How to show that light travels through space, but not time

[relativ]

Homework Statement

Use relativistic equations and γ to demonstrate the following:
b) Light travels through space but not in time

Homework Equations

Lorentz factor γ = 1 / √(1 - [v/c]^2)

Time dilation t = γ t°

Length contraction L = γ L°

Mass relativity m = γ m°

E = m c^2

The Attempt at a Solution

To be honest, I'm not exactly sure how to approach this. I don't quite understand the concept behind what the question is really asking for. Furthermore, I don't know how I can use these equations to prove that light does not travel through time.

 

[slider142]

Consider a particle traveling at a uniform velocity relative to the observer. Compare a fixed time interval t₀, perhaps 1 second, in that particle's reference frame to the corresponding time interval in the observer's reference frame. Ie., pretend the particle is carrying a clock that ticks once every second.
How long does the observer have to wait to observe one tick if the particle travels at 0.9c ? At 0.95c? At 0.99c? 0.999c?
Does this behavior continue if we make the fixed unit of time for a single tick smaller? What does this imply about theoretical particles carrying these same clocks that travel at c?
With the formulas you have, you can only make a weak implication.

 

[relativ]

Consider...

Thank you. I can't quite wrap my head around this, but I think I have a good enough idea to somehow explain this. I'll be sure to ask my teacher when I can.