*Second in an occasional series on the nature of reality from the perspective of quantum physics.*

Two weeks ago, we discussed the famous wave-particle duality in quantum physics. Here, duality means that when we look at, say, an electron in the lab, we can see it *either* behaving as a particle—a little bullet-like thing that hits other bullet-like things—*or* as a wave—a spread-out thing that interferes with other spread-out things.

We also noted that, “strictly speaking, [electrons] are not ‘things,’ like a soccer ball or a car is a thing, but mental idealizations invented to characterize the results of experiments. We don’t see an electron directly, but its existence is undeniable. What happens, then, is that we identify the results of experiments, which we can see and take note of, analyze and quantify, with idealized objects that we can relate to—the electrons, atoms, and molecules of the quantum world.”

The weirdness of quantum physics jumps out full force here: if an electron is not a “thing,” how can atoms—groups of electrons, protons, and neutrons—make up every *thing* around us, from rocks to cakes to frogs?

Somehow, piling up a bunch of quantum particles, we get something that we can relate to—an object in the usual sense of the word. There is, apparently, some kind of dividing line between the quantum world and the classical world—our real, tangible, everyday world. And it’s a line that is as mysterious as it gets in physics.

We sometimes call it the quantum/classical boundary, even though we don’t really think of it as a well-defined boundary. It’s more like a demarcation region, a certain length-scale, a size, where quantum objects begin to lose their “quantum-ness” and start to behave normally. By “normal,” I simply mean the stuff around us. To a physicist, there is no such thing. Every object is a quantum object; what happens is that, above a certain size, the quantum properties get muffled to an imperceptible level.

## The Compton wavelength explained

And what size is this, you may ask? There is no clear answer. But a first ballpark is the so-called Compton wavelength (*L*) of an object, defined as (don’t panic, I will explain) *L = h/mc*, where *h* is the Planck constant, *c* is the speed of light, and *m* is the mass of the object. Since *h* and *c* are constants, what determines the Compton wavelength is the object’s mass. The smaller the mass, the larger the wavelength.

Now, what’s a wavelength? If you imagine a train of waves, like when you throw a rock into a lake, the wavelength is the distance between two consecutive wave crests. Given that quantum physics kicks in when there is more “waviness,” a large Compton wavelength means more quantum-like nature, and a small one means more classical-like nature. Let’s work out a few examples:

For an electron, the Compton wavelength is about two trillionths of a meter (that is, 2.4 x 10^{-12}m). The shorter wavelength of X-rays, for comparison, is about 5 times larger. We can still compare their “wavinesses” here. But if you consider a flea (pictured above), its Compton wavelength would be about one trillionth of a trillionth of a trillionth of a meter (10^{-36}m)—completely imperceptible even for short wavelength X-rays. In other words, a flea would look like a “thing”— a non-wavy object—for X-rays and certainly for our eyes, which can only see in the much larger visible wavelength of light. (If you are rusty on waves and the electromagnetic spectrum, here is a nice video produced by NASA.)

Using the Compton wavelength gives a rough idea of the boundary between classical and quantum. But only rough. If we start asking too many questions, we see that the mystery of the quantum/classical boundary persists.

For an example, let’s go back to the lab. To study particles like electrons, we use detectors, such as the huge ones at CERN’s Large Hadron Collider experiments in Geneva, Switzerland. Since we can’t see electrons or other subatomic particles, these detectors turn the tiniest signals from their mutual collisions into signals we can see. For that, there is a linked chain of amplifications that translate collisions happening at subatomic scales to a blip or a line on a computer screen. The funny thing, though, is that the collider itself is made of electrons and proton and neutrons. It is also a quantum object. We may speak of a collision and see the signals, but by so doing we are relying on this quantum-to-classical amplification chain.

## The central quantum question

The great physicist John Bell was deeply puzzled about this, calling it the “central” question of quantum physics:

The ‘Problem’ [of quantum mechanics] then is this: how exactly is the world to be divided into speakable apparatus … that we can talk about … and unspeakable quantum system that we can not talk about? How many electrons, or atoms, or molecules, make an ‘apparatus’? The mathematics of the ordinary theory requires such a division, but says nothing about how it is to be made. (From *Speakable and Unspeakable in Quantum-Mechanics*.)

What do quantum physicists do? They usually don’t spend too much time pondering the quantum/classical divide. (Although some, like my Dartmouth colleague Miles Blencowe, work precisely on this topic.) Most just go on, using the highly successful quantum theory in their various research projects. One could argue that the division is artificial, that the world is essentially quantum mechanical and that this whole “classical” description is a rough approximation to reality as we sense it, valid for large numbers of quantum particles. (I mean, a flea is small, but it contains trillions and trillions of subatomic particles.)

Still, the question of “how many is too many?” remains, and it seems to be pointing to some hidden secret about the nature of reality. We would like to know at what point the weirdness of quantum mechanics gives way to the world as we know it.

Or, maybe, we shouldn’t. Perhaps we should take quantum physics at face value, and assume that reality is, at its core, as weird as it is impenetrable.

Einstein, for one, would have none of it. Bohr, on the other hand, would embrace our fundamental ignorance about the world. Each thought of the world in very different terms, and fought hard for their worldviews until the end of their lives. A topic for us to dive into next time.