I don't get all this, especially part 2 seems mathematically dense. But mainly I don't get the premise: > but we won’t use any index gymnastics or explicit ran

I don't get all this, especially part 2 seems mathematically dense. But mainly I don't get the premise: > but we won’t use any index gymnastics or explicit rank-2 tensors; just four-vectors. For me the whole point of tensor notation is the power of indice gymnastics. I'd love to know the motivation behind this before spending time understanding. My own notes on covariant notation on this subject: https://0x5.be/physics-notes/four-vectors.html https://0x5.be/physics-notes/four-vectors.html