When an electron approaches the speed of light, the emission pattern is sharply collimated forward, in the direction of motion. I can see how this is mathematically true from taking the relativistic limit of the angular distribution of the radiated energy (as is done on the Wikipedia page about s...

Suppose I have some colorful solid, which I cut into two halves (both are identical). Take the first and cut it into two parts, and then repeat this again and again. I know that a single atom doesn't have a color. So there will be a point at which the solid loses its property of being colorful. I...

https://en.wikipedia.org/wiki/Blast_wave#Characteristics_and_properties says: "A blast wave travels faster than the speed of sound and the passage of the shock wave usually lasts only a few milliseconds." I thought a blast wave was a sound wave, so I don't understand this.

Consider an arbitrary set of coordinates $x^\mu$ and another set of coordinates $y^{\mu}$, which is a (lorentzian) transformation from $x^\mu$ given by $y^\mu = f(x^\mu)$. So I want to know whether $\frac{\partial}{\partial x^\alpha}\frac{\partial}{\partial y^\beta} = \frac{\partial}{\partial y^\...