The Big Picture
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has taught us about nature. It bequeaths to us the responsibility and op-
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portunity to make life into what we would have it be.
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Poetic naturalism offers a rich and rewarding way to apprehend the world,
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but it’s a philosophy that calls for a bit of fortitude, a willingness to discard
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what isn’t working. In the enthusiasm of my first public acknowledgment
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of my atheism, I tended to embrace the idea that science would eventually
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solve all of our problems, including answering questions about why we are
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here and how we should behave. The more I thought about it, the less san-
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guine I became about such a possibility; science describes the world, but
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what we’re going to do with that knowledge is a different matter.
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Facing up to reality can make us feel the need for some existential ther-
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apy. We are floating in a purposeless cosmos, confronting the inevitabil-
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ity of death, wondering what any of it means. But we’re only adrift if we
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choose to be. Humanity is graduating into adulthood, leaving behind
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the comfortable protocols of its childhood upbringing and being forced to
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fend for itself. It’s intimidating and wearying, but the victories are all the
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more sweet.
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Albert Camus, the French existentialist novelist and philosopher, out-
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lined some of his approach to life in his essay “The Myth of Sisyphus.” The
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title refers to the Greek legend that describes a man who was cursed by Zeus
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to spend eternity pushing a rock up a mountain, only to have it fall back
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down, where he would have to start pushing it up again. The metaphor for
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life in a universe without purpose should be clear. But Camus turns the
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obvious lesson of the myth on its head, making Sisyphus into a hero who
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creates his own purpose.
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I leave Sisyphus at the foot of the mountain! One always
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finds one’s burden again. But Sisyphus teaches the higher fidel-
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ity that negates the gods and raises rocks. He too concludes that
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all is well. This universe henceforth without a master seems to
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him neither sterile nor futile. Each atom of that stone, each
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mineral flake of that night- filled mountain, in itself forms a
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world. The struggle itself toward the heights is enough to fill a
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man’s heart. One must imagine Sisyphus happy.
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I’m not sure whether Sisyphus was actually happy, but I suspect he
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found meaning in his task, and perhaps took pride in pushing rocks like
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nobody else. We work with what life gives us.
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Earlier in his essay, Camus described the universe as “unintelligible.” It’s
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actually the opposite of that— the fact that the universe is so gloriously
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knowable is perhaps its most remarkable feature. It’s one of the aspects of
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reality that helps make our Sisyphean struggles so ultimately rewarding.
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•
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While writing this final chapter of the book, thinking about my late grand-
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mother and going to church and having pancakes, I became hungry. I
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needed to refill my body’s supply of free energy. There were no pancakes
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available, and certainly no strawberry syrup, so I got up and made one of
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my grandmother’s favorite breakfast recipes, a “bird’s nest.” A simpler dish
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could not be imagined: use a shot glass (there was always one nearby in my
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grandparents’ house) to carve out a circular hole from the center of a piece
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of bread, drop it in a frying pan, and follow with an egg, the yolk nestled
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snugly into the hole. Salt, pepper, butter, that’s it.
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Delicious. I love fine dining, and this was not that, but it hit the spot. A
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fond memory, simple tastes and smells fulfilling a basic need, the uncom-
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plicated pleasure of cooking for yourself. This is life— a tiny sliver of the 05
tangible, real experience of the world.
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I miss my grandmother, but I don’t need to imagine that she’s still alive
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somewhere. She lives on in memories, but eventually even that will pass.
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Change and passage are part of life— not just a part we reluctantly accept,
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but its very essence, enabling our hopeful anticipation of what is to come. I
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care about my remembrances of the past, hopes for the future, the state
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of the wider world, and the life I have now, with a wife I love more than all
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of the galaxies in the sky and an abiding joy in puzzling out the nature of
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reality.
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All lives are different, and some face hardships that others will never
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know. But we all share the same universe, the same laws of nature, and the
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same fundamental task of creating meaning and of mattering for ourselves
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and those around us in the brief amount of time we have in the world.
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Three billion heartbeats. The clock is ticking.
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Appendix: The Equation Underlying You and Me
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The world of our everyday experience is based on the Core Theory: a quantum field theory 14
describing the dynamics and interactions of a certain set of matter particles (fermions) and 15
force particles (bosons), including both the standard model of particle physics and Einstein
’s general theory of relativity (in the weak- gravity regime). Though we don’t need it 16
for the rest of the book, in this appendix we’re going to very briefly dig into some of the 17
specifics of those fields and interactions in the Core Theory. The discussion will be tele-18
graphically concise, full of buzzwords and jargon and tricky ideas. You can think of this 19
either as extra credit that you are welcome to skip, or a welcome reward for making it this far.
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The capstone of our discussion will be a single formula, the Feynman path integral
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for the Core Theory. It encapsulates all there is to know about the quantum dynamics
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of this model: starting from one configuration of fields, how probable is it that the fields 23
end up in some other configuration at a later time? If you know that, you can calculate anything you want to about the behavior of the Core Theory. It’s worth putting on a
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T-shirt.
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•
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There are two kinds of quantum fields: fermions and bosons. Fermions are the particles of 27
matter; they take up space, which helps explain the solidity of the ground beneath your 28
feet or the chair you are sitting on. Bosons are the force- carrying particles; they can pile 29
on top of one another, giving rise to macroscopic force fields like those of gravity and 30
electromagnetism. Here is the complete list, as far as the Core Theory is concerned:
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Fermions
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1. Electron, muon, tau (electric charge –1).
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2. Electron neutrino, muon neutrino, tau neutrino (neutral).
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3. Up quark, charm quark, top quark (charge + 2/ 3).
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4. Down quark, strange quark, bottom quark (charge –1/ 3).
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bosons
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5. Graviton (gravity; spacetime curvature).
6. Photon (electromagnetism).
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7. Eight gluons (strong nuclear force).
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8. W and Z bosons (weak nuclear force).
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9. Higgs boson.
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In quantum field theory, it doesn’t take that much information to specify the proper-
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ties of a particular field or, equivalently, the particle with which it is associated. Each 08
particle has a mass, and it also has a “spin.” We can think of the particles almost like little 09
spinning tops, except elementary particles (which are really vibrations of quantum fields) don’t actually have any size; their spin is an intrinsic property, not the revolution of their 10
bodies around an axis. Every particle associated with a particular field has exactly the same 11
spin; all electrons are “spin –1/ 2,” while all gravitons are “spin –2,” for example.
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How particles interact with one another is governed by their charges. When used with-13
out modification, the word “charge” is short for “electric charge,” but the other forces—
gravity and the nuclear forces— also have charges associated with them. The charge of a 14
particle tells us how it interacts with the field that carries the associated force. So elec-15
trons, which have electric charge –1, interact directly with photons, which carry the elec-16
tromagnetic force; neutrinos, which have electric charge 0, don’t interact directly with 17
photons at all. (They can interact indirectly, since neutrinos interact with electrons, which then interact with photons.) Photons are neutral themselves, so they don’t interact di-18
rectly with one another.
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The gravitational “charge” is just the energy of the particle, which is equal to the
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mass times the speed of light squared when the particle is at rest. Every single particle 21
has a gravitational charge; Einstein taught us that gravity is universal. All of the fermions we know about have a weak nuclear charge, so they interact with W and Z bosons.
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Half of the fermions we know about interact with the gluons that carry the strong force, 23
and we call those fermions quarks; the other half do not, and we call them leptons. There 24
are up-type quarks, with (electric) charge + 2/ 3, and down- type quarks, with charge –1/ 3.
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The strong force is so strong that quarks and gluons are confined inside particles like protons and neutrons, so we never see them directly. The charged leptons are the electron 26
and its heavier cousins, the muon and the tau, and there are three neutrinos associated 27
with them, imaginatively labeled the electron neutrino, the muon neutrino, and the tau 28
neutrino.
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Then there is the Higgs field and its associated particle, the Higgs boson. Proposed in the 1960s, the Higgs boson was finally discovered at the Large Hadron Collider in Geneva 30
in 2012. Although it’s a boson, we don’t usually talk about a “force” associated with the 31
Higgs field— we could, but the Higgs is so massive that the corresponding force is ex-32
tremely weak and short- range. What makes the Higgs special is that its field has a nonzero value even in empty space. All of the particles of which you are made are constantly swim-33
ming in a Higgs bath, and that affects their properties. Most important, it gives mass to 34
the quarks and charged leptons, as well as to the W and Z bosons. Discovering it put the 35S
final touches on the Core Theory.
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I know what you’re thinking. “Sure, all of these fields are colorful and enchanting. But what we really want is an equation.”
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Here you go.
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quantum mechanics
spacetime gravity
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√
m 2
W =
[ Dg][ DA][ Dψ][ DΦ] exp i
d 4 x −g
p
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2 R
k< Λ
λ
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1
10
−
¯
Φ
+ h.c.
4 F a
Φ
Φ
µν F aµν + i ¯
ψiγµDµψi + ψiLVijΦ ψjR
− |DµΦ | 2 − V ( )
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other forces
matter
Higgs
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The essence of the Core Theory— the laws of physics underlying everyday life—expressed 15
in a single equation. This equation is the quantum amplitude for undergoing a transition from one specified field configuration to another, expressed as a sum over all the paths that 16
could possibly connect them.
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To be compatible with our earlier discussion of how quantum mechanics works, what
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I really should give you is the Schrödinger equation for the Core Theory. That’s what tells 19
you how the wave function of a
given quantum system evolves from one moment of time
to the next. But there are many ways of encapsulating that information, and the one
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shown here is an especially compact and elegant one. (Though it might not appear that
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way to the naked eye.)
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This is what’s called the path- integral formulation of quantum mechanics, pioneered by Richard Feynman. The wave function describes a superposition of every possible configu-23
ration of the system you are working with. For the Core Theory, a configuration is a par-24
ticular value for every field, at every point in space. Feynman’s version of quantum
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evolution (which is equivalent to Schrödinger’s, just written differently) tells you how 26
likely it is that the system will end up in a particular configuration within the wave function, given that it started at some previous time in a different configuration within an 27
earlier wave function. Or you can start with a later wave function and work backward;
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Feynman’s equation, like Schrödinger’s, is perfectly reversible in the Laplacian sense. It’s 29
only when we start observing things that quantum mechanics violates reversibility.
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That’s what the quantity W is; it’s what we call the “amplitude” to go from one field configuration to another. It’s given by a Feynman path integral over all of the ways the 31
fields could evolve in between. An integral, as you may remember if you ever took calculus, 32
is a way of summing up an infinite number of infinitely small things, such as when we add 33
up infinitesimal regions to calculate the area under a curve. Here, we’re summing up con-34
tributions from each possible thing the fields can do in between the starting and ending points, which we simply call a “path” the field configuration can take.
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So what exactly is it that we are integrating, or summing up? For every possible path a 03
system can take, there’s a number we calculate called the action, traditionally written as S.
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If the system is jumping willy- nilly all over the place, its action will be very large; if it moves more smoothly, the action will be relatively small. The concept of the action along 05
a path plays an important role even in classical mechanics; among all of the possible paths 06
we can imagine the system taking, the one it actually does take (that is, the one that obeys 07
the classical equations of motion) will be the one that has the least action. Every classical 08