To understand things moving at the speed of light, we refer to Einstein's Theory of Special Relativity. Einstein invented the idea of space-time: thinking about time as just another dimension. What makes it hard to imagine is the fact that we can't "see" it (time).

The speed of light is a constant and it is measured in time always (299,792,458meters/second or 186,000 miles/second).

Light changes its speed when it moves from one medium (say air) to another (say glass), but it is still measured in distance units per time. The reason why light changes its speed is that it consists of electromagnetic waves that interact with the atoms of the medium through which it travels. This phenomenon is called refraction and slows the speed of light.

What we usually call the speed of light is really the speed of light in a vacuum (the absence of matter). In space, the density of matter between the stars is sufficiently low that the actual speed of light through most of interstellar space is essentially the speed it would have through a vacuum, so we can ignore the difference. You can also think about the earth's atmosphere and the space as different mediums, but the light traveling through them, still will be measured in time, and will be a constant.

If you are really interested in this topic, try to read on the next address,where you will find interesting things about the speed of light: lightspeed.

First, the Lorentz transformation and time dilation is a result of coordinate shifts in relativity. At some level, it does not make sense to talk about photons "experiencing" time.

Nonetheless, you are right: if you are not traveling at C (speed of light), anything that is traveling at C could be said to have infinite time dilation, i.e. for a given period iftime that passes for you, no time passes for the object traveling at C. In this way, photons are timeless entities - time does not exist for them -because they always travel at C.

Now, at some point somebody is going to ask what happens if a photon starts moving through a medium other than vacuum (and thus has an index of refraction other than 1). In this case, the photon is interacting with the substance it is passing through, even being absorbed and continually re-emitted. The medium certainly does experience time.

Now, your second question: What your student quoted is one of the principles of general relativity. The idea here is that space-time is a curved, four-dimensional hyperspace, with time being one of the dimensions, but the geometry is Riemannian, not Euclidean. Namely, the distance, called the "interval" between two points is the square root of the sum of the squares of the distance in x,y, and z dimensions, MINUS the square of the distance in the time dimension (and the distance-time conversion factor is c).

Under this calculation, anything that is traveling at the speed of light will actually travel zero distance, since the sum of squares of the distance traveled in the space dimensions will equal the square of the time passed. Anything moving less than the speed of light will have an imaginary interval, because square of the time passed will be greater than the space distance traveled, and so the interval will be the square root of a negative number.

I think that what your student found was a reference to the imaginary sums of distances and of times. I unfortunately cannot explain any further how the interval works in a physical sense. A complete understanding of Einstein general relativity requires an understanding of mathematics that you normally don't get until you are in graduate school, and my degree is in paleontology, not physics. Photons of course are a quantum phenomenon, and I think that I can safely say that whoever figures out how general relativity fits together with quantum mechanics is going to get the Nobel Prize.