Tuesday, February 20, 2018

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".

 I wouldn't advise you to actually see Quantum of Solace. Seriously underwhelming.
Image Credit: MGM Productions
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.

A creative "vaper" excites standing waves on a vortex ring by changing the air pressure around it at its resonant frequency. You can't split electrons in two like that, but the analogy between vortices and charged particles is otherwise pretty strong.
Image Credit: vAustinL, via Youtube.
So the energy levels of matter are quantized because matter behaves like waves, and light is said to be quantized because it behaves like a particle. But, as circular as it might seem, it's also true that the quantization of light is a result of the quantization of energy in matter
In one sense, this is because all electromagnetic waves have to come from the motion of charged particles—so light behaves like a particle because it's given off by a particle. But for an electron that's bound to an atom to emit energy, it needs to jump from one resonance to another. Because this takes a very certain amount of energy, light resulting from that jump will come off as a packet containing just that amount—meaning it will have a certain color, or frequency.
This is the science at the root of spectral analysis—the technique that lets us learn about the composition of distant stars by looking at the light that comes from them. It's also why you can turn fire different colors by throwing certain elements into it—the flame gives off a broad spectrum of photons, some of which happen to be the right frequency to excite a transition in the atoms' electrons. When they jump back down, they give off their characteristic color.

A series of different elements mixed with fuel, in a classic demonstration of a "flame test"
"Quantum" also refers to things happening on the ultra-small scale where matter's wavelike properties become relevant, and it obviously has a multitude of other uses, some of which—like quantum entanglement—are more complicated than what we've covered here; hopefully, we'll have a chance to dig into those in a future post. Regardless, if you can keep your eyes from glazing over when you hear the word, you'll often find that things are simpler—and more intuitively friendly—than you'd expect!
—Stephen Skolnick

1 comment:

  1. Hey, Skolnick- Your posts are great, keep ‘me up. I have always been bothered by the way that photoelectric effect was presented in textbooks. Tell me what you think, if you feel like sharing your point of view. They make it sound as though the assumption, from the point of view of classical EM, is that a low frequency, high intensity wave should be adequate to liberate electrons from atoms. But that assumption relies not only on classical EM, but also on a primitive theory of electrodynamics, in which the electron is just sitting there, waiting to be accelerated, like in the “plumb pudding” model of the 1800’s. But we know now that they are not in such a condition in atoms. In plasmatized matter, as in a star, I believe it is possible to liberate electrons with a low frequency wave, or even a static field. So in that state of matter, it does behave as you might expect the classical EM wave and the plumb pudding electron to behave. If I understand correctly, that is why stars radiate not only with certain peaks in their spectrum, but also on a continuum of wavelengths. Because free electrons in them can indeed be accelerated by intermediate (not quantized) degrees.

    The process of liberating the electron in an atom is different than merely applying a field strong enough to accelerate a charge. A field that pushes on the electron will push on the nucleus. But since the electron is not stationary, that means that on one side of the atom, the field will be pushing them together, and on the other side, it will be pulling them apart. So from that point of view, of the more realistic atom, it is easy to see why a static field or a low frequency wave is not adequate to liberate electrons, even if we take the EM wave to be nothing but a classical EM wave.

    I sometimes use an analogy of a boat being tipped by a wave in the water. Because a water wave has a wavelength, it will always have a certain scale on which it is able to affect anything else that has scale. So a a wave with great energy but great wavelength, as sometimes occurs at sea, will not tip a boat significantly, because stern and bow are being raised at the same time, to almost the same degree. But a shorter wavelength, with less total energy, will tip a boat, because the two ends are pushed by different degrees, or in different directions.

    The atom is the same, because it has a certain size defined by its electron orbitals. A classical EM wave would only be expected to “tip” the atom, that is, liberate its electrons, if th wavelength was short enough that one side could be pushed, while the other is pulled. For this reason, I have always said that photoelectric effect is consistent with classical. I’d be curious what you think.