How to Teach Physics to Your Dog goes on sale in fine bookstores everywhere tomorrow. But maybe the four previous posts explaining why dogs should care about quantum physics haven’t yet convinced you to go buy a copy. So here’s another reason, one appropriate to this solstice season, when dogs in the Northern Hemisphere will start to enjoy longer days again: Sunlight.
You like sunlight, right? Of course you do, unless you’re a vampire. And what dog doesn’t like a sunny day? Well, you have quantum physics to thank for sunlight, because as hot as the Sun is, it’s not nearly hot enough to burn without a little help from the wave nature of matter.
As all good dogs, and even most cats, know, the Sun generates energy through nuclear fusion, a process in which two hydrogen nuclei are stuck together to form the nucleus of a helium atom (actually, you end up needing four hydrogen nuclei to make helium, but it starts with two). In order for this to happen, you need to bring the two hydrogen nuclei very close together– about 10-15 m.
The two nuclei are positively charged, though, so they repel each other. If you want to shoot one nucleus at another and get them close enough to touch, the energy required is equivalent to a temperature in the neighborhood of fifteen billion Kelvin. The temperature at the center of the Sun is only around fifteen million Kelvin, a factor of a thousand too low. Which suggests that it shouldn’t be possible to fuse hydrogen into helium in the Sun.
Of course, this is manifestly untrue, at least here in Niskayuna where the sun is shining. The thing that allows the Sun to burn in spite of its low temperature is a quantum phenomenon called “tunneling.” The energy of one hydrogen nucleus close to another is low when the distance between them is relatively large, and gets bigger as they get closer together. If you manage to get them close enough, though, the energy drops again, and in fact the energy for the two stuck together is slightly lower than the energy of the two apart. So a graph of the energy of the two hydrogens will look like a big hill between two low-energy regions.
A hydrogen nucleus starting a long way away from another can be thought of like a ball rolling along the “hill.” As it gets closer to the other nucleus, it rolls up the hill, and slows down. It would need a gigantic amount of energy to make it all the way to the top of the hill, so most of the time, it will come to a stop, turn around, and roll back down the hill, separating the two again.
Every once in a while, though, something odd happens– a proton will just pass right through the “hill” as if it isn’t there, even though it doesn’t have the energy to get over the top. This is called “tunneling,” because it’s sort of like the proton dug a tunnel through the hill to avoid needing to climb all the way to the top.
This is a very rare process, and happens due to the wave nature of matter– because the hydrogen nucleus needs to behave like a wave, and not just a classical particle, the wavefunction describing it extends beyond the point where a classical ball would turn around. This means there’s a tiny chance of the hydrogen nucleus making it through the hill, and that, in turn, means that every once in a while, one makes it through. And because there are something like 1057 hydrogen nuclei in the Sun, all moving around at high speeds and bumping into one another, a very large number of them are fusing every second. When they do, it releases energy, which is what keeps the Sun hot, and some of that energy makes its way to us in the form of light.
So, the next time you have a nice sunny day where you are, remember that you have quantum physics to thank for it.