So I know that when you collide particles with high enough kinetic energy, (kinetic energy = at least the rest mass of the particles you are making), you get particles.
How come potential energy cannot make particles? Say you have an electron held at a potential such that the amount of potential energy it has equals at least the rest mass of a particle you want to make. How come potential energy does not convert into rest mass energy directly? Would this require whatever is creating the potential to disappear because the potential energy turns into a particle? This shouldn't violate any conservation of energy laws does it?
Another question that kind of relates to my previous question is, say we have a 512 keV photon. What prevents this photon from turning into an electron that then has kinetic energy of 1 kev?
Best Answer
A strong enough static electric field can create real particle-antiparticle pairs out of the vacuum, so yes, potential energy can contribute to creating particles. This is called the Schwinger effect and was predicted by Schwinger in the 1950s. The original paper is here Link.
Schwinger's formula gives $$\frac{N}{VT}=\frac{e^2E_0^2}{4\pi^3}\sum_{n=1}^{\infty}\frac{1}{n^2}\mbox{exp}(-\frac{nm^2\pi}{eE_0})$$ where $N$ e+e- pairs are produced in a volume $V$ and time $T$ by a static uniform electric field $E_0$. This means that the threshold to see any pair production is about $m^2/e$ or approximately $1.3$ x $10^8$ V/m.
As for your last question, a photon cannot turn into an electron because of charge conservation (and several other conserved numbers). It cannot turn into an e+e- pair in vacuum either because energy and momentum cannot be conserved simultaneously - this is a consequence of the masslessness of the photon. A photon can however decay into e+e- in the presence of some other matter that it scatters off, which allows it to conserve both energy and momentum.