Preprint A Symmetry and Conservation Framework for Photon Energy Inte...

Consideration 1: The Photon’s Initial Straight-Line Trajectory

The photon begins its journey from the source along a straight-line trajectory with velocity c. Here, an initial redshift occurs as the photon loses a slight amount of energy due to gravitational interaction with the source’s gravitational well, resulting in a corresponding increase in wavelength (Δλ>0). This change follows the relationship E = hf = hc/λ, where the energy E and frequency f are inherent to the photon and directly proportional to the wavelength.

Consideration 2: Arc Path and Energy Exchange During Gravitational Bypassing

As the photon approaches and passes an external massive body, it undergoes a temporary arc-shaped deviation in its trajectory due to the external gravitational influence. This interaction involves two phases:

First Half-Arc: A blueshift occurs, corresponding to a wavelength decrease (Δλ0) occurs, returning the photon’s wavelength to its original state as it completes the arc and leaves the gravitational field. This reversible shift is due to energy exchange within the field, summarized by E + Eg= E + 0, where Eg represents the energy gained and then lost by the photon within the gravitational arc path.

Consideration 3: Return to Original Straight-Line Trajectory

After exiting the gravitational field, the photon resumes its original straight-line path. At this point, it retains its inherent energy, with any additional energy or momentum imparted by the gravitational field removed. Its wavelength also remains as it was upon entry into the gravitational encounter, indicating no net change in wavelength (Δλ=0) beyond that caused by its initial emission.

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