The Big Picture
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be substantially weaker than the force of gravity. That doesn’t sound so
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weak, but keep in mind that gravity is extraordinarily feeble; every time you
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jump in the air, the puny electromagnetic forces in your body are overcom-
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ing the combined gravitational force of the entire Earth. To say that a force
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t h E S t u F F O F W h IC h W E A R E M A dE
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1,000,000
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100,000
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10,000
vity)
Ruled Out
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1,000
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100
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(relative to gra
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Allowed
ength
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.001
Str
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.0001
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.001
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.1
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Range of Force (centimeters)
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A rough guide to experimental constraints on new forces that could affect ordinary
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matter. To have escaped detection thus far, a new force must either be sufficiently
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weak or operate only over a very short range.
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is as weak as gravity is to say that it is about one billionth of a billionth of a
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billionth of a billionth the strength of electromagnetism. An even weaker
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force would be completely negligible in everyday circumstances.
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Here in our daily environment, the world of people and cars and houses,
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we have a complete inventory of the particles and forces and interactions
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that are strong enough to have any noticeable effect on anything. That’s a
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tremendous intellectual achievement, one of which the human race can be
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justifiably proud.
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The Effective Theory of the Everyday World
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All of this talk of particles and quantum fields can seem almost infi-
nitely far away from the human side of the big picture— the cares
and concerns of our personal and social lives. But we are made of
particles and fields that obey the ironclad laws of physics. Everything we
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want to think about human beings has to be compatible with the nature
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and behavior of the pieces of which we are made, even if those pieces don’t
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tell the whole story. Understanding what those particles and fields are and
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how they interact with one another is a crucial part of comprehending what
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it means to be human.
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The constraints provided by quantum mechanics and relativity make
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quantum field theory an extremely restrictive and unforgiving framework.
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We can use that rigidity to map out how well we’ve tested the Core Theory,
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the specific set of fields and interactions that governs our local environ-
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ment. The answer is: really well. Enough to be convinced that we know
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what the relevant particles and fields are in this regime, and any new dis-
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coveries will involve phenomena that only manifest themselves elsewhere—
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at higher energies, shorter distances, more extreme conditions.
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But how do we know, even if we can’t directly see new particles or fields,
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that they can’t exert some subtle but important influence on the particles
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that we do see? The answer can be traced to another feature of quantum
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fields: an idea called effective field theory. In quantum field theory, the mod-35S
ifier “effective” doesn’t mean something like “does a good job fitting the
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data.” Rather, an effective theory is an emergent approximation to a deeper
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t h E E F F E C t I v E t h E OR y OF t h E E v E R y dA y WO R l d theory. A kind of approximation that is specific, reliable, and well
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controlled— all due to the power of quantum field theory.
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Given some physical system, there are some things you care about, and
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some you don’t. An effective theory is one that models only those features
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of the system that you care about. The features you don’t care about are too
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small to be noticed, or moving back and forth in ways that everything just
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averages out. An effective theory describes the macroscopic features that
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emerge out of a more comprehensive microscopic description.
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Effective theories are extremely useful in a wide variety of situations. When
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we talked about describing the air as a gas rather than as a collection of mole-
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cules, we were really using an effective theory, since the motions of the indi-
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vidual molecules didn’t concern us. Think about the Earth moving around the
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sun. The Earth contains approximately 1050 different atoms. It should be nearly
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impossible to describe how something so enormously complex moves through
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space— how could we conceivably keep track of all of those atoms? The answer
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is that we don’t have to: we have to keep track of only the single quantity we
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are interested in, the location of the Earth’s center of mass. Whenever we talk
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about the motion of big macroscopic objects, we’re almost always implicitly
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using an effective theory of their center-of-mass motion.
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The idea of an effective theory is ubiquitous, but really comes into its glory
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when we’re dealing with quantum fields. That’s because of an insight due to
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Nobel laureate Kenneth Wilson, who thought deeply about the “field” na-
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ture of quantum field theory.
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Wilson focused on a fact well-known to physicists: if you have a vi
brat-
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ing field, you can always break those vibrations up into a certain contribu-
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tion at each different wavelength. That’s what we’re doing when we pass a
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beam of light through a prism and decompose it into different colors; red
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light is a long- wavelength vibration in the electromagnetic field, blue light
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is a short- wavelength vibration, and so on for all the colors in between. In
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quantum mechanics, short- wavelength vibrations are oscillating faster, and
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therefore have more energy, than long- wavelength ones. The things we care
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about are the low- energy, long- wavelength vibrations; those are the ones
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that are easy to make and observe in our everyday lives (unless your every-
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T H E B IG PIC T U R E
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So, Wilson says, quantum field theory comes automatically equipped with
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a very natural way to create effective theories: keep track of only the long-
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wavelength/ low- energy vibrations in the fields. The short- wavelength/ high-04
energy vibrations are still there, but as far as the effective theory is concerned,
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all they do is affect how the long- wavelength vibrations behave. Effective field
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theories capture the low- energy behavior of the world, and by particle- physics
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standards, everything we see in our daily lives is happening at low energies.
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For example, we know that protons and neutrons are made out of up quarks
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and down quarks, held together by gluons. The quarks and gluons, zipping
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around at high energies inside the protons and neutrons, are short- wavelength
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field vibrations. We don’t need to know anything about them to talk about
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protons and neutrons and how they interact with each other. There is an effec-
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tive field theory of protons and neutrons that works perfectly wel , as long as we
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don’t zoom in so closely that we can see the individual quarks and gluons.
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This simple example highlights important aspects of how effective
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theories work. For one thing, notice that the actual entities we’re talking
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about— the ontology of the theory— can be completely different in the ef-
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fective theory from that of a more comprehensive microscopic theory. The
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microscopic theory has quarks; the effective theory has protons and neu-
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trons. It’s an example of emergence: the vocabulary we use to talk about
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fluids is completely different from that of molecules, even though they can
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both refer to the same physical system.
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Two features characterize how wonderfully simple and powerful effec-
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tive field theories are. First, for any one effective theory, there could be
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many different microscopic theories that give rise to it. That’s multiple re-
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alizability in the context of quantum physics. Consequently, we don’t need
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to know all the microscopic details to make confident statements about
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macroscopic behavior. Second, given any effective theory, the kinds of dy-
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namics it can have are generally extremely limited. There simply aren’t that
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many different ways that quantum fields can behave at low energies. Once
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you’ve told me what particles are in your theory, all I need to do is measure
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a few parameters like their masses and interaction strengths, and the theory
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is completely specified. It’s like the planets orbiting the sun; it doesn’t make
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a single whit of difference that Jupiter is a hot gas giant and Mars is a cold
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rocky planet; they both move on orbits such that their centers of mass are
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obeying Newton’s laws.
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t h E E F F E C t I v E t h E OR y OF t h E E v E R y dA y WO R l d This is why we’re so confident the Core Theory is basically correct in its
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domain of applicability. Even if there were something utterly different at the
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microscopic level— not a field theory at all, perhaps not even space or time as
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we understand them— the emergent effective theory would still be an ordi-
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nary field theory. The fundamental stuff of reality might be something wholly
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distinct from anything any living physicist has ever imagined; in our everyday
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world, physics will still work according to the rules of quantum field theory.
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All of which is enormously frustrating if you’re a physicist who wants to
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construct a Theory of Everything, but the flip side is that we have a really
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good handle on the Theory of Some Low- Energy Things— in particular,
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the kinds of things we encounter in our everyday lives.
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We know that the Core Theory isn’t the final answer. It doesn’t account
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for the dark matter that dominates the matter density of the universe, and
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neither does it describe black holes or what happened at the Big Bang.
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We can, therefore, imagine improving it by adding some as- yet- unknown
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“new physics,” which would be enough to account for astrophysical and
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cosmological phenomena. Then we can describe the domains of applicabil-
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ity of various theories in the kind of Venn diagrams we looked at in chapter
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12. Astrophysics needs more than the Core Theory, but our everyday experi-
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ence is well within its domain of applicability.
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Underlying Reality
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Core Theory + New Physics
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Core Theory
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Everyday
Astrophysics
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Experience
& Cosmology
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T H E B IG PIC T U R E
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Another way of conveying the same idea is to think about which phe-
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nomena depend on which other phenomena— what supervenes on what, as
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<
br /> the philosophers would say. This is shown in the next figure. Astrophysical
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phenomena depend on the Core Theory, but also on new physics. And ev-
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erything, of course, depends on the same underlying reality. But crucially,
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the emergent phenomena we see in our everyday lives do not depend on
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dark matter or other new physics. Moreover, they only depend on underly-
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ing reality through their dependence on the Core Theory particles and in-
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teractions. That’s the power of effective field theory. All sorts of microscopic
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quantum- gravitational craziness could be breaking out deep within the
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underlying reality, but none of that matters for the behavior of chairs and
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cars and central nervous systems; it’s all subsumed in the effective field
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theory of the Core Theory.
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Higher-level
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macro-phenomena
Astrophysics &
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of everyday life
Cosmology
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Core Theory
Dark matter, black holes,
(known particles & forces)
“new physics”
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Underlying reality
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Different ways of talking about the world, and how they relate to each other. Solid
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arrows indicate how one theory depends on another; for example, astrophysics de-
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pends on the Core Theory and also on dark matter and dark energy. Dashed arrows
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show dependencies that could have existed but don’t; everyday life does not depend
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on dark matter, and depends on underlying reality only through the Core Theory.
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t h E E F F E C t I v E t h E OR y OF t h E E v E R y dA y WO R l d The strength of effective field theory is what allows us to assert “This
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time is different” when we make our audacious claim that the laws of phys-
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ics underlying everyday life are completely known. When Newton and La-
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place contemplated the glory of classical mechanics, they may very well have
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considered the possibility that it would someday have to be superseded by
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more comprehensive theories.
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And eventually it was— by special relativity, general relativity, and quan-
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tum mechanics. Newtonian theory is a good approximation in a certain
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domain of applicability, but ultimately it breaks down and we need a better