Soumendra Nath Thakur
Tagore's Electronic Lab, W.B., India
Correspondence:
postmasterenator@gmail.com|postmasterenator@telitnetwork.in
18 November 2024.
Abstract
This study supplements A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields by Soumendra Nath Thakur,[1][2] providing a deeper exploration of the distinctions between gravitational and anti-gravitational redshifts of light. It identifies two primary mechanisms: gravitational redshift (due to ΔEg), arising from localized photon interactions within gravitational fields, and cosmic redshift (due to ΔE), resulting from energy loss as photons interact with the anti-gravitational field of dark energy over vast intergalactic distances. By incorporating field-specific energy dynamics, this study enhances the understanding of symmetry, conservation principles, and photon behaviour across diverse gravitational and cosmological contexts.
Keywords: Photon energy interactions, gravitational redshift, cosmic redshift
Introduction
This supplementary analysis delineates the mechanisms behind light's redshift phenomena within gravitational and anti-gravitational fields. While traditional approaches often attribute redshifts to generalized spacetime dynamics, this study refines the framework by distinguishing between localized gravitational redshifts and cosmological redshifts arising from dark energy interactions, offering a perspective that aligns with conservation principles.
Key Insights
1. Gravitational Redshift (Redshift due to ΔEg):
• Mechanism: This redshift occurs as photons escape a gravitational field, where the interactional energy (ΔEg = hΔf) diminishes as gravitational influence decreases.
• Energy Conservation: While the interactional energy ΔEg decreases, the photon's intrinsic energy (E = hf) remains constant, reflecting the localized nature of this redshift.
• Significance: This redshift is predominantly observed in systems with strong gravitational wells, such as stars or galactic clusters, underscoring the photon’s interaction with gravitational fields rather than spacetime curvature.
2. Cosmic Redshift (Redshift due to ΔE):
• Mechanism: Cosmic redshift arises as photons interact with the anti-gravitational field of dark energy while traversing within intergalactic expanding space.[3] This interaction results in a loss of intrinsic energy (ΔE), manifested as wavelength elongation.
• Cosmological Scale: Unlike gravitational redshift, cosmic redshift is a cumulative effect observed over vast distances, beyond the zero-gravity sphere of gravitational influence. It is directly driven by the expansion of intergalactic spatial distances and the dynamics of dark energy.
Wavelength, Frequency, and Redshift Dynamics
Redshift phenomena fundamentally depend on the interplay between changes in wavelength (Δλ) and frequency (Δf), as these quantities are inversely related. This relationship can be expressed mathematically as:
f = − (c/λ²) Δλ
Where c is the speed of light and λ is the wavelength of light.
The negative sign here indicates that an increase in wavelength (Δλ>0) will cause a decrease in frequency (Δf<0) — this is a redshift. Conversely, a decrease in wavelength will lead to an increase in frequency — a blueshift. When the wavelength decreases (Δλ<0), the frequency increases (Δf>0), resulting in a "blueshift" — the light is compressed.
In this context:
1. Gravitational Redshift (Redshift due to ΔEg):
• Occurs due to a reduction in photon interactional energy (ΔEg = hΔf) as the photon escapes a gravitational well.
• Despite the change in frequency (Δf), the photon's intrinsic energy (E = hf) remains conserved, reflecting localized field-specific interactions.
2. Cosmic Redshift (Redshift due to ΔE):
• Arises as photons lose intrinsic energy (ΔE) while interacting with the anti-gravitational field of dark energy across intergalactic distances. This manifests as an elongation of the wavelength (Δλ > 0), leading to a decrease in frequency (Δf < 0).
By examining the relationship between wavelength and frequency in both redshift contexts, this section strengthens the distinction between gravitational and cosmic redshift, providing a precise framework for understanding their physical origins and implications.
Framework
This framework emphasizes field-specific dynamics:
• Localized Redshift: Gravitational redshift (ΔEg) reflects localized photon interactions in gravitational fields, independent of intrinsic energy (E = hf).
• Cosmic Redshift: The energy loss during cosmic redshift (ΔE) underscores large-scale photon interactions with anti-gravitational fields.
By accurately delineating these two redshift mechanisms, this study enhances conceptual clarity, ensuring the distinctions between gravitational and cosmological redshifts are evident.
Conclusion
This supplementary research offers pivotal insights into the mechanisms underlying light's redshift phenomena within gravitational and anti-gravitational fields. By distinguishing between Redshift due to ΔEg and Redshift due to ΔE, it refines our understanding of photon energy interactions, shedding light on localized versus cosmological processes.
Gravitational redshift highlights the conservation of intrinsic photon energy during localized interactions within gravitational fields. In contrast, cosmic redshift underscores the cumulative energy loss experienced by photons as they traverse the anti-gravitational field of dark energy over vast cosmological distances. These distinctions deepen our understanding of photon behaviour, symmetry, and conservation across varying gravitational contexts.
By integrating these findings with the framework outlined in A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields, this study advances the interpretation of redshift phenomena, enhancing their significance for both gravitational and cosmological research.
References
[1] Thakur, S. N. (2024). A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. Preprints.org (MDPI), 202411.0956/v1. https://www.preprints.org/manuscript/202411.0956/v1
[2] Thakur, S. N. (2024). A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. EasyChair. https://easychair.org/publications/preprint/SsTn
[3] Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781
