Now, you are probably wondering why the fuck is this post titled "Mommy issues". I will get to that... soon. In this post I?will be introducing?relativistic energy and momentum, as well as four vectors. From this we can derive expression of speedy particles. Lightning McQueen is not the only speed here.
ANYWAYS, THIS IS GOING TO BE SO MUCH FUN.
Warning:?Keep your tongue straight in your mouth as Norwegians says. This is probably going to be a confusing as shit, but I will try my very best.
Here is the scenario:
"A free neutron has a mean life time of about 12 minutes after which it disintegrates into a proton, an electron and a neutrino (we'll ignore the neutrino now, what a loser).?A neutron moves along the positive x-axis in the laboratory frame with a velocity close to the velocity of light. It disintegrates spontaneously and a proton and an electron is seen to continue in the same direction as the neutron."
Here is the task:
Try to calculate the speed of the proton and the electron in the lab-frame. Ps. easier to do it in the rest frame.
I will do this using four vectors, relativistic energy and momentum :)
?
You are probably already confused as shit (me too tbh). Allow me to illustrate it with videos.
Lab-frame (t, x):
We observe a neutron with a velocity moving along the x-axis where it?disintegrates.
We have?\(P_\mu(n) = P_\mu(p) + P_\mu(e)\)
(I will get back to the?equation later. As for now, read it as a neutron disintegrated and becomes proton and electron)
Rest frame (t', x'):
Neutron stays at the origin.?
We have?\(P'_\mu(n) = P'_\mu(p) + P'_\mu(e)\)
?
Do you see why it is easier to work in rest frame rather than lab-frame? In lab frame the neutron, proton AND?electron has velocity! That makes every calculations so much harder!!
This was only the introduction. Now it is time for some hardcore (BUT SUPER COOL) physics (theory, we need some knowledge before beginning to solve anything)!
Let's start with familiar stuff.
You have all probably learned that:?
- momentum,?\(\vec{p}=m\vec{v}\).?
- energy,?\(\vec{E}