I don't quite get the following: Every year I shoot a laser beam into space, say into the x-direction of my frame of reference. Then the world-lines of the photons are specified by $x_{\mathrm{Photons}}=ct-n$, where $n=1,2,3,...$ represents the year.
For me this looks like all the beams start in the past. Intuitively I would have said it should be $x_{\mathrm{Photons}}=ct+n$. Where is my error in reasoning?