I'm very much in favor of removing the Ghostbusters song from canon, and putting it in the Omakes.

I'm not a physicist, but when I looked into this, I found this well-written article:

The Stability of Matter: From Atoms to Stars

It goes into lots of detail of what's happening with a single hydrogen atom, then a large atom, then bulk matter. It doesn't require quantum physics knowledge from a reader, but it does require mathematical maturity, and isn't easy reading.

The short of it is that you're right, the Pauli exclusion principle is more important than electrostatic repulsion.

I know that you know, but trivial obstacles and all that...

Changing your comment now could be a service for a few dozens of people who will see this article in the proximate future.

So, in this fic, you time travel and you wind up in the "same place" as you started. The concept of "same place", however, is actually really complicated. The earth is spinning and orbiting the sun, which is itself orbiting the center of the galaxy, which is in turn....

My first intuition was that, if you traveled in time, you would wind up floating in space. However, it's not at all obvious that a reference frame where the sun is stationary is better than any other, which is how I got to using your current stationary inertial reference frame: it's the only one that's unique from all the other possible ones, and yields the behavior above.

General Relativity, actually. You could also look for "gravity as a fictitious force".

Imagine you're on a merry-go round. You could calculate physics as if you and the merry-go-round were rotating, and that will be fine. Alternatively, you could pretend you're not rotating (choosing a non-inertial reference frame). However, if you want physics to still work, you have to introduce centrifugal and coriolis forces to make everything work out properly (this is the force you feel "pushing" you out to the edge).

Now in general relativity, inertial reference frames are those that are in free fall. An example of an inertial reference frame would be an orbiting satellite. Note that there is no gravity in an inertial reference frame like a satellite. Now, you can pretend that standing on the surface of the earth is an inertial reference frame (ignoring totally the rotation for now), but to make everything work out properly, you need to introduce a new force accelerating you downward: gravity.

First, imagine yourself in a spaceship far away from any gravitational sources. If your rockets are off, objects inside the ship left at rest relative to it will stay at rest. In this situation, your ship is in an inertial reference frame, so called because in it the law of inertia is valid. (By contrast, if your rockets are on, objects left at rest will start accelerating towards the back wall, unless there is some countervailing force acting on them).

Now imagine your spaceship close to Earth, within its gravitational field. What is an inertial frame now? Not the situation of the ship at rest relative to Earth: in this situation, objects will accelerate ("fall", as we usually say) towards the bottom of the ship. The ship is in an inertial frame only if it is freely falling towards Earth[1], like an elevator when the cable breaks: then, objects left at rest inside it will stay at rest relative to it absent countervailing forces (because they will be "falling" at the same universal rate g = 9.8 m/s^2).

So a frame accelerating towards Earth with g is an inertial frame. If we abstract away all other forces that will come into play when the ship crashes hitting the Earth and think only of the effects of gravity (which is what determines the inertial frames, according to GR), the freely falling trajectory would continue straight through Earth, emerge at the other side, reach a maximum altitude, fall again, and so on like a mass on spring. Thus the frame that follows Earth in its trajectory through space while oscillating back and forth through it is an inertial frame.

[1] IActually, it could also be shooting up from Earth but decelerating (to fall eventually), or be in a stable orbit around it. All these situations have the key property that objects at rest relative to the ship tend to stay at rest relative to it.

If you're not willing to have a privileged reference frame, how do time turners know where to go?

(Especially thorny is that the surface of the earth accelerates upwards relative to inertial reference frames; if you stay in your inertial reference frame played backwards through time, you don't lose the earth in space, but you do oscillate through it like a mass on a spring. I personally think this is a really cool way for time travel to work, but it's clearly not how time turners do).

That's well done.

Can you make one about taking over the world?

Right here.