CMBR - the Observable and Non-Observable II:

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CMBR, the Observable and Non-Observable Universes, and Their Respective Distances:

Abstract:                              

This research paper embarks on a captivating exploration of cosmic vistas, delving into the enigmatic origins of the universe, the cosmic microwave background radiation (CMBR), and the intricate interplay between observable and non-observable universes. Guided by the monumental Big Bang theory, we journey through the emergence of the universe from an infinitesimal singularity and its expansive phase governed by inflationary forces. The CMBR, an echo from the universe's dawn, unveils the saga of its early epochs and the daring journey of the first light. Mathematical frameworks like Hubble's Law, co-moving distance, redshift-distance relation, future visibility limit, and non-observable universe's extension lay the foundation for our cosmic exploration. We reveal the expansion of the universe, the distribution of observable and unobservable galaxies, and the size of the observable Universe. This narrative unfolds a tale of emergence and evolution over eons, resonating with themes of curiosity and understanding that span unfathomable timescales.

Introduction:

The introduction sets the stage for an exploration of cosmic history, beginning with the cataclysmic event known as the Big Bang, which ignited the universe's expansion. Central to this discourse is the concept of the cosmic microwave background radiation (CMBR), an echo from the universe's inception that sheds light on its formative stages. The paper embarks on a voyage into the realm of profound cosmic ideas, including the nature of the observable and non-observable universes and their intricate spatial connections. The monumental backdrop of the Big Bang theory guides our exploration, leading us through the emergence of the universe from an infinitesimal singularity, followed by its expansive phase governed by inflationary forces. Anchoring our journey is the CMBR—an echo from the universe's primordial dawn that reveals the saga of its early epochs and the daring journey of the first light. The tapestry of time itself is probed, unveiling the temporal intricacies of these realms shaped by phenomena like redshift and the relentless cosmic expansion. The current observational frontier extends 46.5 billion light-years, unveiling 43% of galaxies while leaving 57% unseen. Rigorous mathematics, including Hubble's Law and the redshift-distance relation, frame our exploration of cosmic mechanics, nurturing the growth of understanding and discovery.

Methods:

In this section, the mathematical tools that underpin our analysis are presented. Equations central to our exploration are described, including Hubble's Law, the co-moving distance calculation, the redshift-distance relation, the future visibility limit, and the non-observable universe's extension. Each equation is elucidated, with its relevance and implications for our understanding of cosmic phenomena explained. The timeline of cosmic events and the quantitative aspects of observable and unobservable galaxies are elucidated through mathematical presentation.

Relevant Equations:

1. Hubble's Law: v = H0 * d

2. Co-moving Distance: D = c * ∫(from 0 to z) [dz' / H(z')]

3. Redshift-Distance Relation: z = {λ(obs) - λ(emit)} / λ(emit)

4. Future Visibility Limit: d(future) = c / H0

5. Non-Observable Universe's Extension: Extension = Expansion factor * Observable Universe's Size = 250 * 46.5 b.ly = 11,625 billion light-years

6. CMBR Spectrum: I(λ,T) is the intensity of radiation at wavelength λ and temperature T. h is the Planck constant. c is the speed of light. k is the Boltzmann constant.

7. CMBR Anisotropy: T(θ,ϕ) is the temperature fluctuation at a point on the sky characterized by angles θ and ϕ. l represents the multipole moment, which quantifies the scale of the fluctuation pattern. m is the azimuthal quantum number. Ylm(θ,ϕ) are the spherical harmonics.

8. Alignment and Axis of Evil: where alm and ′alm are coefficients of different multipole moments l and l′.

9. Quadrupole and Octopole Cold Points: The patterns are represented by the coefficients a2m and a3m respectively.

Results:

Our exploration yields profound insights into the cosmic narrative. The Big Bang's occurrence 13.8 billion years ago marked the universe's inception, and the initiation of the Cosmic Microwave Background (CMB) radiation at 13.79962 billion years serves as a beacon from its dawn. The observable universe stretches 46.5 billion light-years in every direction, granting visibility to 43% of galaxies while leaving 57% concealed in the non-observable universe. Rigorous mathematical frameworks like Hubble's Law reveal the expansion's mechanics, and our voyage through cosmic equations provides a quantitative grasp of the universe's structure.

Discussion:

The discussion unravels the implications of our findings. We delve into the intricate patterns within the CMBR, from concentric circles to the Axis of Evil and Quadrupole and Octopole Cold Points. These anomalies, revealed by satellites like COBE, WMAP, and Planck, challenge our understanding of the universe's early moments. The co-moving distance and redshift-distance relation offer insights into cosmic expansion, while the future visibility limit and non-observable universe's extension shape the limits of our perception. We contemplate the nature of observable and unobservable galaxies, their spatial relationships, and the implications for our understanding of cosmic evolution.

Conclusion:

In the grand symphony of cosmic exploration, our journey through time and space has illuminated the universe's enigmatic origins and evolutionary tapestry. The CMBR's echoes carry whispers of the universe's dawn, revealing its early epochs and the journey of the first light. Mathematical equations, from Hubble's Law to the redshift-distance relation, have woven a thread of understanding that binds cosmic theory and observation. As we conclude this chapter of exploration, we stand at the precipice of curiosity, poised to venture further into the mysteries that the universe continues to unveil. Our endeavor echoes the timeless themes of human discovery and the pursuit of knowledge across the cosmic expanse.

References:

[1]. Planck Collaboration. (2016). Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics, 594, A13. DOI: https://doi.org/10.1051/0004-6361/201525830

[2]. Riess, A. G., et al. (2019). Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, 876(1), 85. DOI: https://doi.org/10.3847/1538-4357/ab1422

[3]. Peebles, P. J. E., & Ratra, B. (2003). The Cosmological Constant and Dark Energy. Reviews of Modern Physics, 75(2), 559-606. DOI: https://doi.org/10.1103/RevModPhys.75.559

[4]. Dunkley, J., et al. (2009). Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP Data. The Astrophysical Journal Supplement Series, 180(2), 306-329. DOI: https://doi.org/10.1088/0067-0049/180/2/306

[5]. Komatsu, E., et al. (2011). Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series, 192(2), 18. DOI: https://doi.org/10.1088/0067-0049/192/2/18

[6]. Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.

[7]. Carroll, S. M. (2004). Spacetime and Geometry: An Introduction to General Relativity. Pearson.

[8]. Spergel, D. N., et al. (2003). First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. The Astrophysical Journal Supplement Series, 148(1), 175-194. DOI: https://doi.org/10.1086/377226

[9]. Peacock, J. A. (1999). Cosmological Physics. Cambridge University Press.

[10]. Liddle, A. R., & Lyth, D. H. (2000). Cosmological Inflation and Large-Scale Structure. Cambridge University Press.

[11]. Mukhanov, V. F. (2005). Physical Foundations of Cosmology. Cambridge University Press.

[12]. Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press.

Cosmic Microwave Background Radiation, the Observable and Non-Observable Universes, and Their Respective Distances:

Abstract:

This research paper explores cosmic concepts like the cosmic microwave background radiation (CMBR), observable and non-observable universes, and their spatial relationships. Guided by the Big Bang theory, it delves into the universe's origin - a story of emergence from a tiny singularity and subsequent inflation. The CMBR, an echo from the universe's dawn, reveals its early history and the first light's journey. The paper probes the temporal dimensions of observable and non-observable universes, shaped by redshift and expansion. Our observational limit lies 46.5 billion light-years away, unveiling 43% of galaxies, leaving 57% unseen. Mathematical frameworks like Hubble's Law elucidate cosmic mechanics, fostering understanding and discovery. This journey of exploration uncovers the universe's grand design, echoing themes of curiosity and evolution over billions of years.

Introduction:

The introduction sets the stage for an exploration of cosmic history, beginning with the cataclysmic event known as the Big Bang, which ignited the universe's expansion. Central to this discourse is the concept of the cosmic microwave background radiation (CMBR), an echo from the universe's inception that sheds light on its formative stages. The paper embarks on a voyage into the realm of profound cosmic ideas, including the nature of the observable and non-observable universes and their intricate spatial connections. The monumental backdrop of the Big Bang theory guides our exploration, leading us through the emergence of the universe from an infinitesimal singularity, followed by its expansive phase governed by inflationary forces.

A pivotal focus is the cosmic microwave background radiation (CMBR), which serves as a beacon from the universe's dawn, preserving the footsteps of its early luminal journey. This ethereal radiation, barely perceptible to our telescopic instruments, offers a unique window into the universe's nascent moments - an echo of the first light that ventured through space. A crucial juncture lies 380,000 years post-Big Bang, where the seeds of galaxies and stars were sown, leaving their imprint on the canvas of the CMB.

Beyond this, the inquiry delves into the temporal intricacies of the observable and non-observable universes, intricately interwoven in their dynamics and boundaries. Over the expanse of 13.8 billion years, celestial objects emitting light have gradually distanced themselves, etching the phenomenon of redshift into the universe's narrative. However, our ability to observe is restricted by a frontier - 46.5 billion light-years distant-beyond which 57% of galaxies lie, unseen and non-observable, while 43% remain within our perceptible realm.

Guided by rigorous mathematics, the paper reveals the cosmic mechanics underpinning our explorations. Hubble's Law, the redshift-distance relation, and the future visibility limit are among the mathematical tools that frame our investigations. These equations are seamlessly woven into our narrative, unravelling the grand design of the universe, from its inception to the expansive horizon that stretches beyond our current grasp.

This paper beckons readers to embark on a journey of discovery and exploration, using analytical lenses to demystify the origins of the cosmos and the infinite expanse that urges us to venture further. This endeavour highlights the spectacular evolution of our universe - a cosmic symphony composed over eons - that resonates with themes of curiosity, understanding, and the eternal pursuit of knowledge.

Methods:

In this section, the mathematical tools that underpin our analysis are presented. Equations central to our exploration are described, including Hubble's Law, the co-moving distance calculation, the redshift-distance relation, the future visibility limit, and the non-observable universe's extension. Each equation is elucidated, with its relevance and implications for our understanding of cosmic phenomena explained. 

The timeline of cosmic events and the quantitative aspects of observable and unobservable galaxies are elucidated through mathematical presentation -

1. The Big Bang occurred 13.8 billion years ago. 

2. The initiation of the Cosmic Microwave Background (CMB) radiation occurred 13.79962 billion years ago.

3. The co-moving distance of the observable Universe is given as 14.26 gigaparsecs, which can be converted to other units: 

Observable Universe distance = 46.5 billion light-years = 4.40e26 meters

4. The extension of non-observable Universe distance = 250 * 46.5 b.ly = 11,625 billion light-year

5. Currently, we have visibility of only 43% of galaxies from the observable Universe, with the observable Universe extending 46.5 billion light-years in any direction from the Earth.

6. In the distant future, an additional 57% of galaxies from the observable Universe will become observable.

7. Number of observable galaxies from the observable Universe: 

Number of observable galaxies = (Percentage of observable galaxies) × Observable Universe size 

= (0.43) × (46.5billion light-years) 

≈ 19.995 billion light-years

8. Number of unobservable galaxies from the observable Universe: 

Number of unobservable galaxies = (0.57) × (46.5billion light-years)

≈ 26.505 billion light-years

These mathematical expressions and calculations provide a quantitative understanding of the expansion of the universe, the distribution of observable and unobservable galaxies, and the size of the observable Universe.

Relevant Equations:

Hubble's Law: 

The relationship between the recessional velocity of a galaxy, denoted as v, and its distance from an observer, denoted as d, is described by Hubble's law:

v = H0 * d

Where H0 is the Hubble constant, representing the rate of cosmic expansion -.

Co-moving Distance: 

The co-moving distance, denoted as D, takes into account the expansion of the universe over time. It can be calculated using the formula:

D = c * ∫(from 0 to z) [dz' / H(z')]

Where c is the speed of light, z is the redshift of the object, and H(z) is the Hubble parameter as a function of redshift.

Redshift-Distance Relation: 

The redshift of an object, denoted as z, is related to its distance through the equation:

z = {λ(obs) - λ(emit)} / λ(emit)

Where λ(obs) is the observed wavelength of light from the object and λ(emit) is the wavelength of light emitted by the object.

Future Visibility Limit: 

The distance beyond which objects are receding from us faster than the speed of light, making them unreachable and invisible, is calculated using the equation:

d(future) = c / H0

Beyond this distance, objects are forever beyond our observational reach.

Non-Observable Universe's Extension: 

The extension of the non-observable universe, compared to the observable universe, is given by:

Extension = Expansion factor * Observable Universe's Size = 250 * 46.5 b.ly

= 11,625 billion light-years

Results:

Here, we unveil the outcomes of our investigations. Calculations reveal the temporal milestones of the Big Bang and the inception of CMBR. The percentages of observable and non-observable galaxies are derived, shedding light on our current observational capabilities. The co-moving distance of the observable universe is quantified, and the extension of the non-observable universe is unveiled, emphasizing its vastness.

Discussion:

The discussion section engages with the profound implications of our findings. We delve into the CMBR as a portal to the universe's primordial era, deciphering its importance in deciphering the seeds of galaxies and stars. The expanding observable and non-observable universes are contextualized within the broader narrative of cosmic evolution. The limitations of our observational capacities and the potential for future advancements are explored.

Conclusion:

The conclusion encapsulates the essence of our research journey. The significance of the CMBR and its implications for cosmology are underscored. The paper reiterates the magnitude of the non-observable universe and the ongoing pursuit of understanding our cosmic origins. We emphasize the ongoing importance of research in unravelling the mysteries of the universe.

References:

[1]. Planck Collaboration. (2016). Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics, 594, A13. DOI: https://doi.org/10.1051/0004-6361/201525830

[2]. Riess, A. G., et al. (2019). Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, 876(1), 85. DOI: https://doi.org/10.3847/1538-4357/ab1422

[3]. Peebles, P. J. E., & Ratra, B. (2003). The Cosmological Constant and Dark Energy. Reviews of Modern Physics, 75(2), 559-606. DOI: https://doi.org/10.1103/RevModPhys.75.559

[4]. Dunkley, J., et al. (2009). Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP Data. The Astrophysical Journal Supplement Series, 180(2), 306-329. DOI: https://doi.org/10.1088/0067-0049/180/2/306

[5]. Komatsu, E., et al. (2011). Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series, 192(2), 18. DOI: https://doi.org/10.1088/0067-0049/192/2/18

[6]. Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.

[7]. Carroll, S. M. (2004). Spacetime and Geometry: An Introduction to General Relativity. Pearson.

[8]. Spergel, D. N., et al. (2003). First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. The Astrophysical Journal Supplement Series, 148(1), 175-194. DOI: https://doi.org/10.1086/377226

[9]. Peacock, J. A. (1999). Cosmological Physics. Cambridge University Press.

[10]. Liddle, A. R., & Lyth, D. H. (2000). Cosmological Inflation and Large-Scale Structure. Cambridge University Press.

[11]. Mukhanov, V. F. (2005). Physical Foundations of Cosmology. Cambridge University Press.

[12]. Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press.

[13] Longair, M. S. (2013). The Cosmic Century: A history of astrophysics and cosmology. Cambridge University Press. https://doi.org/10.1080/00107514.2013.868524

[14] Matravers, D. (2008). Steven Weinberg: Cosmology. General Relativity and Gravitation, 41(6), 1455–1458. https://doi.org/10.1007/s10714-008-0728-z 

[15] Roos, M. (2005). Introduction to cosmology. Wiley. 

[16] Weinberg, S. (1980). The first three minutes: A modern view of the origin of the universe. Fontana etc.

Relativistic effects and photon-mirror interaction - energy absorption and time delay:

Soumendra Nath Thakur¹

¹Tagore's Electronic Lab. India

RG DOI : 10.13140/RG.2.2.20928.71683

  23 AUG 2023

                          Abstract:

This research paper explores the intricate interplay between photons and mirrors, shedding light on the processes that occur during photon-mirror interactions. We delve into the absorption of photons by electrons on a mirror's surface, which leads to energy gain and movement of electrons to higher energy levels. This interaction, akin to photoelectric absorption, is fundamental to understanding the behavior of light and mirrors. The paper investigates the principles of mirror reflectivity, highlighting the optimization of reflectivity by minimizing energy absorption (ΔE) to maintain high reflectivity. We also examine the angles of incidence and reflection, emphasizing their equal values and the related sum of angles.
Through careful analysis, we establish that the energy difference between incident and reflecting photons, denoted as ΔE, corresponds to a time delay (Δt) between the photons. This unique relationship between energy and time delay introduces the concept of infinitesimal time delay during reflection, contributing to a time distortion in the behavior of light. The research culminates in the assertion that the constancy of motion of a photon of light is disrupted when it is reflected by a mirror due to the introduced time delay.

 Introduction:

The interaction between photons and mirrors is a fundamental phenomenon with profound implications for our understanding of light and its behavior. In this research, we delve into the intricate details of photon-mirror interactions, energy absorption, and the subsequent time delay introduced by the interaction.

 Photon-Mirror Interaction and Energy Absorption:

When a photon collides with an atom on a mirror's surface, it has the potential to be absorbed by an electron within the atom. This absorption results in the electron gaining energy (hf) and transitioning to a higher energy level. This process, analogous to photoelectric absorption, is central to the interaction between photons and mirrors. The mirror's reflectivity is optimized by minimizing energy absorption (ΔE), ensuring that high reflectivity is maintained. The energy of the reflected photon, denoted as hf-ΔE, represents the energy loss within the mirror.

 Angle of Incidence and Reflection:

The angles of incidence and reflection play a pivotal role in photon-mirror interactions. The relationship between these angles is such that the angle of incidence (θi) is equal to the angle of reflection (θr). This relationship is also expressed in terms of angles in degrees (θi and θr), where θi+θr=180°. This symmetry in angles contributes to the predictable behavior of reflected photons.

 Photon Energy Absorption and Time Delay:

The difference in energy between the incident photon (γi) and the reflecting photon (γr) is represented as ΔE, which signifies the energy absorbed by the mirror. Remarkably, this energy difference also corresponds to a time delay (Δt) between the incident and reflecting photons. This intriguing relationship between energy and time introduces the concept of infinitesimal time delay during reflection, leading to a time distortion in the behavior of light.

 Equations and scientific foundations:

When a photon (hf) interacts with an atom on a mirror's surface, it can indeed be absorbed by an electron in the atom. This interaction results in the electron gaining energy (hf) from the absorbed photon. This increase in energy can cause the electron to move to a higher energy level within the atom, farther away from the nucleus. Photoelectric absorption takes place. Mirrors are made to minimize absorption (ΔE) in order to maintain high reflectivity.  Optimize reflectivity (hf- ΔE) and minimize light absorption (ΔE). The reflected photon will have energy (hf- ΔE). The reflected photon will have energy of (hf−ΔE).

 The angle of incidence (θi) is equal to the angle of reflection (θr). Since, the angle of incidence (θi) is equal to the angle of reflection (θr), θi = θr; and, the sum of the angles of incidence (θi) and reflection (θr) always equals 180°, θi + θr = 180°. Therefore, if the angle of incidence (θi) = 180°, so the, angle of reflection (θr) = 180°.

 The reflected photon having energy (hf- ΔE) travels in the opposite direction of the interacting photon with energy (hf), the angle of incidence is equal to the angle of reflection. This means that the direction of the reflected photon is related to the direction of the incident photon but is not necessarily opposite to it.

 Briefly, incident photon energy (γi) = hf; reflecting photon energy (γr) = (hf−ΔE); photon energy absorption (γi - γr) = (ΔE);

 So, when a photon of light at the speed of light strikes or collides with a mirror wall, initially, the photon is absorbed by electrons in the mirror's surface atoms. In effect, the collision causes another photon to detach from an electron in an atom on the mirror surface, and the detached photon travels at the speed of light but in the opposite direction to the colliding photon. As a result, some of the energy of the colliding photons is lost in the collision with the mirror surface.

The reflected photon having energy (hf- ΔE) travels in the opposite direction of the interacting photon with energy (hf), at a 180° angle, when the angle of incidence was 180°.

Briefly, when a photon collides with a mirror surface, it is initially absorbed by electrons in the mirror's surface atoms. The collision causes another photon to detach from an electron in an atom on the mirror surface. The detached photon travels at the speed of light but in the opposite direction to the colliding photon. Some energy of the colliding photons is lost in the collision with the mirror surface.

The energy of the incident photon is hf, where h is Planck's constant and f is the frequency of the photon. The energy of the reflecting photon is hf−ΔE, where ΔE represents energy loss due to interactions within the mirror. The difference in energy between the incident and reflecting photons is ΔE. This difference represents the energy absorbed by the mirror and not reflected.

The photon energy absorption = (γi - γr), the difference in energy between the incident and reflecting photons = ΔE.

Assuming, the incident photon frequency = f1; when, the incident photon energy = (γi); and, the reflecting photon frequency = f2; when, the reflecting photon energy = (γr); the change in energy between incident photon and reflecting photon = ΔE;

The change in energy (ΔE) is equal to the time delay (Δt) between the incident photon and the reflecting photon. This suggests a relationship between the energy difference of the incident and reflecting photons and the difference in frequencies (f1 and f2) of those photons., presented by the equation,

Given Equations:

• ΔE = γi−γr = Infinitesimal loss in wave energy
• f1 = incident photon frequency
• f2 = reflecting photon frequency
• T(deg) = T/360 = (1/f)/360 = Δt
• f = E/h = 1/360*T(deg)
• T(deg) = 1/f*360 = Δt 

So, the relationships are -

• ΔE =γi−γr
• Δt=f1−f2     

Hence,

• ΔE = Δt. *(Update below)

Therefore when, there is an infinitesimal time delay (Δt) between the colliding photon (γi) and the diffusing photon (γr) to change direction of travel. Therefore, the constancy of motion of a photon of light is broken when it is reflected by a mirror.

Conclusion:

This research paper explores the intricate interactions between photons and mirrors, revealing the processes of energy absorption and time delay. We have shown that the energy absorbed by a mirror during photon-mirror interaction is intricately tied to the time delay between incident and reflecting photons. This relationship challenges our conventional understanding of the constancy of motion of light, as the introduced time delay disrupts this constancy during reflection. By investigating these phenomena, we gain deeper insights into the behavior of light and its interactions with mirrors, contributing to our broader understanding of the fundamental principles of physics.

References: 

[1] Elert, G. (n.d.). Photoelectric effect. The Physics Hypertextbook. https://physics.info/photoelectric/ 

[2] Einstein, A. (1905) On a Heuristic Viewpoint Concerning the Production and Transformation of Light. Annalen der Physik, 17, 132-148   https://doi.org/10.1002/andp.19053220607

[3] Filippov, L. (2016) On a Heuristic Point of View Concerning the Mechanics and Electrodynamics of Moving Bodies. World Journal of Mechanics, 6, 305-322. doi: http://dx.doi.org/10.4236/wjm.2016.69023 

[4] P. Ewart 1. Geometrical Optics - University of Oxford Department of Physics. Geometrical Optics. https://users.physics.ox.ac.uk/~ewart/Optics%20Lectures%202007.pdf 

[5] Planck, M. (n.d.). On an Improvement of Wien’s Equation for the Spectrum. M. Planck . http://www.ub.edu/hcub/hfq/sites/default/files/planck_1900_llei%281%29.pdf 

[6] Louis-Victor de Broglie (1892-1987). (1925). On the Theory of Quanta: Recherches sur la théorie des quanta. (Ann. de Phys., 10e serie, t. III). Janvier-F evrier https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf

[6] 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

* Updated 08 Sep 2023 :

ΔE = hΔf; where, h is Planck's constant. Δf = 1/Δt; (Fourier transform); Δt = h / ΔE

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. 

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