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The Big Picture

Page 32

by Carroll, Sean M.

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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

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  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

 

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