24.11 Lorentz Transformation: Examples

Problem

## Module 24: Lorentz Transformation: Examples - Problem 6

Bart races by you on his skateboard at speed $v$, headed in the positive $x$-direction. Bart uses spatial coordinate axes $(x^\prime,y^\prime,z^\prime)$ that are each parallel to your $(x,y,z)$ axes. You both set your watches so they read $0$ as he passes you. You are both at the spatial origin of your coordinate systems. At that moment ($t = t^\prime = 0$), Bart sets off a firecracker that creates a spherical shell of light that spreads outward. Bart says that the equation of this spherical light wave is $x^{\prime 2} + y^{\prime 2} + z^{\prime 2} = c^2t^{\prime 2}$ reflecting that the shell is growing at the speed of light.