A photon traveling an arc path does not change its displacement time:

Summary: A photon exchanges momentum as it bypasses a large gravitational well during transit. The photon experiences a change in momentum and its path is bent as it interacts with the gravitational field. A photon simultaneously gains and loses momentum (p) from a gravitational interaction with a massive object. However, a photon maintains its relative path with speed c and covers the same distance (d) as compared to its constant speed. The curvature of the photon's path is understood in terms of the exchange of momentum experienced by the photon.

In relativity, a photon is a relativistic particle and it has a relativistic speed. Whereas, the equation 𝑝 = hf/c = ℎ/𝜆, used herein, is not a relativistic equation.

The previous article was titled, "Electromagnetic - Gravitational Interactions between Photons and Gravitational Masses", and by using the equation 𝑝 = hf = ℎ/𝜆, we see that a photon travels an arc path in a strong gravitational field because the photon releases the excess energy gained, by converting this energy into its momentum, as such the photon travels an arc path.

However, since the photon carries its own energy, it should continue its original path and motion in constant speed, but without gaining additional energy in absence of said Electromagnetic - Gravitational field interactions.  

In the image referred here, we see that the photon field, as it enters the strong gravitational field of a massive body at point A, and as it leaves the gravitational field at point B, the photon's path becomes an arc as it leaves the gravitational field at point B. Whereas, its original travel path should have been a straight line unless the photon was subjected to a strong gravitational field.

Therefore, irrespective of the photon travels a straight path (without external influence), or an arc path (with a temporary additional energy) due to the external influence of the gravitational field, the photon intersects both the points A and B at the same time for both of its possible paths, – straight or curved – the relative times taken by the photon remains constant, the only difference in case of curved path is both gaining and losing additional energy converted into the curvature, while the photon maintains its relativistic speed.

Read more MASS DOES NOT WARP THE SPACE-TIME

#ElectromagneticGravitationalInteractions #FieldsInteraction #PhotonInteraction #EnergyExchange