# One Concept That Gives Physicists A Casper-Like Haunting

Here at 1*3.7: Cosmos & Culture,* we strive to bring you only the finest, most complete "big answers" to life's enduring "big questions."

And when there is more than one point of view to be explored, we lock our jaws onto the issue like a metaphysical pit bull and stay that way until someone calls animal control on us. It is that relentless commitment to the truth that brings us back today to the eternal question of why, exactly, your butt doesn't fall through your chair.

A few weeks ago, we raised the whole butt-chair issue as a way of exploring how modern physics thinks about solid matter. My goal in that post was to dispose of the notion that the atoms in your butt and in your chair can be thought of as a bunch of marbles rubbing up against each other. Instead, each atom is made of electrons and a nucleus that are all the merest flecks of matter separated by oceans and oceans of nothingness.

But that is not all there is to the story. After the post came out, I received an email from Sean Carroll — physicist, philosopher and writer of good books — who chastised me for not taking quantum mechanics properly into account. In Sean's own words:

"The electron isn't a little speck of dirt that orbits the nucleus, that's the whole point. It's a wave function, very close to its ground state, without a well-defined position or momentum. And what is the distance over which that wave function spreads? The size of the atom! And suddenly everything makes sense. Atoms aren't "mostly empty space," they are "mostly the wave function of the electron," because we're in a realm where it's not at all okay to pretend that quantum mechanics doesn't exist."

Sean is quite right, here, in the sense that once you get to scale of atoms the rules of reality (in terms of physics) change substantially. Things get weird, at least in terms of our everyday conception of how reality should behave.

One of the most profound forms of "quantum weirdness" lies at the heart of our butt/chair/empty space question. It's called the wave-particle duality. It tells us that something, like an electron, can behave like a particle — if you do experiments that look for particle-like behavior. Particles only exist in one place at a time. But electrons can also exhibit wave-like behavior — if you do experiments that look for wave-like properties. Unlike particles, waves spread out and exist in many places at the same time. That is why everyone at a concert hall can hear the same sound wave from a plucked violin string.

Now, let's forget, for a moment, about how strange this wave-particle duality is and just focus on how it affects our questions about butts and chairs.

To understand the behavior of electrons whizzing around a nucleus in an atom, physicists use what's called Schrodinger's wave equation. When we properly solve that equation, we get what is called the electron's *wave function.* As the name implies, the wave function describes the electron as being spread out all around the nucleus in what can be thought of as an "electron cloud." As Sean points out, the electron cloud (it's description as a wave function) is not psychotically tiny but is the size of, well, it's the size of an atom. From the point of view of the wave function, the electron does fill the space around the nucleus and, in that way, atoms *are not* mostly empty space and, by inference, neither is your butt — or the chair on which it rests.

But, now comes the really interesting part (for me at least). What, exactly, is the wave function? What is it composed of? What is it that is waving in the wave function?

The formalism of quantum mechanics tells us that what we really get from the wave function (actually it's the square of the wave function) is a description of the *probability* that the electron will be in any particular location at any particular time around the nucleus. The "electron cloud" we physicists like to talk about is really *a cloud of possibility*. If you tried to ask *where* exactly the electron is at any moment, then the wave-particle duality kicks back in and you'd find a super-minuscule-tiny-speck of something: a particle. And, of course, that just brings us back to the "your butt is all empty space" perspective.

But, it's the explicit properties of the wave function that control so much of the atomic world's behavior. That is why asking about the fundamental reality of the wave function is so fascinating. What is this strange mathematical object which, when multiplied by itself (with some complex number stuff happening, too), gives you the probability of electron positions? Is the wave function a real in-and-of-itself part of the foundational structure of reality? Or does it, and its weirdness, reflect our interactions with the electron (whatever that electron is in-and-of-itself)? This is the place where Sean and I, and many other physicists, can hold a range of very different opinions.

Add to the argument the remarkable fact that this question has haunted quantum mechanics for a good portion of 100 years. But, like Casper the Friendly Ghost (for those who remember him), it's a good haunting. The question about the reality of the wave function tells us there is something else, something deeper, going on in quantum mechanics. It may be telling us that there are infinite parallel universes that split apart with every quantum event. It may be telling us that we never can get perfect information about the world in-and-of-itself, independent of the way we ask questions. There are many possibilities and each one has *profound consequences* for the nature of this reality we are all born into.

These are "big questions," indeed. And, to think it all began from pondering empty space, your chair and, of course, your butt.

*Adam Frank is a co-founder of the 13.7 blog, an astrophysics professor at the University of Rochester, a book author and a self-described "evangelist of science." You can keep up with more of what Adam is thinking on *Facebook and Twitter:* *@adamfrank4.