DOI: http://dx.doi.org/10.13140/RG.2.2.30958.38721
Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Photon Energy Dynamics in Strong Gravitational Fields: Understanding the Equivalence of E and Eg:
In the context of the relationship between the initial photon energy (E) received from the source gravitational well and the total photon energy in the gravitational field (Eg) in energy expressions, the discussion highlights the algebraic equivalence derived from the condition E + ΔE = E − ΔE. This relationship elucidates that change in photon energy (ΔE) under strong gravitational fields balance out, resulting in the total energy (Eg) being equivalent to the initial energy (E). This algebraic manipulation demonstrates how the gravitational field's influence on photon energy can be comprehensively understood within the framework of photon energy. Thus, the equation Eg = E + ΔE = E − ΔE encapsulates the total energy of a photon in a gravitational field, emphasizing the equivalence between the initial energy (E) and the total energy in the gravitational field (Eg). This understanding underscores the intricate interplay between photon energy dynamics and the gravitational environment.
Symmetry in Photon Dynamics: A Comprehensive Analysis of Energy and Momentum Interplay:
In the realm of photon dynamics within strong gravitational fields, the discussion dives into the symmetrical relationship between energy (E) and total energy in the gravitational field (Eg) as well as momentum changes (Δρ) and wavelength alterations (λ). This analysis begins with an exploration of the algebraic equivalence derived from the condition E + ΔE = E − ΔE, elucidating how changes in energy (ΔE) ultimately reconcile to maintain the initial energy (E) itself. This understanding is extended to Eg, where Eg = E + ΔE = E − ΔE, highlighting the equivalence between the initial energy (E) and the total energy in the gravitational field (Eg) amidst gravitational influences.
Moreover, the narrative delves into the symmetrical relationship between momentum changes (Δρ) and wavelength shifts (λ) under gravitational effects. The equation Eg = E + Δρ = E − Δρ = E signifies the interaction between photon energy and changes in momentum, emphasizing the constancy of total energy amidst momentum variations.
Additionally, the equation h/Δλ = h/−Δλ underscores the dual nature of photon behaviour, showcasing the symmetrical effects of positive (redshift) and negative (blueshift) wavelength alterations induced by gravity. These opposite shifts in photon wavelength cancel out the total change in wavelength of the photon between entering and leaving the influence of external gravitational fields, providing further insight into the intricate dynamics of photon behaviour in strong gravitational environments.
This holistic examination reveals the intricate harmony between photon characteristics and the gravitational environment, shedding light on the nuanced interplay between energy, momentum, and wavelength changes in strong gravitational fields.
Algebraic Equivalence: The Relationship between E and Eg in Energy Expressions:
The condition E + ΔE = E − ΔE implies that ΔE is equal in magnitude but opposite in sign to ΔE. So, when ΔE is added and ΔE is subtracted from a value E, it essentially results in adding zero to the value of E because they cancel each other out. Thus, E + (ΔE − ΔE) simplifies to just E.
Eg = (E + ΔE = E − ΔE) presented as Eg = E + (ΔE−ΔE).
This algebraic manipulation demonstrates the equivalence between the expressions. Both expressions indicate the same relationship where the change in energy (ΔE) cancels out when added and subtracted from E, resulting in E itself. Therefore, Eg remains as E, expressed as Eg = E.
Applicable to:
• Photon paths bend due to momentum exchange, not intrinsic spacetime curvature.
• The Dynamics of Photon Momentum Exchange and Curvature in Gravitational Fields.
• Direct Influence of Gravitational Field on Object Motion invalidates Spacetime Distortion
• Enhanced Insights into Photon Interactions with External Gravitational Fields
• Distinguishing Photon Interactions Source Well vs. External Fields
• Photon Interactions in Gravity and Antigravity Conservation, Dark Energy, and Redshift Effects
• Understanding Photon Interactions: Source Gravitational Wells vs. External Fields
• Exploring Symmetry in Photon Momentum Changes: Insights into Redshift and Blueshift Phenomena in Gravitational Fields
