Science is full of amazing stories. I’ve written about some of them in some of the articles I’ve done for magazines, but there are always more to tell. For me, these stories stir the soul. There’s something magical about understanding a deep connection, an unexpected truth, a hidden symmetry. Science and technology can do a lot to make life better. Scientists can cure disease, fight hunger, keep the world connected, produce a new source of energy. But the discoveries of science, those connections and deep truths that cause me to gasp or even laugh out loud for joy, those are the discoveries that make life worth living.

In 1928 George Gamow, an immigrant scientist from Russia, discovered how alpha particles escape the nucleus in radioactive decay. Here’s the story. Alpha particles come flying out of certain atomic nuclei. When a uranium 238 nucleus, for instance, shoots out an alpha particle, the nucleus changes into thorium 234. Thorium 234 plus an alpha particle weighs a little bit less than uranium 238. Where does that little bit of mass go? Through E=mc2, that mass comes out as energy. The energy is essentially constant for each kind of radioactive atom.

But here’s the puzzle. It takes a lot of energy to get an alpha particle in to a uranium nucleus, a lot more than the energy the alpha particle gets when it leaves a uranium 238 nucleus. If you try to fire alpha particles into a uranium nucleus, you’ll never get one in if it has only the energy of an alpha particle that leaves a uranium nucleus.

Why is that a puzzle? Think of the uranium nucleus as a high shelf, and the alpha particles as balls falling off the high shelf. When those balls fall from the shelf, they have a certain energy, depending on how far they’ve fallen. You catch the balls and find out how much energy they’ve got. Now you throw the balls back up to the shelf, using that same amount of energy. You discover, though, that there is no way the balls can make it back up to the shelf with that amount of energy. They fall far short.

Alternatively, try throwing the balls up to the shelf. Measure the energy needed to get a ball up to the shelf. You find the amount is far more energy than the balls have when they fall off the shelf. How did the balls get down to the ground with such little energy?

So that’s the puzzle. How did the alpha particles get “off the shelf” with so little energy? Here’s Gamow’s answer (two other scientists named Gurney and Condon came up with the same answer at around the same time). The alpha particles aren’t particles. They’re waves. Think of an alpha particle inside the nucleus as a smeared out wave. A wave of what? A wave of probability! So almost all the time the wave is inside the nucleus, and it can’t escape. But very rarely, the alpha particle might find itself outside the nucleus. When that happens, the positive charge of the alpha and the positive charge of the nucleus push against each other, and the alpha flies away.

Here comes the amazing part. If the alpha appeared in the wrong place, it would fly off with too much energy. It would be as if the ball fell off the shelf and hurtled to the ground. But remember where the alpha energy comes from: it’s from the lost mass of the nucleus. That lost mass is too small to give the alpha energy to fly away from the edge of the nucleus. If that happened, energy would have appeared from nowhere.

Nature’s solution is beautiful and elegant. The alpha never appears at the forbidden distance. It appears only at one spot, just exactly far enough away from the nucleus to get just the energy available from E=mc2. No more, no less. It’s as if nature is covering her tracks, hiding all the internal workings of the decay process and fixing the game so that the alpha always, always has just the energy available from the lost mass.

It’s very much as if the balls had suddenly appeared midway between the shelf and the ground. How did they get there? They just appeared there, without ever being in the space between. This idea, called quantum tunnelling, appears again and again in modern science. It explains a whole host of behaviors, including why you’re able to twist two copper wires together and get electricity to flow through them.

With radioactive decay, though, there’s even more. Because the alpha wave is a probability wave, we can never know just when the alpha decay will happen. It might be tomorrow. It might be ten seconds from now. It might be ten billion years from now. There is absolutely no difference between the U-238 nucleus that decays tomorrow and the one that decays in a billion years. They’re exactly the same. Yet somehow the decay happens, regularly, like clockwork, just as it must, just as it has for billions of years. 

And that is pretty cool!