Matter is everywhere: we eat it, breathe it, drink it; it is who we are.
But what is matter?
The most basic particle physics definition of matter comes down to one surprising rule:
the Pauli exclusion principle - or, essentially, electrons hate being alike.
To understand why, we have to remember the fact that every electron is exactly the same.
Not "kind of the same"…
They're perfectly identical.
Just as you can at anytime, anywhere, spontaneously write down the number three and it will mean
exactly, perfectly, three… as if there were some everywhere-permeating "three-ness" always
available to produce a three at your whim.
It's the same case with the electron: there's an everywhere-permeating "electron-ness" called
a "quantum field," and from that field every electron in existence has been summoned, and
they are all, exactly, "electron".
So when someone says "every time you breathe, you inhale a few of the same electrons that
used to be in Jesus or Mozart"… that's about as deep as saying that every time you do arithmetic
you use the same number three as Archimedes.
What's more, just like you can call on the "three-ness" to summon "negative-three", which
has all the exact same properties of three except opposite and when it meets three they
annihilate - you can summon "anti-electron" from the electron field and it will annihilate
electron when they meet.
Given that electrons are all exactly alike, it might seem surprising that they actually
hate being like each other.
Electrons despise alikeness so much, in fact, that the universe is forbidden from summoning
two or more into the same quantum state.
This is called "the Pauli Exclusion principle," and what it means in practice is that you
can't cram too much matter into the same place – like a city where building higher than
one story is prohibited: instead of skyscrapers, compounds sprawl outwards.
So at the most fundamental level, matter is just any field (like "electron", "quark",
or "neutrino") from which you can summon particles and anti-particles, but only one at every
point, which means that, quite literally, matter is everything that takes up space.