I am trying to understand the issue of light bending in relativity vs classical physics. I will clearly describe my understanding/assumptions in case I am wrong on those.
- In relativity, unlike classical physics, gravitation is not a force that act between two bodies, rather it is the effect of the space-time distortion caused by a large mass
- The "curving" is independent of the mass of the second body (to an approximation, because the second body will also distort space-time, but the geodesics in the "curved" space by the first object are the same for any other object)
- In classical physics, since photons have no mass, their trajectory will not be bent by the large body
- In classical physics, if we add to the 0-inertial mass the relativistic mass $E=m*c^2$, then, even in classical physics the bending of the trajectory for a photon should be apparent
- However, the bending due to the relativistic mass in classical physics is different than the bending predicted by the theory of relativity
- This link describes the bending using relativistic mass and Newtonian physics to be a deflection of 0.87, while the deflection due to Relativity should be 1.75 in the famous 1919 experiment
Is this difference due to the fact that in Newtonian physics the deflection depends on the energy of the light (using the formula $E=m*c^2$) and, in the experiment, it was calculated to be about 0.87, while, in Relativity, such deflection is for the most part independent of the energy of the photon?
More in general, how were those values calculated? Did they know the energy for the photons for the particular star, and calculated the photons relativistic mass using $E=m*c^2$ in the first case, while they simply calculated the space-time distortion caused by the mass of the Sun in the second case, calculated the geodesics, and ignored the mass of the photons and assumed the photons would just move along those geodesics to calculate the deflection? Or am I totally off in my assumptions and overly simplifying a much more complex theory?