In an online article that describes condensed matter physics for laypersons, the author describes various so-called "designer materials" that have exotic properties, including one in which the path that light travels along is constrained to a two-dimensional plane, and time measurements operate in two dimensions:
But there is also much more to the field than quasiparticles. Physicists can now create materials in which the speed of light is much slower than usual, say 40 miles an hour. They can even create materials in which light moves as if there were two space dimensions and two time dimensions, instead of the usual three dimensions of space and one of time! Normally we think that time can go forward in just one direction, but in these substances light has a choice between many different directions it can go “forward in time.” On the other hand, its motion in space is confined to a plane.
My very basic understanding of time is related to measurements of causality or increase in disorder. Movement of light in that context is measured as distance-over-time, where distance is the length of a path between two points in space ("start" and "end"), and time is some unit (e.g., "seconds").
What does it mean for a light particle or wave to move within such a material along two dimensions of time, as described above?