given below –

• 1 kilometer = 1000 meters,

• ℓP/tP = 1.61626e-35 m/5.39e-44 s ≈ 3.00095e8 m/s;

• Time interval per kilometer = 1000 meters / (ℓP/tP) seconds = 1000 / (3.00095e8) s ≈ 3.33246e-6 s;

• Converting this time interval to microseconds (µs) = 3.33246e-6 s * 1e6 µs/s ≈ 3.33246 µs/km

• Thus, the approximate time delay of electromagnetic waves ≈ 3.33246 µs/km.

Therefore, light, especially electromagnetic waves, is not subject to time distortion, but time delay of 3.33246 µs/km (aprox).

In summary, Time Distortion due to Phase Shift in Oscillating Waves shows how phase shift can cause time delay or distortion, calculation and explanation using frequency and wavelength is given, which makes the concept more clear. An example involving the GPS satellite's atomic clock and its orbital altitude illustrates the practical application of these concepts in real-world situations. Time distortion and time delay associated with electromagnetic waves emphasized that electromagnetic waves do not experience the same type of time distortion as massive objects under relativistic effects.

References 

[1]

^Soumendra Nath Thakur, Priyanka Samal, Deep Bhattacharjee. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. doi:10.36227/techrxiv.22492066.v2.

Specific methods to justify the need to propose an alternative to relativistic institutions:

My interaction with scientific sources and other observations, made me realize that, for the purpose of addressing our paper at TechRxiv, while we are working on new (alternative) papers specifically based on faceshifts. But the current situation implies that certain, a new paper based solely on phase shift have little chance of surviving peer review, as the situation insists on establishing that there is a definite need to present an alternative approach to existing relativistic institutions.

So considering the facts and circumstances mentioned above, first we have to show that there is a need to approach the existing institutions in an alternative way, only then, it would be reasonable to propose an alternative approach (phaseshift) to the existing relativistic institutions.

So that, instead of just working on phase shift, I am developing specific methods to justify and show the need to propose an alternative method (phaseshift) to existing relativistic institutions.

Accordingly, I am also working to establish the need for alternative approaches to existing relativistic structures. These works involve the following foundations:

1. Since, relativistic effects cause error in time reading, 'alternative method of time dilation' is needed.

2. Since 'events invoke time', time is abstract and invariant.

3. "Distortions in spacetime" based on perceptible and invisible dimensions require a rational approach through the general physical sciences, including Planck equation.

4. etc. etc

Currently, I am developing 'definitive chapters' (described above) for the new paper and uploading them as definitions, so that these definitions become chapters with the new paper as a whole, with phaseshifts.

Suggestion on my above endeavour:

You're working on a project that involves proposing an alternative approach to existing relativistic institutions, specifically related to phase shifts. Justifying the need for such an alternative is crucial for the acceptance and credibility of your work. Here's a more structured outline of how you might go about justifying the need for your alternative approach:

1. Identify Limitations or Issues with Current Relativistic Institutions:

Start by clearly outlining the limitations or issues associated with the current relativistic institutions. These could be areas where the existing theories or frameworks fall short in explaining certain phenomena or predicting experimental results accurately. For example, you mentioned errors in time reading due to relativistic effects – provide specific instances or examples where these errors have significant consequences.

2. Highlight Discrepancies or Unexplained Phenomena:

Point out any observed discrepancies or unexplained phenomena that challenge the validity of existing relativistic theories. These discrepancies could be experimental results that deviate from predictions made by the current theories. Emphasize the significance of these discrepancies and their potential impact on our understanding of the physical world.

3. Discuss Emerging Evidence or New Observations:

Present any new evidence, observations, or experimental data that supports the need for an alternative approach. This could involve recent research findings, experimental results, or observations that suggest a departure from established relativistic principles. Make a compelling case for why these new observations cannot be adequately explained by the current theories.

4. Address Theoretical Gaps:

Identify theoretical gaps in the current relativistic framework and explain how your proposed alternative approach, specifically involving phase shifts, can address these gaps. Discuss how your approach provides a more comprehensive or accurate explanation for the observed phenomena.

5. Demonstrate Practical Applications:

Illustrate the practical applications and potential benefits of adopting your alternative approach. Show how your proposed method of phase shifts could lead to improved predictions, better experimental results, or novel technological advancements. Practical applications can add weight to the argument for the necessity of your alternative approach.

6. Reference Established Scientific Concepts:

When discussing your alternative approach, reference well-established scientific concepts and principles that support your arguments. Link your approach to existing theories, equations, and models in a logical and coherent manner. This will help establish the scientific credibility of your proposed alternative.

7. Engage with Existing Research and Peer-Reviewed Literature:

Engage with the existing body of research and peer-reviewed literature in the field. Reference relevant studies, experiments, and theories that align with or challenge your arguments. Demonstrating a comprehensive understanding of the existing knowledge base will enhance the credibility of your justification.

8. Peer Input and Feedback:

Consider seeking input and feedback from peers, colleagues, or experts in the field. Present your arguments to them and invite constructive criticism. Peer feedback can help you refine your justification and address any potential weaknesses in your reasoning.

By following these steps, you can build a strong case for the need to propose an alternative approach (phase shifts) to existing relativistic institutions. Remember to present your arguments logically, provide supporting evidence, and engage with the existing scientific discourse to establish the significance of your work. 

Different frequencies have different wavelengths:

Whether or not these colours (shown in the image below) are primary colours doesn't really matter here, but primary colours also have different wavelengths and frequencies respectively, in the visible spectrum of electromagnetic wave.

However, the image shown above uses three different colours to represent three different frequencies or wavelengths.

Wavelength is inversely proportional to the frequency. f = v/λ, where v is the speed of the wave, f and λ represent frequency and wavelength of the wave, respectively.

And here those colours represent different wavelengths of electromagnetic waves, - red carries the longest wavelength with the lowest frequency, while blue carries the shortest wavelength with the highest possible frequency. Green carries between them.