Relativity #16 - Vectors, tensors and coordinate invariance скачать в хорошем качестве

Relativity #16 - Vectors, tensors and coordinate invariance

Notes are on my GitHub! github.com/rorg314/WHYBmaths Here I begin to illustrate the notion of coordinate invariance by discussing how vectors will appear in various coordinate systems with some particular set of components, tied to the basis vectors. In future videos we will derive the general transformation laws for how the coordinate basis vectors will change under an arbitrary (non-linear) coordinate transformation, but for now we simply consider it intuitively. This brief interlude to discuss Lorentz invariance was needed such that we can realise that the metric, a (0, 2) tensor, will also be an invariant quantity, as I briefly discuss here. In upcoming videos the invariance of the metric (and hence the line element ds^2) will be an incredibly powerful tool that will allow us to explore many features of the Minkowski geometry and the Lorentz transformations between frames.