The Shapiro effect, also known as gravitational time delay, is a phenomenon predicted by general relativity. It describes the gravitational bending and delay of light as it passes through a gravitational field. While it is true that photons do not directly interact with each other in the traditional sense, the Shapiro effect is not a result of photon-photon interactions.
Instead, the Shapiro effect arises due to the curvature of spacetime caused by massive objects, such as stars or planets. According to general relativity, massive objects curve the fabric of spacetime, and light traveling through this curved spacetime follows a curved path. This gravitational bending of light is known as gravitational lensing.
When a photon passes near a massive object, such as the Sun, it follows a curved path due to the curvature of spacetime caused by the Sun's mass. As a result, the photon's path is slightly longer compared to what it would be in the absence of the gravitational field. This lengthening of the photon's path leads to a time delay in its travel.
The Shapiro effect has been observed and confirmed through various experiments and observations, such as the deflection of starlight during solar eclipses. Although photons do not directly interact with each other, they do interact with the gravitational field created by massive objects, and this interaction is responsible for the gravitational time delay predicted by general relativity.