In the case of turning on pure sinusoidal acceleration of the source charge, after a transient, in the steady state, the timing of maxima of E at the observation location is the same that you would get if light traveled at a speed c/n through the glass, and this effect is due to the superposition of the field you would get without the glass and the field due to reradiation.

In order for these two approaches to give the same result we must suppose that the original and the secondary wave are in antiphase at the first moment when they arrive at the observation location. And they stop canceling out each other after a delay which corresponds to the delay we can obtain from the group velocity conception. Makes sense to me. Is this what you meant?

Continuing to observe after first noting a nonzero electric field, the shape of the pulse will be different from the original pulse because there is a transient behavior of the bound electrons in the glass which is often modeled by an electron bound to the atom by a spring-like force, with damping. Of course the usual term for this is dispersion, that the phase velocity depends on the frequency.

I’ve deliberately avoided using the terms “phase velocity” or “group velocity” to make the point as clearly as I know how. This doesn’t mean that these concepts aren’t useful, but the fundamental physics of the situation is that the speed of light is 3e8 m/s.

On the other hand, the cost of going from 3D to 4D is very small compared to the benefits. For one thing, in 4D as in 3D, it is often possible to deal with two dimensions at a time, which makes things very much easier to visualize. Also, computer graphics can help.

The 4D point of view simplifies all of physics, even the most elementary physics, not just electromagnetism. For example, on page 4 of the book, compare Figure 1.5 to Figure 1.6. The latter looks like straight-line motion on a plot of X versus Y. However, on a plot of X versus T, it would be conspicuously non-straight motion. The spacetime view captures the essential physics. Specifically, it makes manifest the fact that the physics in Figure 1.5 is fundamentally the same as the physics in Figure 1.6.

Plotting X versus T is not rocket science. Students “should” have been doing this for years, starting in grade school.

As stated in the preface, the whole book is predicated on the idea that the modern approach to physics is /easier/ and in every way better than the premodern approach. This is particularly true when it comes to the post-1908 idea that X, Y, Z, and T cannot be separated. All physics is spacetime physics.

For details, see
http://www.av8n.com/physics/spacetime-welcome.htm#sec-straight-line-motion

I would say to this student — and to the gazillions of other students with the same problem — that this is not a new issue. It is pretty well understood. Take a look at these dolls:
http://1.bp.blogspot.com/-J69dxj7Ld90/TyNQAf2U-UI/AAAAAAAABFs/SE0oco24vgQ/s1600/elinor+and+prudence.jpg
Each button is a symbol. It symbolizes an eye. You are supposed to look past the symbol to understand what it represents. This was pretty well figured out 2000 years ago. Let me tell you the story of Plato’s Cave.
http://faculty.washington.edu/smcohen/320/cave.htm
There is this abstract, ideal chair that you cannot see. You can however see shadows, i.e. projections of the chair. From this, if you are clever, you can figure out what the chair must be like. In the present case, there is an abstract, ideal thing called a derivative. We don’t get to see it, but we do get to see things like dy/dx. That’s not really the derivative, but merely a shadow thereof. When you tell me that you recognize dy/dx as a derivative, but do not recognize dE/dS as a derivative, it means you have not been watching the shadows closely enough, because on Tuesdays the derivative projects out as dy/dx, and on Wednesdays it projects out as dE/dS. I am not however saying that you should focus more attention on the shadows. Instead, go for the big picture! You need to wrap your head around the abstract, ideal, Platonic derivative. When you understand the derivative, you know that it projects out as all sorts of things of the form d(…)/d(…) with some variable in the numerator and some other variable in the denominator. The idea of derivative transcends the choice of variables.

The nice thing about math and physics is that we are much better off than those old Greek guys. We are better off because our cave has multiple walls, allowing us to look at multiple projections of the same ideal thing. For example: On one wall the derivative projects out as symbols of the form d(…)/d(…). Meanwhile, on another wall, it projects out as a diagram with a tangent vector that indicates the instantaneous slope. On yet another wall, dE projects out as the gradient vector aka the exterior derivative, which we can diagram as a set of contours of constant E, such that dE = T dS can be considered a statement about proportionality between two exterior derivatives, in some subspace. Your job is to look past all these representations to see the referent, to see the thing being represented.

Applying the same logic to our own discussion, calculus is not an important part of the story, but is a mere symptom or shadow of a larger idea. That is to say, the same story could be told using any other mathematical or physical abstraction, such as “vector” or “energy” or whatever. The key idea is to understand the relationship between the symbol and the thing being symbolized.

At this point the students may be wondering whether they signed up for physics or metaphysics, but I make no apologies. It’s important to handle this issue correctly.

BTW, here is yet another way to get across the point that students (and everybody else) must sometimes use their powers of abstraction, induction, and generalization to figure things out. Here is a way of explaining what a blue triangle is, without actually drawing the blue triangle:
http://www.av8n.com/physics/causation.htm#fig-blue-triangle