# Relativity

# Special Relativity

Why is it I donâ€™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

Metric and coordinates

Curvature

differential forms covariant derivative Lie derivatives

Ray tracing Penrose diagrams

Einstein Equations

Blackhole solution Uniform solutions