Just What IS a “Quantum”?

Quantum is one of those words that’s a godsend if you’re a lazy science-fiction author in need of a plot device, or someone trying to scam people into buying your crappy, overpriced jewelry. It evokes scientific knowledge and mystery all at once; it lets things be in two places at the same time, or jump to alternate universes.

It’s a word that practically everyone’s heard, but that relatively few people understand properly. Part of the reason for this is because it has multiple meanings in various contexts, but more, it’s because the word is so often misappropriated. Usually, when you see “quantum _______” in pop culture, it’s shorthand for “don’t look too close here, there’s little or no actual science involved so we’re going to pretend the science is so impossibly complex that it’s basically magic.”

Now that’s perfectly fine, if you’re a writer on Doctor Who trying to explain why your alien statues can’t move when someone’s looking at them, but it’s had the accidental effect of turning the word into a huge stumbling block for those of us who are in the business of demystifying science—encouraging people to see physics as something that anyone is capable of understanding. So we’re here to take a minute and clear the air a bit about what, precisely, “quantum” means, because it’s really not too hard.

In the broadest sense, “quantum” as a noun just refers to an individual packet, or countable bit of something, usually the smallest possible amount; see, for instance, the James Bond film “Quantum of Solace”.

For instance, the work that won Einstein his Nobel prize actually had nothing to do with his most famous work on relativity—it was his realization that light comes as particle-like packets, or quanta (the plural of quantum), better known these days as photons. In the modern day, where this fact is taken for granted, it can be hard to appreciate the depth of this insight without a little background on the problem Einstein was trying to solve when he came up with his hypothesis.

Around the beginning of the 1900s, it was well understood that light is a wave in the electromagnetic field, but a few shreds of evidence suggested that this wasn’t the whole story. One is a phenomenon known as the photoelectric effect—the way light can knock electrons free from a metal surface and out into the surrounding space. This in itself wasn’t the problem—electrons are charged particles, so they “ride” that wave, gaining energy and sometimes breaking free of the surface, like a surfer catching air.

But if it were simply a matter of energy transfer, a dim light might be expected to produce electrons that moved at a lower speed than an intense light—and this simply wasn’t the case. A bright (or intense) light source would produce more electrons than a dim one, but they wouldn’t move any faster. The other major clue was that, no matter how bright your light source is, it generally won’t produce electrons if it’s not the right color—you can shine all the microwaves you want at a solar panel, but it won’t make a single volt of difference.

Einstein’s stroke of genius came in the realization that these results fit perfectly with a description of light as both wave and particle. If energy comes in discrete, particle-like packets, then sending a lot of low-energy photons wouldn’t be enough to stimulate a high-energy process, like liberating an electron, unless two photons happened to hit the same electron at almost exactly the same time.

So, in the context of light, “quantum” refers mostly to the particle-like behavior of waves. Easy enough! But paradoxically, when it comes to matter, it’s almost precisely the opposite; quantum mechanics arises entirely from the wavelike nature of particles. So what does it mean when we say the energy levels of the electron in an atom are “quantized”?

In this context, “quantized” refers to the fact that the electron’s orbit (technically orbital) around the nucleus is only really stable with certain amounts of energy—and the reason why has to do with the fact that electrons move in accordance with a wave equation. Where a planet’s trajectory around the sun can be described by the equations of ellipses, electrons move around the nucleus in a way that’s guided by the more complex wave function of Schrödinger’s equation.

So let’s talk waves. In the video below, a man holding the end of a rope shakes it up and down. He can shake his hand up and down at any frequency (a continuum—sort of the opposite of “quantum”) but there are certain speeds where he creates a standing wave, e.g. at 0:19 (3 peaks, known as anti-nodes) or 1:25. (1 anti-node)

The hand-shaking frequencies where the standing waves appear are the rope’s resonant frequencies, and they arise when one wave travels down the rope, reflects back, and reaches his hand again at just the right time to be self-reinforcing, making it easier for him to move his hand in the direction it was going. The thing about standing waves is that you never see one with two-and-a-half peaks or troughs; they only come in integer numbers. In other words, they’re quantized!

If you imagine the electron as behaving like a standing wave in the electric field around a nucleus, you can hopefully see the similarity to the rope demonstration above. The first energy level, the ground state, is something like the “jump rope”-style motion seen at 1:25. Exciting the electron to a higher-energy state is like jumping to the three-wave frequency seen at the beginning of the video.

Where these frequencies lie depends on things like the weight of the rope, the tension in it, etc. but just about any closed system that can contain energy has resonant frequencies like this. You can see a similar phenomenon in a ring being shaken up and down—here, rather than reflecting off a wall, the waves simply go around and around the circle.