Upon that realization, the division of experience into internal and external worlds comes to seem superficial. For babies, that division is a useful discovery, and for adults, it is a convenient rule of thumb. But our best understanding suggests that there is just one world, after all. Matter, deeply understood, has ample room for minds. And so, also, it can be home to the internal worlds that minds house.
There is both majestic simplicity and strange beauty in this unified view of the world. Within it, we must consider ourselves not as unique objects (“souls”), outside of the physical world, but rather as coherent, dynamic patterns in matter. It is an unfamiliar perspective. Were it not so strongly supported by the fundamentals of science, it would seem far-fetched. But it has the virtue of truth. And once embraced, it can come to seem liberating. Albert Einstein spoke to this, in a kind of credo:
A human being is part of a whole, called the Universe, a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest, a kind of optical delusion of his consciousness. This delusion is a kind of prison for us.
* * *
• • •
I have been at pains to be clear that science teaches us what is, not what ought to be. Science can help us attain our goals, once they are chosen, but it does not choose our goals for us.
Still, in this last section, I’d like to make a connection between the unified view of the world our heroine has achieved and a moral attitude. The connection will not be a scientific proof. What recommends it is its harmony.
Notoriously, views of morality have changed over time. (Here I am looking backward, from the perspective of American culture in the early twenty-first century.) Based on experience and consensus, people have gradually abandoned old views and adopted new ones. Thus, it is fair to say that, judged by experience and consensus, the new views are improvements on the old ones. Slavery was taken for granted by many in the ancient world, but now it is almost universally condemned, as are racism, sexism, nationalistic aggression, and cruelty to animals. A common theme in all these developments is a widening circle of empathy. With progress, we’ve come to consider people and creatures as having intrinsic value and being worthy of profound respect, just like ourselves. When we see ourselves as patterns in matter, it is natural to draw our circle of kinship very wide, indeed.
Here is the continuation of Einstein’s credo:
[This delusion is a kind of prison for us], restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circles of compassion to embrace all living creatures and the whole of nature in its beauty.
Those tasks of liberation and empathy are not separated from understanding the fundamentals of science. Indeed, understanding helps us to achieve them. The universe is a strange place, and we’re all in it together.
Acknowledgments
I have been blessed throughout my life with wonderfully supportive parents, family, teachers, and friends too numerous to mention individually. It seems appropriate, though, to especially acknowledge my debt to the public school system of New York City.
Alfred Shapere, Wu Biao, Thomas Houlon, and Patty Barnes read this book in draft form and gave valuable feedback. I worked closely with Christopher Richards and Elizabeth Furlong as editors, and got help from many others at Penguin Press. John Brockman, Katinka Matson, and Max Brockman encouraged me in this project and helped me to see it through.
Appendix
In this appendix, I’ve gathered together brief discussions of some informative material that supplements the main text but that seemed either tangential to the discussion or too technical for the spirit of this book.
MASS AS A PROPERTY
Mass plays a role in two aspects of a particle’s behavior, governing both its inertia and its gravity. The inertia of a body measures its resistance to changes in its motion. Thus, a body that has large inertia will tend to keep moving at its present velocity unless it is subjected to large forces. The gravity of a particle is a universal attraction it exerts on other particles. The larger the mass of a particle, the larger its gravity. Each kind of elementary particle has a definite value for its mass. The values for different particles are generally different. They don’t appear to fit into any simple pattern. Many physicists have tried to explain the observed values of elementary particle masses, but nobody has succeeded.*
Some of the most important particles, including photons, gluons, and gravitons, have zero mass. This does not mean that they have no inertia, or that they exert no gravity. In fact, they do. Let me explain that paradox, which in my experience often troubles thoughtful learners.
Mass contributes to inertia and gravity, but it is not the only factor. In particular, a moving particle has more inertia, and exerts more gravity, than a particle at rest. Indeed, the theory of relativity teaches us that it is energy, not mass, that controls inertia and gravity. For bodies at rest, energy and mass are proportional, according to Einstein’s famous formula E = mc2, so in that case we can express inertia and gravity using either one, interchangeably. When bodies move slowly, relative to the speed of light, E = mc2 remains true to a good approximation. In that case, we don’t make a big mistake if we say that inertia and gravity are proportional to mass.
For bodies whose speed is close to the speed of light, however, E = mc2 is way off. It’s not that Einstein blundered, but that a more general and sophisticated version of the formula, also devised by Einstein, should be used. The more general formula shows that photons carry energy, and thus that they have inertia and exert gravity, despite having zero mass.
CHARGE AS A PROPERTY
A particle’s electric charge governs the strength with which it participates in the electromagnetic force. We’ve explored the nature of that force in the main text. Here we focus on electric charge itself, as a property of elementary particles.
Two facts about electric charge make it especially easy and pleasant to work with. One is that it is additive—which is to say that you can calculate the total electric charge of a collection of objects simply by adding up the electric charges of its component parts. The second is that it is conserved. This means that the total electric charge in an isolated region of space will stay the same no matter what happens within that region. The charge can change if you bring things in or take them out, but not if you rearrange them or bash them into one another.
Quantities that are additive and conserved embody the intuitive notion of “substance.” They add up and don’t get lost. You can literally count on them.
The electric charges of elementary particles follow a much simpler and more regular pattern than do their masses. Many elementary particles have zero electric charge, and all the nonzero charges are whole-number multiples of a common unit.* Some are positive, and some are negative.
A body’s electric charge, as I mentioned, governs the strength of its response to electric and magnetic fields. There are two other kinds of charge, analogous in many ways to electric charge, that play a similar role in the other fundamental interactions. They are called color charge and weak charge.
A body’s color charge governs the strength of its response to gluon fields. I like to say that color charge is like electric charge, but on steroids. The unit of color charge, which governs the strength of the strong force, is bigger than the unit of electric charge (that is, the charge of the electron). This is what makes the strong force strong. Not only that, but there are three different kinds of color charge, and eight different kinds of gluons that respond to them, as opposed to one kind of electric charge and one photon.
Altogether, the system of equations that govern the strong force, known as quantum chromodynamics (QCD), is a larger, more symmetrical version of Maxwell’s equations, which govern quantum electrodynamics (QED), the modern theory of electromagnetism. QCD is QED on steroids.
Weak charge comes in two kinds, and their unit is slightly larger than the unit of electric charge. The physical significance of weak charge becomes clear only within the context of ideas around the Higgs condensate, as featured in chapter 8.
PARTICLES OF CHANGE
What I’ve called the particles of change are of two sorts. W and Z bosons, and the Higgs boson, are about a hundred times heavier than protons. They are also highly unstable. These two facts—their heaviness and their instability—imply that they are both difficult to produce and transient. Their production and detection was a major achievement of work at high-energy accelerators in recent decades. Neutrinos are very light and they are basically stable, but they interact very feebly with ordinary matter (that is, matter made from the particles of construction). Here is a table, parallel to the similar one for particles of construction in the main text:
mass
electric charge
color charge
spin
neutrinos (3 kinds)
< .00001
0
no
½
W
157,000
1
no
1
Z
178,000
0
no
1
Higgs particle
245,000
0
no
0
Though they are not significant ingredients of ordinary matter, these particles play a crucial role in the natural world. They are involved in processes of transformation: the so-called weak interaction, or weak force. In the natural world, energy released in some of these weak force processes drives plate tectonics and gives stars their power. It also makes nuclear reactors and nuclear weapons possible.
There are three kinds of neutrinos, distinguished by different masses and subtly different interactions. They are all extremely light. As indicated in the table, their masses are a tiny fraction of the electron’s, but in at least two cases (and probably all three) it is not zero. Since they have zero electric charge and no color charge, neutrinos interact feebly with ordinary matter. This makes them difficult to study. When Wolfgang Pauli proposed, for theoretical reasons, the existence of neutrinos, he didn’t write a regular journal article about it. Instead, he sent a jocular letter to a conference of nuclear physicists that included this self-reproach: “I have done something very bad today by proposing a particle that cannot be detected; it is something no theorist should ever do.”
But experimenters rose to Pauli’s backhanded challenge by building and instrumenting gigantic detectors. Today, neutrino physics is a thriving experimental activity. It gives us, among other things, clear looks into the Sun’s core and into the violent transformations that power supernova explosions.
Finally, the Higgs particle is described at length in chapter 8, where it is a featured player.
BONUS PARTICLES
Now we come to a group of elementary particles nobody really knows what to make of. The bonus particles are all unstable. They were discovered among the debris of high-energy collisions, either in cosmic rays (early in the twentieth century) or at particle accelerators (more recently). When the first of them, the muon, was discovered in 1936, the renowned physicist I. I. Rabi captured the community’s bewilderment in a quip that’s become legendary: “Who ordered that?”
The masses of these bonus particles span a wide range and form no obvious pattern, as you can see from the following table.
mass
electric charge
color charge
spin
c quark
2,495
⅔
yes
½
t quark
339,000
⅔
yes
½
s quark
180
−⅓
yes
½
b quark
8,180
−⅓
yes
½
muon
207
−1
no
½
tauon
3,478
−1
no
½
These particles form three groups. Looking at their properties, you’ll see that the c and t quarks are heavier, unstable versions of the u quark, while the s and b quarks are heavier, unstable versions of the d quark, and the muon and tauon are heavier, unstable versions of the electron.
Our final “elementary particle” is a work in progress. Astronomers have observed, in many situations, more gravity than they can account for. It is not a small discrepancy: To get the observed gravity, we need about six times more mass than ordinary matter provides. This is the so-called dark matter problem, as described in chapter 9.
An elementary particle with the right properties could solve the dark matter problem, by providing a source for the otherwise mysterious gravity. The observed facts are broadly consistent with that explanation, but they don’t provide enough information to pin down crucial properties of the particle, such as its mass and spin.
mass
electric charge
color charge
spin
dark matter
unknown
0
no
unknown
FOR MORE INFORMATION: A GO-TO CATHEDRAL
The website of the Particle Data Group is http://pdg.lbl.gov. It chronicles and documents the empirical evidence for our fundamental understanding of cosmology and of matter and its interactions in full technical detail. It is a scientific cathedral, dutifully erected by a human community spanning several generations and all of Earth’s continents, in tribute to the glory of physical reality.
QCD LAID BARE: JETS
The strong force among quarks and gluons becomes feeble not only for small separations in time and distance, but also for large changes in energy and momentum. These behaviors are two facets of asymptotic freedom. Using the equations of quantum mechanics, either one can be derived from the other.
The rarity of large changes in energy and momentum leads us to a striking phenomenon, which has emerged as a dominant feature of ultra-high-energy interactions. This is the phenomenon of jets. Jets lay bare the essence of QCD. They exhibit quarks, gluons, and their basic interactions in an amazingly direct, tangible form.
Let’s consider what happens when a quark within a proton is suddenly jerked by an external force. The external force might come from a bombarding elec
tron, for example. The quark, ripped from its normal environment, starts with a lot of energy and momentum, and leaves the proton. An isolated quark is an untenable situation, however. Its uncompensated color charge interferes with the equilibrium of the color gluon fields, and the quark thereby radiates gluons, shedding energy and momentum. Those secondary gluons will also radiate, either into other gluons or into quarks and antiquarks. In this way, the initial jerk leaves a trail of quarks, antiquarks, and gluons, which then congeal into protons, neutrons, and other hadrons. As always, the quarks, antiquarks, and gluons do not materialize as individual particles, but only within associations (hadrons).
This might sound like complicated business, and it is. But asymptotic freedom gives structure to the mess. Since radiation that involves large transfers of energy and momentum is rare— that’s what asymptotic freedom says—all the particles in the cascade tend to be moving in the same direction. In the end, we observe many particle tracks emerging within a narrow cone. We say they make a jet. Since energy and momentum are conserved, overall, the total energy and momentum of all the particles within our jet add up to the energy and momentum of the original quark.
Jets are a wonderful gift to physicists. Because they encode the energy and momentum of the particles that initiated them, they serve as avatars for those particles. In this way, quarks and gluons become quite tangible things, even though they themselves do not exist as isolated particles. We can translate predictions for quark and gluon behavior into predictions for jets. Jets thereby allow us to check the basic laws of QCD, which are statements about quarks and gluons, precisely and in great detail. They also give us a handle on other processes, known or hypothetical, that involve quarks and gluons.
Fundamentals Page 19