by Caleb Scharf
From 10 picometers to 1 femtometer
From X-ray wavelengths to the approximate size of a carbon nucleus
Make a fist. Now imagine that your fist represents the size of an atomic nucleus. If it did, the entire atom would extend to about five kilometers in all directions. Atoms are 99.9999999999999 percent empty space (a typical atomic nucleus takes up one-trillionth of its atom’s volume but holds 99.9 percent of the mass).
Consequently, you could crush all seven-plus billion humans into a single mass the size of a sugar cube simply by squeezing out all that empty atomic space. In exotic locales like neutron stars, that is precisely what gravity does, creating an object made of a special state of nuclear matter (degenerate matter) that is only ten to twenty kilometers across, yet contains the mass of a star.
All that emptiness also means that the next leg of your journey, from a scale of 10−11 meters (10 picometers) down to 10−15 meters (a femtometer), is phenomenally dull. It’s actually worse than your much earlier traversal of the scales of intergalactic and interstellar space. At least there you’d occasionally have a molecule or an interstellar dust grain for company. Within the atom, even the flitting electrons are scant compensation. Although their physical size is not an easily definable thing (or even very meaningful), some experiments suggest that an electron is at least ten million times smaller than an atomic nucleus.
What this trip through the emptiness of an atom does give you is more time to think about the fundamental nature of the space enveloping you, and how it’s connected to the strange phenomena you experienced at your smallest in the last chapter.
If your fist were a nucleus, this would be the extent of the atom.
The quantum nature of fundamental reality is one of the most conceptually challenging pieces of our current quest to understand the universe. Yet, as mind-bending as quantum physics is, this is evidently the way the universe works.
Where we have successfully melded mathematical descriptions of quantum physics to nature (such as in atomic physics), we’ve produced some of the most precise and accurate predictive tools yet known to humans. In the quantum domain we’ve also conducted some of the most precise experimental measurements of any fundamental cosmic properties. For example, we’ve measured esoteric yet important quantities such as the so-called anomalous magnetic moment of the electron with an astonishing precision of more than eleven decimal places. Our theory of quantum electrodynamics (QED, which contains relativistic physics) had accurately predicted this quantity to the same level of precision.
Still inside the atom; a speck appears in the distance
Our mathematical physics of the very small works exceedingly well, and it’s a framework containing many versatile tools. These range from the constructions of wave functions and Dirac matrices to the elegant intuition of Feynman diagrams for describing particle interactions. We’ve also come up with powerful, highly mathematical devices with imposing names like “symmetry groups,” “Hilbert spaces,” “operators,” and “eigenvalues.”
But at the core of it all is a type of counterintuitive physics that still baffles us. The Heisenberg uncertainty principle tells us that properties of objects and systems can be inextricably connected by being complementary. For example, the position and momentum of a particle can never both take on exact values: the better one of those is defined, the less defined the other. That uncertainty is not simply an effect of our observation of the particle; it is intrinsic.
Tiny objects exhibit properties that can be attributed to either discrete particles or to wavelike entities—characteristics that in our classical, macroscopic world are typically incompatible with each other.
Scientists are still trying to sort all of this out, and we have a few options to turn to for help making sense of our quantum reality.
THREE TAOS FOR QUANTUM PHYSICS
For example, the so-called Copenhagen interpretation of quantum mechanics says that the only reality is one of probabilities and statistics. It’s dice rolling all the way down. Particles are literally neither here nor there until something interacts with them. Their whereabouts are given by a cloud of probabilities, described by a wave function, whose precise behavior is captured by a mathematical device called the Schrödinger Equation. Observe (interact with) the particle, and the wave function “collapses” to define the particle’s location and properties.
The Copenhagen interpretation says that before the wave function collapses, the particle literally does exist anywhere and everywhere that the equation says it might. If we don’t like it, that’s tough—nature doesn’t care whether or not we’re happy.
While that’s the most popular view of the underlying nature of quantum mechanics, it’s not the only one. For example, an alternative view was proposed back in the early and mid-twentieth century, which says that there really are particles that exist as discrete “classical” entities with definite locations, but that they exist hand in hand with something called a “pilot wave.” The pilot wave determines the way the particles move and how, for example, they diffract and interfere (an otherwise wavelike property that you encountered briefly at the 10−10-meter scale—the final shrinking doorway that diffracted your body). We need two equations to work with this interpretation of quantum reality: one is a wave function, and the other links the particle’s behavior to the wave.
Farther still into the atom
This so-called de Broglie–Bohm version of quantum mechanics makes many of the same predictions as the Copenhagen Interpretation, but it sticks to having particles be particles and waves be waves. This version also implies that the universe is deterministic. So if you knew all properties of matter in the universe at this instant, you should (in principle) be able to predict what will happen in the future.
But a thorny issue called non-locality comes into play. In essence, two particles that have once been associated with each other—for example, produced in the same subatomic process—will remain linked (entangled) when they head off into the cosmos. The subsequent state of one particle will appear to affect the state of the other—even if they are great distances apart. It’s a property that can be verified in experiments using photons, atoms, or even tiny solid objects. It is also one of the weirdest aspects of the quantum domain.
Wavelike interference patterns
Does each event split reality into an infinity of possible worlds?
The Copenhagen interpretation deals with this “spooky action at a distance” (Einstein’s phrasing, to describe his skepticism about the whole nature of quantum physics) by essentially shrugging and saying, “That’s just how it is.” The de Broglie–Bohm interpretation tries to one-up this by stating that the wave function of a system has no spatial limits—it literally spans the universe—and the behavior of one particle is always bound to any other particles governed by the same wave function.
But there’s yet another way of trying to understand quantum mechanics: the many-worlds, or Everett, interpretation. In basic terms the many-worlds picture says that wave functions describing the probabilities of certain things happening neither “collapse” nor “guide” particles. Instead, all eventualities that can happen do happen—they just don’t happen in a single reality.
It is a hugely provocative meta-theory: for every possible outcome of an electron’s bumping, every photon’s refraction or diffraction, every radioactive decay, every subatomic event in the universe, there is a separate reality—a parallel existence—in which that specific outcome occurs. In other words, the instantaneous reality we experience is merely one pathway through an infinite tree of alternate pathways all happening at the same instant.
With ideas like this, no one can accuse physics of being boring!
COLORS, FLAVORS, AND COMPOSITES
All these quantum cogitations help you pass the time during your descent into the emptiness of an atom. But as we approach a scale of 10−15 meters, it’s time to take a closer look at some of the raw ingredients of the universe. We�
��re about to come nose-to-nose with nuclear physics.
At the core of every atom is its nucleus. The simplest of all is a single proton, a positively charged particle with a mass about 1,836 times that of an electron. To add more protons together, nature also requires the addition of neutrons—electrically neutral particles barely 0.14 percent more massive than protons. Roughly speaking, stable nuclei tend to have very similar numbers of protons and neutrons. But overall, the ratio of neutrons to protons gradually grows with the size of the nucleus. For example, the most common stable iron nucleus has 30 neutrons and 26 protons.
Atomic nuclei are tricky beasts. They’re complicated in the sense that the protons and neutrons “feel” the presence of all the other protons and neutrons through a nuclear force (the “residual strong force”). And the complete nucleus can exhibit a range of behaviors. These include “excited” energy states, and even situations where pairs of neutrons lurk outside the primary nucleus—so-called halo nuclei. Over the years, physicists’ models for nuclei have included characterizing them as liquid drops, or as full quantum objects with energy shells much like those of an atom’s electrons.
The variable number of neutrons that can bind into nuclei with a given number of protons results in variants of elements called isotopes, a remarkable array of species that are often unstable (radioactive). The elements xenon and cesium hold the record for the most isotopes. Each totes up a staggering 36 varieties. Xenon has 9 stable isotopes and 27 radioactive ones. Cesium has just 1 stable variety and 35 unstable.
The atoms of different isotopes of the same element have similar chemistry, because the way they share and exchange electrons doesn’t change much. But a combination of different isotopic masses and subtle shifts in electron energy levels does result in a number of detectable variations in behavior. Biology, for example, generally prefers lighter isotopes, for the simple reason that it takes less energy to do stuff with lighter atoms. That preference helps us detect the presence and decode the actions of living systems by looking at what isotopes exist in environmental samples. Temperature also differently influences the chemical reaction rates of different isotopes. This changes the ratio of isotopes in chemical compounds, and leaves telltale signatures that can last for hundreds of thousands, even millions or billions of years.
Earth’s nuclear garden has its origins in our earlier travels through the realm of galaxies. Because our solar system is an interstellar condensation, all the atomic nuclei of the Earth have a deep history locked inside their 10−15-meter span. In nature, nuclear fusion in stars builds heavy elements up to iron (with its stable total of 56 protons and neutrons). Beyond iron, fusion reactions are endothermic, meaning that they no longer release more energy than is required to start them. It takes violent supernovas, or the slow cooking of old and very massive stars, to form heavier nuclei. In these very high-energy environments, extra neutrons and protons can, in effect, be forced together even if the process absorbs rather than generates energy. These are places where elements like cobalt, nickel, uranium, and even plutonium are forged.
We have also devised ways to form even larger, more massive nuclei than nature typically makes. Super-large nuclei are peculiar: an island of relative stability appears at very high proton and neutron counts, related to favored energy levels within the nuclei themselves. The record holder for now is oganesson (formerly called ununoctium, from the Latin for “one-one-eight”), with a colossal 118 protons (and 176 neutrons)—but it has a half-life of a mere 890 microseconds.
But where does all this rich complexity really come from? Critically, neither protons nor neutrons are truly fundamental particles. Rather, they are composites. A proton actually consists of three entities called “quarks” (two “up” quarks and one “down” quark), bound together by the strong nuclear force (or, color force), which is mediated by the exchange of massless “gluons” over very short ranges. Quarks carry a fractional electrical charge of one-third (one unit being the charge of an electron), and can engage in all the fundamental interactions—gravity, electromagnetism, and the strong and weak forces. A neutron is also composed of three quarks, one up and two down.
An atomic nucleus of carbon
Take a deep breath—there’s more. These are just the lowest-mass quarks. There are also more-massive ones (not found inside protons and neutrons) with different “flavors” called “strange,” “charm,” “top,” and “bottom.” Furthermore, 99 percent of the mass of protons and neutrons is due to the kinetic energy (energy of motion) of the quarks and the energy of the gluons (thanks to Einstein’s relativity). The quarks themselves—if they could be isolated—would be low mass. And in a proton or neutron the three quarks are also awash in a cloud of virtual quark and anti-quark pairs known as “sea quarks.”
If none of this fills you with any sense of security, welcome to the wild, wild world of the subatomic. After your fall through the emptiness of an atom, here is a new level of richness and activity.
Pause for a moment and consider this. Five billion years ago we were cosmic filth, scattered elements drifting through space, themselves composed of electrons, quarks, and gluons. Now we are a self-sustaining life-form that has evolved awareness of both itself and the surrounding universe. We’ve used the eighty-six billion neurons in our brains, and many generations of ourselves, to develop mathematical structures that enable us to grapple with an underlying reality that has almost nothing in common with our daily experiences.
This situation was beautifully summarized by the legendary Albert Einstein, who himself was stunned enough to exclaim that the most incomprehensible thing about the universe is that it is comprehensible. One could also say that the truly incomprehensible thing is that the universe is capable of comprehending itself.
Protons and neutrons are themselves composites.
Farther into the composite proton
10
IT’S FULL OF … FIELDS
10−16, 10−17, 10−18, and … 10−35 meters
From a tenth of a femtometer to the Planck length
From approximate proton radius to nearly nothing
This is our final descent. Starting at 10−16 meters, or the approximate scale of a proton, we hop onto a trajectory that is going to take us all the way down to the very bottom of the rabbit hole.
Our ultimate destination is an astonishing nineteen orders of magnitude away. That’s a journey equivalent to our earlier passage from the scale of the entire observable universe to the parochial familiarity of the Earth-Moon system. And it’s all inside a single proton.
The innards of that proton are far more messy and inelegant than we might have expected. Although this composite object is experienced by the outside world as if it simply contains two up quarks and one down quark, that is only part of the story.
Look closer and we find that the structure of this composite particle is a stew of gluons and virtual quark and anti-quark pairs—popping in and out of existence within the allowances of the uncertainty principle. Energy and time are borrowed and balanced; stuff appears and disappears before the universal bookkeepers can get angry.
If, for an instant, you could set aside all the virtual quarks and anti-quarks that complement one another, the two up quarks and one down quark would be all that remain. These three are what the outside world senses—the asymmetry in the stew.
At these scales, and in such an alien environment, it makes sense to modify our earlier ideas about a reality composed of “particles” and “waves” (although the mathematics of waves is still a critical part of the language on these scales). Instead, we’re better served by thinking about what we’ll call “fields” and “quanta.”
The interior of a proton is a sea of virtual particles.
FROM STONE TOOLS TO FIELD THEORY
A field is a mathematical function—an algebraic contraption that generates a result that in some instances might depend on a physical position (an x, y, and z) and the time. That result might be the length of a pi
ece of elastic, the pressure of air, or the height of the ocean surface at a specific location and moment. The concept of a field is abstract enough so that it might also apply to all sorts of quantities and phenomena, not necessarily material, from esoteric mathematical groups to the scope of a politician’s ego.
A virtual mush
Critically, you can also attribute a field to many fundamental phenomena in physics. For example, electromagnetism can be encapsulated by the mathematics of a field. So too can gravity in Einstein’s formulation of general relativity. In fact, a key property of a field in physics is that it doesn’t necessarily have to concern itself with the medium in which it operates.
Fields can move or change in ways that allow them to carry waves. And those waves may only be able to exist in specific states. This behavior—if we skip a great deal of mathematical physics reasoning—brings us to the threshold of the notion of a “quantum.”
Imagine a type of field within which energy can make waves propagate with a certain amplitude, frequency, and equilibrium (resting level). Ripples on a pond are one analogy. But it just so happens that there is a discreteness to the frequency of those waves. There is a smallest possible frequency (or longest wavelength), and it’s not zero. This would be like seeing the pond ripples never occur farther apart than some maximum distance.
These are the properties of a relativistic quantum field. That smallest possible frequency actually corresponds to a quantum of the field. Like the farthest-spaced ripples on the pond, that quantum has a minimal energy, and that energy corresponds to the mass of what we’ve been calling a particle (thanks to Einstein’s famous E = mc2). Other types of fields don’t entail a mass for particles, like the field theory of quantum chromodynamics and massless gluons.