Small Things: Lightly Toasted


This image by Joe Loong is licensed under CC BY-SA 2.0

Editor’s Note: This is the second article of a column exploring the physical phenomena of “Small Things” in our world. Start from the beginning with Will’s first article on atoms and energy, and stay tuned for more witty scientific explanations coming soon! 

Gather round everyone, it’s story time:

Once upon a time, it was the early 20th century and physics was pretty much over. Yes, that’s right. With classical mechanics (remember what we talked about last time?) having been thoroughly thought out by some of the most brilliant scientific minds in history, the world finally had time to do all those other important things it needed to do–like produce an insane amount of wealth inequality, follow it up with crippling economic collapse, and then start two massive wars that would basically raze half the globe. Good job, humanity.

In fact, some years earlier in 1878, Johann Philipp Gustav von Jolly, a prominent physicist at the University of Munich, advised one of his physics students to get on with his life and please, for the love of God, major in something productive. According to von Jolly, “in this field, almost everything is already discovered, and all that remains is to fill a few unimportant holes.”[1]

A remark to which the Universe, in all of the eloquence it could muster responded:

Welcome back to Strang–I mean Small Things! For those of you who are wondering what I just showed you, don’t worry–all the 20th century physicists were too. Let me show you how truly bizarre this image is.

Imagine yourself at breakfast. You’ve got a long day of work ahead of you, and the only thing that can possibly make your drab existence better right now is some hot coffee and a piece of toast. As you wait for your coffee to brew, you walk over to the toaster, insert a nice, fluffy piece of bread, and then press down the lever. With nothing better to do this early in the morning, you decide to watch the metal coils inside the toaster heat up and turn red, then orange, then yellow, while you savor the delicious smell of the singeing bread. Aaaaand congratulations, you just got off a day of work, because you’re now dead–at least, according to the way classical mechanics treats light.

Since I know you’re simply DYING to know what just happened, let me explain. Light is a form of radiation–you know, that same thing you hear horror stories about every time someone brings up nuclear weapons or the Chernobyl disaster. (Again, good job, humanity!) It’s also, however, the source of other horrifying things you may have heard of, like sunlight and rainbows and your ability to read this sentence. The only reason why rainbows melt your heart with joy and broken nuclear reactors will melt your skin instead is because they emit different wavelengths of radiation.

Believe it or not, light actually shoots around the universe as a wave. The distance between two peaks of this wave is called the wavelength. Now, as you can see from the figure below, this wavelength can range from a really tiny gamma ray to a much larger radio wave. Our eyes can detect what’s called the visible light spectrum, which spans wavelengths from 380 nanometers to 750 nanometers and looks like a RAINBOW!!!


This image by Inductiveload is licensed under CC BY-SA 3.0

You also might notice that you don’t get cancer from listening to the radio (unless it’s Nickelback). This is because radio waves have a much longer wavelength than ultraviolet (UV) radiation. Light with a longer wavelength is generally pretty harmless, but as you get shorter in wavelength, things start to get…edgier.

You see, that graph I mentioned earlier plots the intensity with which the glowing hot metal inside your toaster emits certain wavelengths of light. That graph is also apparently plotting the death of you and all of mankind, because according to that little dashed line that says “Classical theory” and spikes up to who knows where, your toaster is emitting infinite amounts of short-wavelength radiation directly into your face. Painful face-melting, not wholesome heart-melting, ensues.

Max Planck, who had become a famous physicist despite von Jolly’s discouragement, also thought it was a little strange that he wasn’t supposed to be surviving breakfast every morning (this “Classical theory” wasn’t getting him very far with his research on light bulbs, either). Neither light bulbs nor toasters can emit infinite amounts of energy, and the solid lines underneath that “Classical theory” line are what is actually observed. Around 1900, Max Planck decided that everyone else was just wrong–and he was absolutely right. This not-so-little error in classical theory was dubbed “The Ultraviolet Catastrophe.”

As it turns out, the only way to explain the Ultraviolet Catastrophe is that energy can really only be exchanged in packets of set size, or “quanta.” That may sound kind of abstract, but let me explain:

Imagine that I bet you ten bucks that I can lift just as many pounds as you. Then, I lose because I’ve been spending my time banging my head against a keyboard until I write something coherent for this article instead of hitting the gym. I’m also a college student, so when I lose, I’ll probably pay you with a five, maybe a couple ones, a Chuck-E-Cheese token, and the lint I found in my pocket. I paid you ten dollars, yes, but the packets that I distributed that overall value in were on average pretty small.

Now imagine you bet a famous YouTuber ten bucks that he can lift just as many pounds as you. He also loses because he’s been spending his time banging his head against a keyboard until he produces coherent footage. He’d probably just pay you two fives or a whole ten like a normal person, and then go about his day. Since he’s richer and probably hotter than I am, the packets that he distributes money in are, generally speaking, larger.

It’s exactly the same deal with energy! A really hot, high energy object is going to release more of its energy in high energy radiation packets, and a more lukewarm, lower energy object will release most of its energy in lower energy packets. You either have the ability to emit a high energy packet or a low energy packet, and nothing in between. An object at a lower temperature does not have enough energy to emit very many high energy packets (the ones represented on the far left of the curves). An object at a higher temperature does, which shifts its average to the left, towards those shorter, higher energy wavelengths. That’s why the solid lines in that graph are shaped like bell curves rather than murderously high peaks.

Now this sounds rather boring, so let’s give it a sexy name — how about “quantum physics”?
Works for me.

Aaaaand for my next magic trick, I’ll be tackling the one, the only, the truly incomparable double slit experiment. See ya next time!



  1. Lightman, Alan P. (2005). The discoveries: great breakthroughs in twentieth-century science, including the original papers. Toronto: Alfred A. Knopf Canada. p. 8. ISBN 0-676-97789-8.