Zassounotsukushi wrote:Likewise, the event horizon would cover the observable universe (from the moon alone! the Earth would cover... several universes? this is nonsense)
TL:DR version: The proton-earth event horizon is smaller.
(I am not quite sure how Randall calculated the amount of electrons in our universe-destroying moon. I am taking a guess and assume that he took the rest mass of an electron and divided the mass of the moon through that since that approximately lines up.)
The electron moon:
An electron weighs approximately 10-30
kg (rest mass)
The moon weighs approximately 1023
-> Total: 1053
electrons (article said 1052
which is likely to be a rounding error either in my work or Randall's. I don't care which, it's close enough.)
A proton weighs approximately 10−27
kg (rest mass)
The earth weighs approximately 1025
-> Total: 1052
The rest mass is NOT your problem. You see, to get electrons or protons together costs energyΦ
. Energy is mass. The mass-energy you pumped into the system to get the particles that close despite the massive repulsion they have totally eclipses the rest mass. And not by a silly factor of a trillion or so. It's more. So much more.
This means that the mass equivalence is relatively close to each other. The earth has less mass-energy both to having about a tenth of the particles and having a bigger diameter (the protons aren't as close to each other so they need less energy to get that close)
The additional mass-energy means the black hole event horizon is also bigger.Φ
Think of it as magnets. If you have a box of imaginary magnets with only south poles and you try to push two of them together with their that takes energy, since the south poles are pushing away from each other. If you have managed to put two of them together and bind them with a tyrap and push another south pole towards those two south poles the energy you need gets bigger, since the two south poles repel the third one with twice the force. A fourth one needs even more energy.
Now the protons or electrons do the same, but with 1052
of them. The energy required is astounding.
(edited to clear up some use of force and energy. It was needlessly confusing.)