This is a very interesting question and the answer is not straightforward. In classical electromagnetism, the momentum of a photon is given by its energy divided by the speed of light. Therefore, if two photons are perfectly canceling each other in space, their combined momentum would be zero. In this scenario, there would be no net momentum exerted on any objects in their path.
However, in quantum mechanics, photons can also exhibit wave-like behavior and can interfere with each other. In this case, the two canceling photons would still exist, but their interference pattern would result in areas of constructive and destructive interference. In the areas of destructive interference, the energy and momentum of the photons would effectively cancel out. But in the areas of constructive interference, the photons would still have their individual momenta and would exert a net force on objects in their path.
Therefore, in the case of two perfectly canceling photons, the resultant may or may not exist, depending on the nature of their interference. But even if the resultant does not exist, the individual photons would still have their momenta and would exert a force on objects in their path. This can be seen in the phenomenon of laser cooling, where photons are used to slow down and cool atoms by exerting a force on them.
In terms of gravitational bending, the effect would be similar. If the two canceling photons have a net momentum of zero, they would not contribute to gravitational bending. But if their interference creates localized areas of constructive interference, the combined momentum of the photons in those areas would result in a gravitational bending effect.
In conclusion, while the resultant may or may not exist in the case of two canceling photons, the individual photons would still have their momenta and could potentially exert forces on objects in their path. The exact nature of this effect would depend on the specifics of the interference between the photons.
