“I trust in nature for the stable laws of beauty and utility. Spring shall plant and autumn garner to the end of time.” –Robert Browning
Like everything else that we know of in the Universe — galaxies, stars, and planets — human beings are made out of atoms.
And just like galaxies, stars and planets, over 99.9% of the mass of your body isn’t just made up of atoms, it’s made out of the nuclei of those atoms.
And if you go inside these atoms, into the heart of them, you’ll find that these nuclei are combinations of two simple nucleons: the proton and the neutron. Bound together in hundreds of different combinations, protons and neutrons not only determine what type of element your atom is, they also determine whether or not your atom is stable.
And inside the human body, there are, literally, more than 1028 atoms that make you up.
More than 10,000,000,000,000,000,000,000,000,000 atoms in every single human body. Now, some of these atoms are well known to be radioactive, like bismuth, uranium, and thorium, but even these elements always conserve the total number of nucleons.
Even a free neutron — unstable though it is — decays into a proton (and some other stuff), conserving the total number of nucleons.
But what about the protons, you might ask? More than 1027 of the atoms in every human are simple hydrogen atoms, with just a single proton for a nucleus.
Is it possible that these protons themselves are unstable? According to many ideas in physics (such as Grand Unified Theories), the proton itself can decay!
But if it does decay, it must be very long lived. Unlike a neutron, which decays after 15 minutes or so, the proton must live an incredibly long time.
We can figure this out just by using our bodies! With (to be a little more precise) 4 x 1027 plain old protons inside you — from the nuclei of your hydrogen atoms — you couldn’t have too many of them decaying, or you yourself would release too much energy!
The same conversion of matter into energy that drives the Sun and atomic bombs could also result from something as seemingly benign as a proton being inherently unstable.
Well, you know what? Humans do emit energy, like all warm blooded mammals.
It isn’t obvious in visible light, but if you look in infrared light, you get to see that humans, relative to their outside environments, are constantly radiating their heat away to the cooler air around them.
In order to keep yourself at the proper temperature, you need to expend energy to make up for what you’re constantly radiating away, as we learned last time. For a full-grown human about my size, doing the calculation shows that I need to be outputting around 100 Watts of power: that’s 100 Joules of energy every second, just like an incandescent light bulb.
Even if you were getting 100% of this energy from decaying protons, that limits the number of protons that could decay each second, within your body, to no more than about 600 billion.
But based on the tremendous number of protons in your body, you can figure out that — on average — it takes at least hundreds of millions of years for a typical proton to decay. Now in reality, we don’t get our 100 Watts of power from decaying protons.
We get it from chemical energy, mostly from eating bunnies calorie-rich foods. It takes about 2,000 food calories a day just to keep an adult male’s body temperature normal. (In fact, one of the earliest symptoms of undernourishment is a drop in body temperature.)
But if we want to test as accurately as possible whether protons decay or not, you know how to do it. You get as many of them together as possible, build a giant detector around them, and look for the telltale signature of their decay.
In Kamioka, Japan, they did just that. They built a tank with thousands of tonnes of water inside, and photon detectors all around the outside. If any of the protons decayed, the high-energy decay products would give off telltale light signals, allowing us to not only measure whether anything decayed, but how many of these atoms decayed.
You take a tank of 1032 protons, wait a year, and if none of them decay, you know that the proton has a half-life of at least 1032 years!
And while these setups of giant tanks have proven incredibly useful for detecting cosmic neutrinos, all the experiments ever done have given null results for proton decays. Overall, the best constraints we have tell us that the lifetime of a proton is at least 1035 years, which is really not bad, considering that the Universe itself is only about 1010 years old!
The proton is so stable that it actually presents a problem for a significant number of Grand Unified Theories. In fact, just based on this constraint, we can say that, at most, there’s only a 0.001% chance of even one proton in your body decaying over your entire life! And that’s how stable, at a fundamental level, the stuff we’re made out of really is!