by Sean Carroll
More recently, Crispian Jago, a professional software consultant and recreational skeptic, wanted to demonstrate that he doesn’t believe homeopathy is a valid approach to medicine. So he decided to apply the method of serial dilution to an easily obtained substance: his own urine. Which he then proceeded to drink. Because he was a bit impatient, he only diluted the urine thirty times. Except that he didn’t call it “urine,” he called it “piss,” and then proclaimed that he was developing a cure for being pissed, which translates either as angry (for those in the U.S.) or inebriated (for those in the U.K.). The results, naturally enough, were presented to the world in the form of a boisterous YouTube video.
Jago had good reason for being undisturbed by the prospect of drinking urine that had been diluted in a 1:99 concentration thirty times over: By the time he got to the final glass, there was none of the original stuff left. Not just “a minuscule amount” but really none at all, if his dilutions were sufficiently careful.
That’s because everything in our everyday world—urine, diamonds, french fries, really everything—is made of atoms, usually combined into molecules. Those molecules are the smallest unit of a substance that can still be thought of as that substance. Separately, two hydrogen atoms and one oxygen atom are just atoms; combined, they become water.
Because the world is made of atoms and molecules, you can’t dilute things forever and have them maintain their identity. A teaspoonful of urine might contain approximately 1024 molecules. If we dilute once by mixing one part urine with ninety-nine parts water, we’re left with 1022 urine molecules. Dilute twice and we have 1020 molecules. By the time we’ve diluted twelve times, on average there’s only one molecule of the original substance remaining. After that, it’s all window dressing—we’re just mixing water into more water. With about forty dilutions we could dilute away every molecule in the known universe.
So when Jago finished the procedure and took his final triumphant swig, the water he was drinking was as pure as any that would ordinarily come out of the tap. Advocates of homeopathy know this, of course. They believe that the water molecules retain a “memory” of whatever herb or chemical was used in the original dilution, and indeed that the final solution is more potent than the substance was to start. This violates everything we know about physics and chemistry, and clinical trials rate homeopathic remedies no better than placebos at combating disease. But everyone is entitled to their own opinion.
We are not, as the saying goes, entitled to our own facts. And the fact that matter is made of atoms and molecules is a striking one. Really there are two critical facts: first, that we can take matter and break it up into little chunks that represent the smallest possible unit of that kind of thing; and second, that it only takes a few fundamental building blocks combined in different ways to account for all the variety of the observable world.
At first glance the particle zoo can seem complex and intimidating, but there are only twelve matter particles, which fall neatly into two groups of six: quarks, which feel the strong nuclear force, and leptons, which do not. It’s an amazing story, put together over the course of a century, from the discovery of the electron in 1897 to the detection of the last elementary fermion (the tau neutrino) in 2000. Here we’ll take a whirlwind tour, saving the quantitative details for Appendix Two. When the smoke clears we will have a relatively manageable collection of particles from which everything else is made.
Pictures of atoms
Everyone has seen cartoon images of atoms. They are usually portrayed as tiny solar systems, with a central nucleus surrounded by orbiting electrons. It’s an iconic image, which serves, for example, as the logo of the U.S. Atomic Energy Commission. It’s also misleading in a subtle way.
The cartoon atom represents the Bohr model, named after Danish physicist Niels Bohr, who applied insights from the early days of quantum mechanics to the model of atoms that had been previously developed by New Zealand–born British physicist Ernest Rutherford. In Rutherford’s version of the atom, electrons orbit the nucleus at any distance you might imagine, just like planets in the real solar system (except they are attracted to the center by electromagnetism, not by gravity). Bohr modified that idea by insisting that the electrons can travel only on certain particular orbits, which was a great step forward in fitting the data from radiation emitted by atoms. These days we know that the electrons don’t really “orbit” at all, because they don’t really have a “position” or “velocity.” Quantum mechanics says that the electrons persist in clouds of probability known as “wave functions,” which tell us where we might find the particle if we were to look for it.
Cartoon image of an atom; in this case, helium. A nucleus consisting of two protons and two neutrons sit at the center, while two electrons “orbit” on the outskirts.
All that being granted, the basic cartoon we have in mind of what an atom looks like isn’t that bad, if what we’re looking for is some intuitive grasp of what’s going on. Nucleus in the middle, electrons on the outskirts. The electrons are relatively light; more than 99.9 percent of the mass of an atom is located in the nucleus. That nucleus is made of a combination of protons and neutrons. A neutron is a bit heavier than a proton—a neutron is about 1,842 times as heavy as an electron, while a proton is about 1,836 times as heavy. Protons and neutrons are both called “nucleons,” as they are the particles that make up nuclei (plural of “nucleus”). Aside from the fact that the proton has an electric charge and the neutron is a bit heavier, the two nucleons are remarkably similar particles.
Like many things in life, the nature of an atom is one of exquisite balance. The electrons are attracted to the nucleus by the force of electromagnetism, which is enormously stronger than the force of gravity. The electromagnetic attraction between an electron and a proton is about 1039 times stronger than the gravitational attraction between them. But while gravity is simple—everything attracts everything else—electromagnetism is more subtle. Neutrons get their name from the fact that they are neutral, having no electric charge at all. So the electromagnetic force between an electron and a neutron is zero.
Particles with the same kind of electric charge repel one another, while opposites live up to the romantic cliché and attract. Electrons are attracted to the protons inside a nucleus because electrons carry a negative charge and protons carry a positive one. So—you may be asking yourself—why don’t the protons packed so closely inside a nucleus push one another apart? The answer is that their mutual electromagnetic repulsion does indeed push them apart, but it is overwhelmed by the strong nuclear force. Electrons don’t feel the strong force (just like neutrons don’t feel electromagnetism), but protons and neutrons do, which is why they can combine to make atomic nuclei. Only up to a point, however. If the nucleus gets too big, the electric repulsion just becomes too much to take, and the nucleus becomes radioactive; it may survive for a while, but eventually it will decay into smaller nuclei.
Antimatter
Everything you see around you right now, and everything you have ever seen with your own eyes, and everything you have ever heard with your ears and experienced with any of your senses, is some combination of electrons, protons, and neutrons, along with the three forces of gravity, electromagnetism, and the nuclear force that holds protons and neutrons together. The story of electrons, protons, and neutrons had come together by the early 1930s. At that time, it must have been irresistible to imagine that these three fermions were really the fundamental ingredients of the universe, the basic Lego blocks out of which everything is constructed. But nature had some more twists in store.
The first person to understand the basic way fermions work was British physicist Paul Dirac, who in the late 1920s wrote down an equation describing the electron. An immediate consequence of the Dirac equation, although one that took physicists a long time to accept, is that every fermion is associated with an opposite type of particle, called its “antiparticle.” The antimatter particles have exactly the same mass as their m
atter counterparts, but an opposite electric charge. When a particle and an antiparticle come together, they typically annihilate into energetic radiation. A collection of antimatter is therefore a great way (in theory) to store energy, and has fueled much speculation about advanced rocket propulsion in science-fiction stories.
Dirac’s theory became a reality in 1932, when American physicist Carl Anderson discovered the positron, the antiparticle of the electron. There is a tight symmetry between matter and antimatter; a person made of antimatter would undoubtedly call the particles of which they were made “matter,” and accuse us of being made of antimatter. Nevertheless, the universe we observe is full of matter and contains very little antimatter. Exactly why that should be so remains a mystery to physicists, although we have a number of promising ideas.
Anderson was studying cosmic rays, high-energy particles from space that crash into the earth’s atmosphere, producing other particles that eventually reach us on the ground. It’s like you’re using the air above you as a giant particle detector.
To create images of the tracks of charged particles, Anderson used an amazing technology known as the “cloud chamber.” It’s an apt name, as the basic principle is similar to that of the actual clouds we see in the sky. You fill a chamber with gas that is supersaturated with water vapor. “Supersaturated” means that the water vapor really wants to form into droplets of liquid water, but it won’t do it without some external nudge. In a regular cloud, the nudge typically comes in the form of some speck of impurity, such as dust or salt. In a physicist’s cloud chamber, the nudge comes when a charged particle passes through. The particle bumps into the atoms inside the chamber, shaking loose electrons and creating ions. Those ions serve as nucleation sites for tiny droplets of water. So a passing charged particle will leave a trail of droplets in its wake, much like the contrail created by an airplane, lingering evidence of its passage.
Anderson took his cloud chamber, wrapped in a powerful magnet, up to the roof of the aeronautics building at the California Institute of Technology, or Caltech, and watched for cosmic rays. Obtaining the properly supersaturated vapor inside required a rapid decrease in pressure, caused by a piston that would cause a loud bang each time it was released. The chamber was only operated at night due to its massive electricity consumption. Bangs would reverberate through the Pasadena air every evening, noisy testimony that secrets of the universe were being discovered.
The pictures Anderson took showed an equal number of particles curving clockwise and counterclockwise. The obvious explanation was that there were just as many protons as electrons contained in the radiation; indeed, you might expect exactly that, since negatively charged particles can’t be created without also creating a balancing positive charge. But Anderson had another piece of data he could use: the thickness of the ion trail left in his cloud chamber. He recognized that, given the curvature of the tracks, any protons that would produce them would have to be relatively slow-moving. (In this context, that means “slower than 95 percent the speed of light.”) In that case, they would leave thicker ion trails than what was observed. It seemed that the mysterious particles passing through the chamber were positively charged, like a proton, but relatively light, like an electron.
There was one other logical possibility: Maybe the tracks were simply electrons moving backward. To test this idea, Anderson introduced a plate of lead bisecting the chamber. A particle moving from one side of the lead to the other would slow down just a bit, clearly indicating the direction of its trajectory. In an iconic image from the history of particle physics, we see a counterclockwise-curving particle moving through the cloud chamber, passing through the lead, and slowing down afterward—the discovery of the positron. Giants of the field, such as Ernest Rutherford, Wolfgang Pauli, and Niels Bohr, were incredulous at first, but a beautiful experiment will always win out over theoretical intuition, no matter how brilliant. The idea of antimatter had entered the world of particle physics for good.
The cloud-chamber image from the discovery of the positron by Carl Anderson. The path of the positron is the curved line that starts near the bottom, hits the lead plate in the middle, and curves more sharply as it continues toward the top.
Neutrinos
So instead of just three fermions (proton, neutron, electron), we have three more (antiproton, antineutron, positron) for a total of six—still fairly parsimonious. But nagging problems remained. For example, when neutrons decay, they turn into protons by emitting electrons. Careful measurements of this process seemed to indicate that energy was not conserved—the total energy of the proton and electron was always a bit less than that of the neutron from which they came.
The answer to this puzzle was suggested in 1930 by Wolfgang Pauli, who realized that the extra energy could be carried off by a tiny neutral particle that was hard to detect. He called his idea the “neutron,” but that was before the name was attached to the heavy neutral particle we find in nuclei. After that happened, to stave off confusion Enrico Fermi dubbed Pauli’s particle the “neutrino,” from the Italian for “little neutral one.”
In fact the decay of a neutron emits what we now recognize as an antineutrino, but the principle was absolutely right. Pauli was quite embarrassed at the time for suggesting a particle that didn’t seem detectable, but these days neutrinos are bread and butter for particle physicists (as is proposing hard-to-observe hypothetical particles).
There was still the question of the exact process by which neutrons decay. When particles interact with one another, that implies some kind of force, but the decay of a neutron wasn’t what we would expect from gravity, electromagnetism, or the nuclear force. So physicists started attributing neutron decay to the “weak nuclear force,” because it obviously had something to do with nucleons but also obviously wasn’t the force holding nuclei together, which was dubbed the “strong nuclear force.”
Decay of the neutron into a proton, electron, and antineutrino.
The existence of the neutrino established a nice little symmetry among the elementary particles. There were two light particles, the electron and neutrino, which were eventually dubbed “leptons” from the ancient Greek word for “small.” And there were two heavy particles, the proton and neutron, which were (somewhat later on) dubbed “hadrons” from the ancient Greek for “large.” The hadrons feel the strong nuclear force, while the leptons do not. Each category contained one charged particle and one neutral one. You could be forgiven for thinking that we had it nailed down.
Generations
Then in 1936, a visitor dropped in from the sky—the muon. Carl Anderson, discoverer of the positron, and Seth Neddermeyer were again studying cosmic rays. They found a particle that is negatively charged like the electron but heavier, although lighter than an antiproton would be. It was dubbed the “mu meson,” but physicists later realized that it wasn’t a meson (which is a boson made of a quark and an antiquark) at all, so the name was shorted to “muon.” For a time in the 1930s, fully half of the known elementary particles (electron, positron, proton, neutron, muon, and antimuon) had been discovered in Carl Anderson’s lab at Caltech. Who knows? Maybe a decade or two from now, half of the by-then-known elementary particles will have been discovered at the LHC.
The muon was a complete surprise. We already had the electron; why should it have a heavier cousin? Physicists’ bafflement was captured succinctly in I. I. Rabi’s famous quip, “Who ordered that?” This is exactly the kind of response we’re eventually hoping for from experiments at the LHC—discovering something completely unanticipated, and being sent back to the theoretical drawing board as a result.
It was just the beginning. In 1962, experimentalists Leon Lederman, Melvin Schwartz, and Jack Steinberger showed that there are actually two different kinds of neutrinos. There are electron neutrinos, which interact with electrons and are often created along with them, but also muon neutrinos, which go hand in hand with muons. When the neutron decays, it emits an electron, a proton, a
nd an electron antineutrino; when the muon itself decays, it emits an electron and an electron antineutrino, but also a muon neutrino.
And then the process repeated. In the 1970s, the tau particle was discovered, also negatively charged like the electron but even heavier than the muon. These three particles turn out to be almost identical cousins, differing only in mass. In particular, all of them feel the weak and electromagnetic forces but not the strong interaction. And the tau has its own kind of neutrino, which was long anticipated but not directly detected until the year 2000.
The leptons of the Standard Model, arranged into three generations. Larger circles indicate more massive particles, although the sizes are not to scale.
We’ve worked our way up to no fewer than six leptons, which come in three “families” or “generations”: the electron and its neutrino, the muon and its neutrino, and the tau and its neutrino. It’s perfectly natural to wonder whether there is a fourth generation or beyond lurking out there. Right now the answer is a definite maybe, although there is evidence that three generations are all we get. That’s because the known neutrinos have very small masses—certainly much lighter than the electron. We now know how to search for new light particles, by carefully analyzing the decays of heavier ones. We can count how many neutrino-like particles there must be to account for those decays, and the answer is three. It’s impossible to be sure that there aren’t more lurking out there, perhaps with anomalously large masses, but it may be that we’ve found all the neutrinos (and therefore all the generations of leptons) there are to find.