DOI: http://dx.doi.org/10.13140/RG.2.2.10173.64482
Soumendra Nath Thakur
22nd
February, 2024
Abstract:
This abstract provides an in-depth examination of
photon interactions with external gravitational fields, building upon the
principles discussed in the paper titled "Distinguishing Photon Interactions: Source Well vs.
External Fields." The analysis elucidates how
gravitational effects influence the properties of photons, including momentum
and energy. Symmetry in the changes of photon momentum (Δρ) is explored, where
Δρ = -Δρ signifies the equivalence between redshift and blueshift. Mathematical
presentations demonstrate the conservation principles involved, highlighting
how changes in wavelength affect photon energy while maintaining total energy
constancy. The constancy of the speed of light (c) is emphasized, underscoring
its fundamental nature amidst varying wavelengths. Through this abstract, a
deeper understanding of the complexities of photon interactions with
gravitational fields emerges, enriching the discourse on this intricate subject
matter.
Keywords: Photon Interactions, Gravitational Fields,
Momentum Symmetry, Energy Conservation, Speed of Light,
Tagore’s Electronic Lab, India
The author declared no conflict of Interest.
Introduction:
The interaction of photons with external
gravitational fields constitutes a fundamental aspect of astrophysics and
cosmology, shaping our understanding of the universe's dynamics. In the paper
titled "Distinguishing Photon Interactions: Source Well vs. External
Fields," the complexities of these interactions are explored, laying the groundwork
for further investigation. This introduction provides a comprehensive overview
of the additional insights presented herein, which offer a detailed examination
of photon behaviour under the influence of gravitational forces. By delving into
the symmetry of changes in photon momentum, the equivalence of redshift and
blueshift, and the conservation principles governing photon energy, this
analysis expands our comprehension of how photons respond to gravitational
environments. Through mathematical formulations and conceptual discussions,
this introduction sets the stage for a deeper exploration of the intricate
relationship between photons and gravitational fields, enhancing our grasp of
the underlying physics at play.
Mathematical Presentations:
Symmetry in Photon Momentum Changes:
Equation: Δρ = −Δρ
This equation represents the symmetry observed in
the changes of photon momentum, where the change in momentum (Δρ) is equal in
magnitude but opposite in direction for redshift and blueshift phenomena.
Relationship between Momentum Change and
Wavelength Change:
Equation: Δρ = h/Δλ = h/-Δλ
These equations express the relationship between
changes in photon momentum (Δρ) and changes in wavelength (Δλ). The constant
'h' represents Planck's constant, indicating that the magnitude of the momentum
change is inversely proportional to the magnitude of the wavelength change.
Equation Relating Energy, Frequency, and
Wavelength:
Equation: E = hf = h(c/λ)
This equation relates the energy (E) of a photon
to its frequency (f) and wavelength (λ), where 'h' is Planck's constant and 'c'
is the speed of light. It demonstrates how changes in wavelength correspond to
changes in energy while maintaining the total energy constant.
Energy Conservation Equation for Redshift:
Equation: (E - ΔE) = hc/(λ+Δλ) = hc/(λ-Δλ) = (E +
ΔE)
This equation represents energy conservation in
the context of redshift, where there is a change (Δλ) in the photon's
wavelength. It shows that the change in energy (ΔE) due to redshift is
compensated by the corresponding change in wavelength, resulting in a total
energy that remains constant.
Constancy of the Speed of Light Equation:
Equation: c = fλ
This equation represents the relationship between
the speed of light (c), frequency (f), and wavelength (λ). It illustrates that
even when the wavelength varies, the product of frequency and wavelength (fλ)
remains constant, ensuring the constancy of the speed of light.
These mathematical presentations provide a
quantitative framework for understanding the principles discussed in the quoted
text, including symmetry in momentum changes, conservation of energy, and the
constancy of the speed of light.
Discussion:
The discussion presented in the quoted text
delves into the intricate interplay between photons and external gravitational fields,
shedding light on several key concepts and their implications.
Firstly, the symmetry observed in the changes of
photon momentum (Δρ) is highlighted, where Δρ = -Δρ signifies a fundamental
symmetry between redshift and blueshift phenomena. This symmetry, rooted in the
conservation principles of momentum, underscores the intricate balance at play
in photon interactions with gravitational fields. By acknowledging this
symmetry, researchers gain a deeper understanding of how photons respond to
gravitational influences, whether they are experiencing redshift or blueshift.
Moreover, the mathematical presentation
elucidates how changes in photon wavelength (Δλ) correspond to alterations in
photon momentum and energy. The equations presented, such as E = hf = h(c/λ),
provide a quantitative framework for understanding the relationship between
photon energy, frequency, and wavelength. Through these equations, it becomes
apparent that while changes in wavelength may result in shifts in photon
energy, the total energy remains conserved, underscoring a fundamental
principle of physics.
Furthermore, the discussion emphasizes the
constancy of the speed of light (c) despite variations in wavelength. This
constancy, rooted in the relationship c = fλ, elucidates how the interplay
between frequency and wavelength maintains a consistent speed of light, even in
the presence of gravitational influences. Understanding this fundamental
property of light is crucial for interpreting observations in astrophysics and
cosmology, where gravitational fields often play a significant role.
Overall, the discussion provides valuable
insights into the complexities of photon interactions with external
gravitational fields. By exploring concepts such as symmetry in momentum
changes, conservation of energy, and the constancy of the speed of light,
researchers can deepen their understanding of the fundamental principles
governing the behaviour of photons in gravitational environments. These insights
not only contribute to our theoretical understanding but also have practical
implications for interpreting astronomical observations and phenomena.
Conclusion:
The discussion presented offers a comprehensive
exploration of photon interactions with external gravitational fields,
illuminating fundamental principles and their mathematical representations. By
examining the symmetry in photon momentum changes, it becomes evident that
redshift and blueshift phenomena exhibit a symmetric relationship, encapsulated
by Δρ = -Δρ. This symmetry underscores the intricate balance in photon behaviour under gravitational influences.
Furthermore, the mathematical presentations
elucidate the relationships between momentum changes, wavelength alterations,
and energy conservation. Equations relating energy, frequency, and wavelength
provide a quantitative understanding of how changes in photon properties
manifest while preserving total energy. The analysis of energy conservation in
the context of redshift highlights the compensatory nature of changes in energy
and wavelength, maintaining a constant total energy.
Additionally, the constancy of the speed of
light, emphasized through the relationship c = fλ, underscores a fundamental
property of light unaffected by gravitational fields. This constancy serves as
a cornerstone for interpreting observations in astrophysics and cosmology,
facilitating our understanding of the universe's dynamics.
In conclusion, the insights provided deepen our
understanding of the complexities of photon interactions with gravitational
fields. By combining conceptual discussions with mathematical formulations,
this discussion enriches our comprehension of fundamental principles governing
photon behaviour and lays the groundwork for further exploration in astrophysics
and cosmology.
References:
[1]
(PDF) Understanding Photon Interactions: Source Gravitational Wells vs.
External Fields. (2024) ResearchGate https://doi.org/10.13140/RG.2.2.14433.48487
[2]
Thakur, S. N. (2023b). The dynamics of photon momentum exchange and curvature
in gravitational fields Definitions https://doi.org/10.32388/r625zn
[3]
Thakur, S. N. (2023a). Photon paths bend due to momentum exchange, not
intrinsic spacetime curvature. Definitions https://doi.org/10.32388/81iiae
[4]
Thakur, S. N. (2024c). Direct Influence of Gravitational Field on Object Motion
invalidates Spacetime Distortion. Qeios.com. https://doi.org/10.32388/bfmiau
[5]
Thakur, S. N., & Bhattacharjee, D. (2023b). Cosmic Speed beyond Light:
Gravitational and Cosmic Redshift. Preprints.org.
https://doi.org/10.20944/preprints202310.0153.v1
[6]
Thakur, S. N., Bhattacharjee, D., & Frederick, O. (2023). Photon
Interactions in Gravity and Antigravity: Conservation, Dark Energy, and
Redshift Effects. Preprints.org. https://doi.org/10.20944/preprints202309.2086.v1
[7] Thakur, S. N. (2023d).
Cosmic Speed beyond Light: Gravitational and Cosmic Redshift. ResearchGate https://doi.org/
