The Big Picture
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An assertion like that invites a great deal of skepticism. It’s bombas-
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tic, self- congratulatory, and it doesn’t seem that hard to think of plausible
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ways in which our understanding could be dramatically incomplete.
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It sounds an awful lot like all the many times throughout history when
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some great thinker or another boasted that the quest for perfect knowledge
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was nearly complete. Every one of which turned out to be hilariously pre-
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mature.
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But we’re not claiming that all the laws of physics are known, only
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a restricted set that suffices to describe what happens at the level underly-
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ing everyday life. Even that sounds pretty presumptuous. Surely there must
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be all sorts of ways to add new particles or forces to the Core Theory that
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could be important to everyday- level physics, or for that matter new kinds
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of phenomena that fall outside the scope of quantum field theory en-
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tirely. Right?
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Not so. The situation now really is different from the way it has ever been
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at previous moments in the history of science. Not only do we have a success-
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ful theory, but we also know how far that theory can be extended before it
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ceases to be reliable. That’s just how powerful quantum field theory is.
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The logic behind our audacious claim is simple:
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1. Everything we know says that quantum field theory is the
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correct framework for describing the physics underlying ev-
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eryday life.
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2. The rules of quantum field theory imply that there can’t be
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any new particles, forces, or interactions that could be rele-
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vant to our everyday lives. We’ve found them all.
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Could quantum field theory not apply in the appropriate regime? Of
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course. As good Bayesians, we know better than to set our credences all the
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way to zero even for the most extreme options. In particular, quantum field
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theory could fail to completely describe human behavior, since physics could
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fail to describe human behavior. There could be a miraculous intervention,
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or some inherently non physical phenomenon that affects the behavior of
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physical matter. No amount of scientific progress will ever rule that out
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entirely. What we can do is show that physics by itself is fully up to the task
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of accounting for what we see.
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Einstein’s special relativity (as opposed to general relativity) is the theory 02
that melds space and time together and posits the speed of light as an abso-
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lute limit on the universe. Let’s say you want to invent a theory that simul-
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taneously embraces these three ideas:
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1. Quantum mechanics
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2. Special relativity
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3. Sufficiently separated regions of space behave independently
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from one another
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Nobel laureate Steven Weinberg has argued that every theory that
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fits these requirements will look like a quantum field theory at (relatively)
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long distances and low energies—say, anything bigger than a proton. No
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matter what happens at the ultimate, most fundamental and comprehen-
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sive level of nature, in the regime that humans can probe, the world will be
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well described by quantum field theory.
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If we are interested in describing the everyday low- energy world around
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us, therefore, and we want to stick purely to physics, we should work in the
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framework of quantum field theory.
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Let’s accept the idea that quantum field theory works in the everyday re-
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gime, and ask why there couldn’t be undiscovered particles that are relevant
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to the everyday world.
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First, we need to establish that there can’t be real, tangible particles
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buzzing around and bumping into us, somehow affecting the behavior of
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the particles we know about. Then we’ll have to assure ourselves that there
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aren’t any virtual particles or new interactions that could likewise affect the 29
particles we see. In quantum field theory, virtual particles are ones that
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quickly flick in and out of existence as quantum fluctuations, affecting
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what regular particles do without ever being observed themselves. We’ll
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look at this second issue in the next chapter, and for the moment focus on
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the possibility of real particles.
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The reason why we know there are no new fields or particles that play an
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important role in the physics underlying our everyday lives is a crucial
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property of quantum field theory known as crossing symmetry. This amaz-
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ing feature helps us be sure that certain kinds of particles do not exist; oth-
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erwise we would have found them already. Crossing symmetry basically
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says that if one field can interact with another one (for example, by scatter-
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ing off of it), then the second field can create particles of the first one under 05
the right conditions. It can be thought of as the quantum- field- theory ana-
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logue of the principle that every action implies a reaction.
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Consider a new particle X that you might suspect leads to subtle but
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important physical effects in the everyday world, whether it’s the ability to
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bend spoons with your mind or consciousness itself. That means that the X
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particle must interact with ordinary particles like quarks and electrons, ei-
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ther directly or indirectly. If it didn’t, there would be no way for it to have
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any effect on the world we directly see.
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Interactions between particles in quantum field theory can be visualized
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by the lovely mechanism of Feynman diagrams. Think of an X particle
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bouncing off of an electron by the exchange of some other new particle, Y.
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From left to right in the diagram, an X and an electron came in, exchanged
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a Y particle, then went off on their own ways.
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X
X
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Y
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electron
electron
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time
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The diagram isn’t just a picture of what can happen; it’s associated with
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a number, which tells us how strong the interaction is— in this case, how
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likely an X is to scatter off an electron. Crossing symmetry says that for
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every such process, there is another process of the same strength, obtained
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by rotating the diagram by ninety degrees, and switching any lines that
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changed directions from particle to antiparticles. One result of crossing
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symmetry is shown in the next figure.
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electron
X
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Y
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positron
time
anti- X
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A diagram representing the annihilation of an electron and a positron (anti-
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particle of an electron) into a Y particle, which then decays into an X and an 11
anti- X. This diagram is related to the previous one by crossing symmetry.
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In field theory, every particle has an antiparticle with the opposite elec-
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tric charge. The antiparticle of an electron is a particle called the positron,
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which is positively charged. Crossing symmetry says that the first process,
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scattering of an X off an electron, implies the existence of a related process 17
in which an electron and positron annihilate to create one of our X parti-
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cles as well as its antiparticle.
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Here is the payoff. We have smashed electrons and positrons together,
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often and with great care. From 1989 to 2000, a particle accelerator called
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the Large Electron- Positron Collider (predecessor of today’s Large Hadron
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Collider) operated underground outside Geneva. Within its experiments,
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electrons and positrons collided at enormous energies, and physicists kept
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extremely careful track of everything that came out. They were hoping with
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all their hearts to find new particles; discovering new particles, especially
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unexpected ones, is what keeps particle physics exciting. But they didn’t see
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any. Just the known particles of the Core Theory, produced in great numbers.
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The same has been done for protons smashing into antiprotons, and various
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other combinations. The verdict is unambiguous: we’ve found all of the
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particles that our best current technology enables us to find. Crossing sym-
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metry assures us that, if there were any particles lurking around us that
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interact with ordinary matter strongly enough to make a difference to the
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behavior of everyday stuff, those particles should have easily been produced
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in experiments. But there’s nothing there.
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There are probably more particles yet to be found. They just won’t be
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relevant to our everyday world. The fact that we haven’t yet found such
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particles tells us a great deal about what properties they must have; that’s
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the power of quantum field theory. Any particle that we haven’t yet de-
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tected must have one of the following features:
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1. It could be so very weakly interacting with ordinary matter
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that it is almost never produced; or—
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2. It could be extremely massive, so that it takes collisions at
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energies even higher than what our best accelerators can
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achieve in order to make it; or—
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3. It could be extremely short- lived, so that it gets made but
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then almost immediately decays away into other particles.
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If any particle we haven’t yet found lasted long enough and interacted
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with ordinary matter with sufficient strength that it could possibly affect
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the physics of everyday goings-on, we would have produced it in experi-
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ments by now.
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One as- yet- undiscovered particle we believe exists is dark matter.
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Astronomers, studying the motions of stars and galaxies as well as the large-
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scale structure of the universe, have become convinced that most matter is
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“dark”— some kind of new particle that is not part of the Core Theory. The
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dark- matter particle must be quite long- lived, or it would have decayed away
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long ago. But it cannot interact strongly with ordinary matter, or it would
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have already been found in one of the many dark- matter detection experi-
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ments that physicists are currently running. Whatever the dark matter is,
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it certainly plays no role in determining the weather here on Earth, or any-
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thing having to do with biology, consciousness, or human life.
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There is an apparent loophole in this analysis. There is a particle that we think
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exists but have never directly detected: the graviton. It is light and stable
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enough to be produced, but gravity is such a weak force that any gravitons we
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might make in a particle accelerator will be swamped by the huge number of
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other particles produced. And yet, gravity does affect our everyday lives.
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The basic reason why gravity matters to us is that it is a long- range force
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that accumulates— the more stuff you have causing the gravity, the stronger
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its influence is. (That’s not necessarily true for electromagnetism, for ex-
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ample, since positive and negative charges can cancel out; gravity always just
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adds up.) So while we have no hope of making or detecting an individual
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graviton by smashing two particles together, the combined gravitational
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effect of the whole Earth creates a noticeable amount of gravitational force.
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Is it possible that some other force takes advantage of this loophole— it
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would be weak if we look at just a few particles, but could accumulate if we
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had a lot of matter working together? Absolutely— and physicists have been
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looking for such a “fifth force” for many years now. They haven’t found one.
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The search for new forces is greatly abetted by the fact that ordinary
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objects are made only of three kinds of particles: protons, neutrons, and
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electrons. Another feature of quantum field theory is that you can’t turn
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the forces from individual particles on and off; the associated fields are al-
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ways there. You can create macroscopic forces by arranging positive and
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negative charges in the right way, as in an electromagnet, but particle by
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particle the fields are always present. So we just have to look for forces
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between those three kinds of particles. Physicists have done precisely that:
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constructing impeccably precise experiments that bring objects of different
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compositions close together and then apart again, searching for any hint of
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an influence outside the known forces of nature.
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The results, as of 2015, are shown schematically in the figure. Any pos-
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sible force between two given kinds of particles is parameterized by two
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numbers: how strong it is, and the distance over which it reaches. (Gravity
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and electromagnetism are “ long- range” forces, stretching essentially infi-
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nitely far; the strong and weak nuclear forces have very short ranges, smaller
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than individual atoms.) It’s easiest to measure forces that are strong, and
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that reach over long distances. Those are the possible forces that we’ve al-
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ready ruled out.
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The result is that, if a new force stretches for more than a tenth of a
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centimeter— which it would have to, if you wanted to use it to bend spoons
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or reach from Saturn to the time and place of your birth— it would have to