Why we do not consider trajectories for photons/lightlike curves/radiation? I am having a term confusion Lately I have asked a question about the trajectory of photons and almost everyone told me that I shouldn't talk about trajectories. Also people talked about photons, lightlike curves, light, radiation. It seems like there is an important distinction between all that, which I have no idea.
So why shouldn't I talk about photon trajectories? Probably you will say light is a wave not particle. But what does this even mean, cannot light be particles carrying vectorial fields, and wave is composed of many particles with magnitudes/intensities varying like a wave shape?
What is the difference between all light related terms? Why do we have so many?
 A: The  photon is an elementary point  "particle".

particle between quotation marks because it is not a classical  point particle , it is a quantum mechanical entity. Quantum mechanical entities depending on the boundary conditions display sometime classical point-like elementary particle behavior and sometimes have a probability density for their location that has sinusoidal properties, i.e. wavelike.
A large number of physicists who have progressed and assimilated PhD level second quantization physics object to the term "trajectory", because the higher level description of this underlying quantum mechanical level is considered to be excitations on a large number of fields at each point (x,y,z), each particle in the table being represented by a field . This is too esoteric for most laymen or first year physics students, and in anyway is mathematically isomorphic with the simple description of "trajectories, as seen for example in this electron in the magnetic field displayed in a bubble chamber photo.

The red curve can be fitted very accurately as a classical charged particle turning in the magnetic field with energy loss. So trajectories are in the brain of the thinker.
Back to photons. They have 0 charge and 0 mass. The 0 charge means that they will leave with great difficulty a track in any medium, and the 0 mass that according to special relativity they will be traveling in straight lines. The LHC experiments depend absolutely on this trajectories of photons to identify them with the vertex from which they came.


Candidate Higgs boson event from collisions between protons in the CMS detector on the LHC. From the collision at the centre, the particle decays into two photons (dashed yellow lines and green towers) (Image: CMS/CERN)

That far for photons in the lab.
Now radiation and light. Radiation is a term coming from classical electrodynamics, and light is represented as changing electric and magnetic fields radiating outwards from the source as a wave of energy density in space and time. Optics which has been studied for centuries uses rays to compute where the wave will impact and how it will be reflected or refracted. Indices of refraction and absorption give accurate results for impinging radiation on matter etc etc. So it is not trajectories but rays, classically.
Classical electromagnetic waves are built up in synergy by zillions of photons. This can be seen mathematically for those who can follow the mathematics.
As I hope it is now clear that we have many terms because light and photons are not synonymous, in the way that a brick and a building are not synonymous. When studying individual photons the concept of trajectory is useful in certain boundary conditions.
When studying light optical rays are a good tool in describing and predicting the behavior of light.
