So far in this series I have given the definitions of vectors, scalars, tensors, and manifolds. As a result, much of this series has been mostly mathematics and not necessarily physics. To that end, the purpose of this post is to develop the salient points of special relativity. Namely, the intention of this post is to cover the following:
- Definition of Inertial Reference Frames: Standard Configuration and Einstein’s Postulates.
- Development of the Lorentz Transformation Matrix
- Discussion of the Newtonian geometry of spacetime
- Discussion of the Minkowski geometry of spacetime (i.e. no curvature)
- Finally I will show that the quantity is invariant with respect to Lorentz transformations. This is a pretty standard problem in most GR textbooks and in fact in some introductory books on SR.
Continue reading Basics of Tensor Calculus & General Relativity|A Digression into Special Relativity