Relativity
Special Relativity
Why is it I don’t find special relativity that interesting anymore? It captures the public imagination. This thing that is apparently real.
Proper time t^2 - x^2 = tau^2 Time experienced by an observer moving with the object.
Lorentz Tranformations
Gamow Penrose rotations
Paradoxes
Paradoxes are not paradoxes. They are paradoxes because they are phrased intentionally to give you a mistaken way of thinking about the situation. Most of them come from using the length contraction and time dilation formulas when they are very rarely applicable.
Terrell Rotation Terrell rotation really brings to the forefront a serious issue. When we visualize (and we must?) things in special relativity, we imagine somehow the world operating both in special relativistic terms and ordinary terms (in terms of our methods of observation). We imagine somehow personally watching these things happen in external galilean physics, using some fictional super-light reaching our eyes.
We want the coordinates x and t to somehow correspond to our senses, but it is not at all clear they do. This comes even further into . We can run a ray tracing program, to show what an actual eye might see happening, but it is not at all clear this clarifies the physics.
We can instead visualize space-time diagrams, but it holds less gutty feel.
General Relativity
MIT course
https://www.gravityfromthegroundup.org/ Schutz Wald Carroll MTW Weinberg
Metric and coordinates
Curvature
differential forms covariant derivative Lie derivatives
Ray tracing Penrose diagrams
Einstein Equations
Blackhole solution Uniform solutions