I agree that focusing on Lorentz transformations is the wrong way to approach thinking about special relativity. But It might be the right way to teach it to physics students.

The issue is the level of mathematical sophistication one has when a certain concept is introduced. That often defines or at least heavily influences how one thinks about it forever.

The basics of special relativity came up in my first year of university, and the rest didn't really get focused on until my second year.

The first time around I was still encountering linear algebra and vector spaces, while for the second I was a lot more comfortable deriving things myself just given something like the Minkowski "inner product".

(As an aside: I really love abstract index notation for dealing with tensors)

> The issue is the level of mathematical sophistication one has when a certain concept is introduced. That often defines or at least heavily influences how one thinks about it forever.

That was one of the most interesting things of my EE/CS dual-degree and the exact concept you're describing has stuck with me for a very long time... and very much influences how I teach things when I'm in that role.

EE taught basic linear algebra in 1st year as a necessity. We didn't understand how or why anything worked, we were just taught how to turn the crank and get answers out. Eigenvectors, determinants, Gauss-Jordan elimination, Cramer's rule, etc. weren't taught with any kind of theoretical underpinnings. My CS degree required me to take an upper years linear algebra course from the math department; after taking that, my EE skills improved dramatically.

CS taught algorithms early and often. EE didn't really touch on them at all, except when a specific one was needed to solve a specific problem. I remember sitting in a 4th year Digital Communications course where we were learning about Viterbi decoders. The professor was having a hard time explaining it by drawing a lattice and showing how you do the computations, the students were completely lost. My friend and I were looking at what was going on and both had this lightbulb moment at the same time. "Oh, this is just a dynamic programming problem."

EE taught us way more calculus than CS did. In a CS systems modelling course we were learning about continuous-time and discrete-time state-space models. Most of the students were having a super hard time with dx/dt = A*x (x as a real vector, A as a matrix)... which makes sense since they'd only ever done single-variable calculus. The prof taught some specific technique that applied to a specific form of the problem and that was enough for students to be able to turn the crank, but no one understood why it worked.

> But It might be the right way to teach it to physics students.

Having studied physics, I would disagree rather strongly. I only really started understanding Special Relativity once I had a clear understanding of the math. (And then it becomes almost trivial.) Those of my fellow class mates, however, who didn't take the time to take those additional (completely optional) math classes, ended up not really understanding it at all. They still got confused by what it all meant, by the different paradoxes, etc.

I saw the same effect when, later, I was a teaching assistant for a General Relativity class.

Yeah, I had a slightly odd introduction to these things as I studied joint honours maths and physics. That meant both that I had a bit more mathematical maturity than most of the physics students and that I was being taught the more rigorous underpinnings of the maths while it was being (ab)used in all sorts of cavalier ways in physics. I liked the subject matter of physics more, but I greatly preferred the intellectual rigour of the maths.

Eric Gourgoulhon is a product of the French education system, and I often think I would have done better studying there than in the UK.