Why You Haven’t Fallen Through the Floor

From the time they first told me that the world is made of atoms, one question has always bugged me: If matter is made of mostly of empty space, why can’t my hand go through this table?

Imagine two butterflies flying over Europe—say, one over a French meadow, the other somewhere over the steppes. That’s about the space you’ve got between two typical atoms in a typical chunk of matter. Never mind that the atoms themselves are almost entirely empty space.

Think of it this way: If you took out all the empty space from between the particles that make up the atoms of which planet Earth is composed, the entire ball would fit neatly in the palm of your hand. Now imagine holding a small ball in your hand; imagine that ball exploding until its debris spreads beyond your house, beyond your city, into a space the volume of our planet. Could you walk through that? No problem. If so, why can’t you walk straight through this planet?

You would think that’s the first thing they would want to explain in grade school physics: What exactly is it about this table, or this floor, or keyboard, or any chunk of matter for that matter, that won’t allow another piece of matter to enter into its space? I mean, it’s called physics, right? You would think they would be teaching why physical things are so physical.

Well, after grade school, I did get a few explanations. All quite mystifying. But the winning answer that actually works has a lot to say not just about atoms and matter, but about the universe and life in general.1

You can’t walk through a wall for much the same reason you can’t walk through a baseball diamond when a game is in play.

Here it is: The reason you can’t walk through a wall is much the same reason you can’t walk through a baseball diamond when a game is in play.

Cosmic Baseball

Say one sunny afternoon you and your buddies turn up at your reserved field with all your equipment, and the parks board has messed up again. Another league has their game scheduled on the same diamond overlapping into your time, and they’re only in their first play.

But hey, there’s lots of space, right? Look at those huge gaps of empty space between first and second, for example. So let’s say we move another pitcher just next to where these guys have a pitcher, another shortstop just a few feet from their shortstop—and so on, until we have two games playing in the same space. And why stop there? I mean, there’s so much space, right?

Makes sense, but the other league doesn’t seem happy about it. What’s their excuse? “You can’t do that!” Period. There can only be one pitcher, one batter, one shortstop, one of every position. Those are the rules.

Same with the wall, the table, the planet and your hand. They’re all in the same league, playing the same game.

Matter is made of particles we call fermions (as opposed to force, which is carried by bosons). The Fermion League has two teams, the Leptons and the Quarks. Each team has six players. The Quarks have the more colorful names: up, down, strange, charm, bottom and top. The Leptons include that familiar-to-all electron, while the other names sound like the children of a mixed Oriental-Italian marriage: electron-neutrino, muon, muon-neutrino, tau and tau-neutrino. That makes twelve, but then there are the Anti-Leptons and the Anti-Quarks, making 24 in all (and you don’t want to know what would happen if all of them met).

These team players combine to comprise bigger fermions in the form of protons, neutrons and atoms. (They can also combine to make atoms that are bosons, which is pretty strange.) But, no matter how they combine, there is one rule they all keep: No two of them can do exactly the same thing.

For physicists, “doing the same thing” means occupying the same quantum state. There are four numbers of the quantum state, and one of those numbers tells us which shell the particle occupies—which (sort of) means “where it is.” Turns out that two particles can be in the same place at the same time—but only if the other three numbers of their quantum state differ. For example, maybe one is moving with greater momentum than the other, or in a different direction. Or it has an opposite spin (which, by the way, has nothing whatsoever to do with spinning).

So, what happens when my hand hits the table? Well, here comes a pile of atoms with their particles, and along comes another pile of atoms with their particles, and if they’re going to move here, a lot of those particles are going to match all four quantum states of some other particles.

Two pitchers in the same diamond. Against the rules. Either one of those particles is going to have to be promoted to a higher energy state, or it will just have to stay out of the space of this atomic shell. Absent the huge surge of energy needed to promote all those particles, your hand stays out of the table.

Variety Is Everything

Think about it, and you’ll realize that this rule goes far beyond keeping you from falling into the depths of planet Earth. This is the rule that keeps the universe interesting. Because if particles were allowed to copycat one another, how much variety do you think the universe would contain? All atoms would act as hydrogen and helium, and that would be it. And what would stop everything from being in the same place at the same time? It’s only because every particle must be different from every other particle in such things as energy level, momentum and position that we end up with a hugely variegated universe—or any universe at all.

Wolfgang Pauli (Bettina Katzenstein / ETH Zürich)
Wolfgang Pauli (Bettina Katzenstein / ETH Zürich)

This principle was discovered by one of the fathers of quantum physics, Wolfgang Pauli. If Pauli would have rewritten Genesis, he might have begun, “In the beginning, G‑d granted every particle of matter exclusive rights. And so, a multitude of things came into being.”

Pauli spoke about the “unity of being” of the universe, and sought a unity of the rational and the mystical.

Pauli didn’t rewrite Genesis. But he did hook up with Carl Jung. Pauli’s classmate and confidant, Werner Heisenberg, describes him speaking in rather mystical terms about “the unity of all being,” describing how the particles of the universe follow a kind of “psychophysical interrelation”2—as though the entire cosmos was one great, deep psyche. How else could he explain how all these particles knew just what they were supposed to be and what rules to follow? Heisenberg quotes Pauli discussing his struggle with the theologians, “wrestling with the One,” satisfied with neither the rational nor the mystical:

I consider the ambition of overcoming opposites, including also a synthesis embracing both rational understanding and the mystical experience of unity, to be the mythos, spoken or unspoken, of our present day and age.3

Pauli meant mythos in a Jungian sense, as the very soul and sustenance of our society, that which provides it cohesion and drives it forward. We are all seeking that synthesis, a vision within which we can frame Pauli’s wonderment.

White Space

G‑d looked in the Torah and created the world,” says the Zohar.4If so, as Nachmanides writes in his introduction to Genesis, whatever exists in this world first exists in Torah. So, I figured something as core to reality as Pauli’s exclusion principle should be readily apparent somewhere in Torah.

What do you know, it didn’t take long to find it there.

Look inside a Torah scroll. Unlike Arabic or Sanskrit or cursive writing, Hebrew letters don’t string together. When writing a Torah scroll, the rules dictate that no two letters may touch one another. Each letter must be entirely surrounded by white space.5

Now, because the Torah scroll is a singularity, every one of its basic elements (letters) is of existential value. Practically speaking, the rules are that if one letter is missing, that scroll no longer has the sanctity of a Torah scroll. We tie it up and put it away until it can be fixed.

What’s interesting is that the same applies to two letters touching one another: If any letter is lacking its white space, the wholeness of that Torah is lost.

Paradoxically, integrity of the whole is expressed by exclusivity of the parts.

Paradoxically, integrity of the whole is expressed by exclusivity of the parts.6

(There’s an application here, too, in our personal lives: Like those letters, every soul G‑d sent down to this earth has its particular mission. No two overlap, or even touch each other’s borders. Suppressing that diversity subverts the wholeness of the community.)

Another instance: The Tabernacle we constructed in Sinai and the Temple in Jerusalem are described as miniatures of the entire cosmos. Although they were members of the same Levite tribe, a kohen (priest) was forbidden to do the job of a levi (attendant), and a levi was forbidden to do the job of a kohen. Furthermore, a levi who was appointed to sing was forbidden to help a levi who was appointed to open a gate, and vice versa.7All this from an explicit statement in the Torah: “Each person on his task and to his load.”8

There you have it again: Oneness is expressed as diversity.

How Smart Is a Particle?

Now, there’s a difference here. The letters in the Torah don’t touch one another because the scribe knows the rules and sticks to them—just as the baseball players stick to their bases. The same with the kohanim and levi’im in the Temple.

But when it comes to quantum physics, how does each particle know it’s supposed to keep this rule?

Bigger problem: How does each particle know the state of every other particle in the universe, so that it won’t imitate it?

Even bigger problem: Pauli’s exclusion principle is just that—a principle. Yet it’s due to that principle that matter occupies space—and that we can touch matter. Meaning that the whole concept of matter and substance as we perceive it is really nothing but a baseball-diamond rule. Now, isn’t that strange? How does a rule become so tangible that we can touch it with our hands?

We touch with our fingers not stuff, but deep wisdom. The ultimate wisdom.

We like to bury those issues by saying there are “fields” or “laws.” Words like those are useful at times. But let’s not allow them to blur a deep truth staring us in the face: We touch with our fingers not stuff, but deep wisdom. The ultimate wisdom.

What’s so wise about matter? That will have to wait until the sequel, part 2.