Imagine a really large powerful set of magnets arranged in a row with all their alignments of the N pole pointing the same way. Now try to move another magnet of the same N pole towards the magnets. It's all "empty" space but the magnetic fields won't allow the other magnet through the first set of magnets.

The point is that "empty" is not really a good way to think of it. There are charges that cause an electric field (usually electrons) and whatever you think of "phasing" through also has charges. Those fields repel each other. Therefore the "phasing" won't work.

At the level you're talking about, the idea of "empty space" barely even makes sense.

You probably think about particles as being little solid billiard balls that bounce off of each other. That model can work OK for thinking about some things, but once you get down to the scale of atoms, it breaks down fast.

The state of an electron in an atom isn't a ball orbiting a nucleus. Instead, an electron is smeared-out "cloud" with a particular sort of shape. You can think of this as the electron being a billiard ball that has a certain probability of being at any given point, but thinking of the cloud as the basic truth and the billiard ball as an approximation is closer to the reality. Insofar as the billiard ball model works, electrons (and all other elementary particles) have zero size, but clearly they are taking up space in some sense, so we need to set aside that model if we want to talk about ideas of taking up space.

Instead, when we think of space being occupied, we mean something like "if you try to put something else there, it'll push back". This is why you don't fall through your wall. And it's at the heart of your question.

The reason that your atoms do not fall through the wall's atoms is twofold:

• First, the electrons in your atoms and the electrons in the wall's atoms are both negatively charged, and they get close to each other before they get close to the positively charged protons in the other atoms. That creates an electric repulsion that stops the two from getting too close, or from your atoms passing through the wall's.

• Second, the electron clouds take up space, in the sense that compressing a cloud takes energy. When you get very close to the wall, the electron clouds in your atoms start to press against the electron clouds in the wall's atoms. The clouds resist compression, which can hold you up in much the same way that a spring can hold up a weight.

Both of these effects contribute a fair amount to the "solidness" of solid objects.

You're thinking of "matter" and "touch" in a very specific way, but not in the most accurate way, I think. It's true that matters are mostly empty space - a nucleus surrounded by a handful of electrons, with lots of empty space in between each atom. But what matters are those electrons - they create a magnetic field that repels other atoms and their electrons. And those magnetic interactions are a huge part of what makes up "chemistry" as a science - the interactions between different atoms.

So when your hand touches your keyboard, it's not as though your atoms are brushing against the keyboard's atoms, nucleus to nucleus. Instead, it's that your magnetic fields are brushing up against each other and repelling each other - we feel that resistance as our sense of touch. So what you think of as empty space is actually what matter is - a bunch of magnetic fields pushing against each other, keeping others out of their space.

The are not really empty. But the nucleus of atoms has a lot of matter packed into a small area.

Atoms can be best understood as quantum mechanical objects, which basically means they are waves, kind of like sound waves in air, but they are standing waves, like a vibrating string. The nucleus is is a really intense wave concentrated in a very small area, kind of like the spike of water that leaps up when you drove a small rock into water, whereas the electrons form much smaller waves distributed over a larger area, more like the ripples that radiate out.

The thing about those electron waves is that they like to be pretty close, but not overlap too much, and that’s what allows molecules to form and what keeps molecules from collapsing into a single super-atom, and also what keeps substances made out of molecules from collapsing. If you try to get an atom to pass through another one, those waves will bump up against each other and prevent it from happening, unless they’re moving really fast.

So in short, it’s not that atoms are empty, but that atomic nuclei are really dense.

There are 10^20 atoms in a spoon of material, so trying to pass a spoonful of material through another spoonful of material is less like trying to pass a few ping-pong balls through the spaces in a volleyball net, and more like dumping a truck load of sand onto a beach full of sand. It won't sink.

There are 4 forces in the universe, and if you scroll that wiki article down a bit and look at the relative strength, electromagnetism is extremely much stronger than gravity. And the distances between atoms are very very tiny.

So everything feels "solid" because what you're looking at is forces that have the "push" and "pull" you would feel if you were 5 feet away from a black hole (take a black hole that has 10^36 Earth gravities (which is the strength of electromagnetism compared to gravity) and then go hang out as close as an atomic distance from it).

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Think of it as a very fine mesh. Sure, it's full of gaps, but nothing is small enough to pass through those gaps, maybe except some radioactive particles, so it's effectively solid.

A really small atom, like hydrogen gas can move through what we think of as solid matter. Hydrogen gas can seep through metal! The world of the atom is weird, the iron atom is still tiny to us but it is 55.8 times heavier than a hydrogen atom.

What messes with your head is that the atomic scale is so different than our general experience. If the nucleus is the size of a pingpong ball the electron is about 500 meters away. But... this is an incomplete analogy, the electron isn't solid, like I said, it is weird.