Knocking on Heaven's Door (15 page)

Quantum mechanics tells us that electrons don’t occupy fixed locations in the atoms as the classical picture would assert. Instead, probability distributions tell us how likely electrons are to be found in any particular point in space, and all we know are these probabilities. We can predict the average position of an electron as a function of time, but any particular measurement is subject to the uncertainty principle.

Bear in mind that these distributions are not arbitrary. The electrons can’t have just any old energy or probability distribution. There is no good classical way to describe an electron’s orbit—it can only be described in probabilistic terms. But the probability distributions are in fact precise functions. With quantum mechanics, we can write down an equation describing the wave solution for an electron, and this tells us the probability for it to be at any given point in space.

Another property of an atom that is remarkable from the perspective of a classical Newtonian physicist is that the electrons in an atom can occupy only fixed quantized energy levels. Electron orbits depend on their energies, and those particular energy levels and the associated probabilities must be consistent with quantum mechanical rules.

The electrons’ quantized levels are essential to understanding the atom. In the early twentieth century, an important clue that the classical rules had to radically change was that classically, electrons circling a nucleus are not stable. They would radiate energy and quickly fall into the center. Not only would this be nothing like an atom, it wouldn’t permit the structure of matter that follows from stable atoms as we know them.

Niels Bohr in 1912 was faced with a challenging choice—abandon classical physics or abandon his belief in observed reality. Bohr wisely chose the former and assumed classical laws don’t apply at the small distances occupied by electrons in an atom. This was one of the key insights that led to the development of quantum physics.

Once Bohr ceded Newton’s laws, at least in this limited regime, he could postulate that electrons occupied fixed energy levels—according to a quantization condition that he proposed involving a quantity called
orbital angular momentum.
According to Bohr, his quantization rule applied on an atomic scale. The rules were different from those we use at macroscopic scales, such as for the Earth circulating around the Sun.

Technically, quantum mechanics still applies to these larger systems as well. But the effects are far too small to ever measure or notice. When you observe the orbit of the Earth or any macroscopic object for that matter, quantum mechanics can be ignored. The effects average out in all such measurements so that any prediction you make agrees with its classical counterpart. As discussed in the first chapter, for measurements on macroscopic scales, classical predictions generally remain extremely good approximations—so good that you can’t distinguish that quantum mechanics is in fact the deeper underlying structure. Classical predictions are analogous to the words and images on an extremely high-resolution computer screen. Underlying them are the many pixels that are like the quantum mechanical atomic substructure. But the images or words are all we generally need (or want) to see.

Quantum mechanics constitutes a change in paradigm that becomes apparent only at the atomic scale. Despite Bohr’s radical assumption, he didn’t have to abandon what was known before. He didn’t assume classical Newtonian physics was wrong. He simply assumed that classical laws cease to apply for electrons in an atom. Macroscopic matter, which consists of so many atoms that quantum effects can’t be isolated, obeys Newton’s laws, at least at the level at which anyone could measure the success of its predictions. Newton’s laws are not wrong. We don’t abandon them in the regime in which they apply. But at the atomic scale, Newton’s laws had to fail. And they failed in an observable and spectacular fashion that led to the development of the new rules of quantum mechanics.

NUCLEAR PHYSICS

As we continue our journey down in scale into the atomic nucleus itself, we will continue to see the emergence of different descriptions, different basic components, and even different physical laws. But the basic quantum mechanical paradigm will remain intact.

Inside the atom, we’ll now explore inner structure with size of about 10 femtometers, the nuclear size of a hundred thousandth of a nanometer. So far as we have measured to date, electrons are fundamental—that is, there don’t seem to be any smaller components of electrons. The nucleus, on the other hand, is not a fundamental object. It is composed of smaller elements, known as nucleons. Nucleons are either protons or neutrons. Protons have positive electric charge and neutrons are neutral, with neither a positive nor negative charge.

One way to understand the nature of protons and neutrons is to recognize that they are not fundamental either. George Gamow, the great nuclear physicist and science popularizer, was so excited about the discovery of protons and neutrons that he thought it was the final “other frontier”: he didn’t think any further substructure existed. In his words:

“Instead of a rather large number of ‘indivisible’ atoms of classical physics, we are left with only three essentially different entities; protons, electrons, and neutrons… Thus it seems we have actually hit the bottom in our search for the basic elements of which matter is formed.”
²⁸

That was a little shortsighted. More precisely, it was not shortsighted enough. There does exist further substructure—more elementary components to the proton and neutron—but the more fundamental elements were challenging to find. One had to be able to study length scales smaller than the size of the proton and neutron, which required higher energies or smaller probes than existed when Gamow made his inaccurate prediction.

If we were to now enter inside the nucleus to see nucleons and protons with size about a fermi—about ten times smaller than the nucleus itself—we would encounter objects Murray Gell-Mann and George Zweig suspected existed inside nucleons. Gell-Mann creatively named these units of substructure
quarks,
in his telling inspired by a line from James Joyce’s
Finnegans Wake
(“three quarks for Muster Mark”). The up and down quarks inside a nucleon are the more fundamental objects of smaller size (the two
up
and one
down
quarks inside are shown in Figure 16) that a force called the
strong nuclear force
binds together to form protons and neutrons. Despite its generic name, the strong force is a specific force of nature—one that complements the other known forces of electromagnetism, gravity, and the weak nuclear force that we’ll discuss later.

The strong force is called the strong force because it is strong—that’s an actual quote from a fellow physicist. Even though it sounds pretty silly, it’s in fact true. That’s why quarks are always found bound together into objects such as protons and neutrons for which the direct influence of the strong nuclear force cancels. The force is so strong that in the absence of other influences the strongly interacting components won’t ever be found far apart.

[
FIGURE 16
]
The charge of a proton is carried by three valence quarks—two up quarks and a down quark.

One can never isolate a single quark. It’s as if all quarks carry a sort of glue that becomes sticky at long distances (the particles that communicate the strong force are for this reason known as
gluons).
You might think of an elastic band whose restoring force comes into play only when you stretch it. Inside a proton or neutron, quarks are free to move around. But trying to remove one of the quarks any significant distance away would require additional energy.

Though this description is entirely correct and fair, one should be careful in its interpretation. One can’t help but think of quarks as all bound together in a sack with some tangible barrier from which they cannot escape. In fact, one model of nuclear systems essentially treats the protons and neutrons in precisely this way. But that model, unlike others we will later encounter, is not a hypothesis for what is really going on. Its purpose was solely to make calculations in a range of distances and energies where forces were so strong our familiar methods don’t apply.

Protons and neutrons are not sausages. There is no synthetic caing that surrounds the quarks in a proton. Protons are stable collections of three quarks held together through the strong force. Because of the strong interactions, three light quarks concertedly act as one single object, either a neutron or proton.

Another significant consequence of the strong force—and quantum mechanics—is the ready creation of additional
virtual
particles inside a proton or neutron—particles permitted by quantum mechanics that don’t last forever but at any given time contribute energy. The mass—and hence, a la Einstein’s
E = mc
²
,
the energy—in a proton or neutron is not carried just by the quarks themselves but also by the bonds that tie them together. The strong force is like the elastic band tying together two balls that itself carries energy. “Plucking” the stored energy allows new particles to be created.

So long as the net charge of the new particles is zero, this particle creation from the energy in the proton doesn’t violate any known physical laws. For example, a positively charged proton cannot suddenly change into a neutral object when virtual particles are created.

This means that every time a quark—which is a particle that carries nonzero charge—is created, an
antiquark
—which is a particle identical in mass to a quark but with opposite charge—must also be formed. In fact, quark-antiquark pairs can both be created and destroyed. For example, a quark and antiquark can produce a photon (the particle that communicates the electromagnetic force), which in turn produces another particle/antiparticle pair. (See Figure 17.) Their total charge is zero, so even with pair creation and destruction, the charge inside the proton will never change.

[
FIGURE 17
]
Sufficiently energetic quarks and antiquarks can annihilate into energy that can, in turn, create other charged particles and their antiparticles.

In addition to quarks and antiquarks, the
proton sea
(that’s the technical term)—consisting of the virtual particles that are created—contains
gluons
as well. Gluons are the particles that communicate the strong force. They are analogous to the photon that is exchanged between electrically charged particles to create electromagnetic interactions. Gluons (there are eight different ones) act in a similar manner to communicate the strong nuclear force. They are exchanged between particles that carry the charge that the strong force acts on, and their exchange binds or repels the quarks to or from each other.

However, unlike photons, which carry no electric charge and therefore don’t directly experience the electromagnetic force, gluons themselves are subject to the strong force. So whereas photons transmit forces over enormous distances—so we can turn on a TV and get a signal generated miles away—gluons, like quarks, cannot travel far before they interact. Gluons bind objects on small scales comparable in size to a proton.

If we take a course-grained view of the proton and focus just on the elements carrying the proton charge, we would say that a proton is primarily composed of three quarks. However, the proton contains a lot more than the three
valence
quarks—the two up quarks and the lone down quark—that contribute to its charge. In addition to the three quarks responsible for a proton’s charge, inside a proton is a sea of virtual particles—that is, quark/antiquark pairs and gluons. The closer we examine a proton, the more virtual quark-antiquark pairs and gluons we would find. The exact distribution depends on the energy with which we probe it. At energies with which protons are colliding together today, we find a substantial amount of their energy is carried by virtual gluons and quarks and antiquarks of different types. They are not important for determining electric charge—the sum of the charges of all this virtual stuff is zero—but as we will see later on, they are important for predictions about proton collisions when we need to know exactly what is inside a proton and what carries its energy. (See Figure 18 for the more complicated structure inside a proton.)