The original question was: Given that light is moving at light speed, and time slows down as a massive object approaches the speed of light, does light travel through time? Does the whole time slowing down thing just not apply to massless particles, and if not why not? If light doesn’t travel through time, how does anything make sense, since clearly light moves but movement is dependent on time?
There are some things that behave differently when investigated from an “approaching light speed” way of thinking and the “being at light speed” way of thinking. In this case there’s no difference. When something travels at the speed of light it really doesn’t experience any time.
On the flip side of that coin, it also doesn’t experience any distance. The time and location of its emission and the time and location of its absorption are the same from a photon’s perspective.
This may not make sense, and it’s a little mind bending, but consider this:
Movement isn’t dependent on the time experienced by the moving thing, it’s dependent on your time. If you see someone pass by, you can say (for example) “that person is moving at 100 kph, because during one of my hours they’ve traveled 100 of my km”. That may seem a little over-exact, but the time and distance between things changes for observers that are moving differently, so you have to be especially careful.
If, however, you were to ask the person who passed by “how fast are you moving?” they’d say that they’re not moving at all. They’d say that during one of their hours they traveled zero of their km. These different measurement systems / perspectives are called “reference frames”.
Here on Earth we feel like there’s such a thing as “non-relative movement”, since we all agree (very naturally) on the same reference frame: the (local) surface of the Earth. That is, you probably frequently refer to yourself as moving, while you rarely think of the Earth as moving. You’d have to be pretty full of yourself to drive down the street and claim that you’re stationary and that the rest of the world is moving past you. But at the same time: you’d be right.
The point is: everything always thinks of itself as stationary (you don’t move with respect to yourself), and movement is a property assigned to other things based on each observer’s reference frame. So light may not experience either time or distance itself, but to move, all it needs to do is get from one point in your spacetime to another point in your spacetime.
Answer Gravy: As a needless side-note: when physicists talk about the path of an object through spacetime they usually “parametrize” it using that object’s on-board (or “proper”) time. That is, you give them a time on the on-board clock, and they’ll tell you where the object is at that time.
Using on-board time is convenient for a number of subtle reasons. It even makes one of the derivations of E=MC2 run a lot smoother!
But a photon can’t have an on-board-clock, so physicists instead use an “affine parameter”, which is fancy-speak for “screw it, we’ll just use my clock”.