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Physics + MathPhysics & Math

Ten Lessons from the Standard Model

Nobel Prize-winning physicist Frank Wilczek reflects on what the successes of the standard model of physics teach us.

ByFrank WilczekThe Nature of RealityThe Nature of Reality

The most recent Nobel Prize in physics,

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awarded to Francois Englert and Peter Higgs for the prediction of the Higgs boson, marks the apotheosis of the Standard Model in two ways. First, the Higgs particle is a milestone in itself: It is the last ingredient required to complete the Standard Model. But second, and more profoundly, the discovery process bore witness to the extraordinary power of the Standard Model. Higgs particles are rare and fleeting visitors to our world. Even at the Large Hadron Collider (LHC), where the discovery was made, they are produced in less than a billionth of all collisions. When they are produced, they quickly decay, leaving behind just a few extra tracks among hundreds of others from more conventional sources. It is only because physicists can so reliably predict such “backgrounds,” as well as the rate of Higgs particle production and the modes of its decay, that the discovery experiments could be planned and their results interpreted.

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After this crowning triumph it seems appropriate to reflect on the big picture. What does the Standard Model teach us? What does it mean?

To answer that, I’ve adopted the List of Ten format pioneered by God and copied by Letterman and the “For Dummies” series. Here follow ten big lessons from the Standard Model organized into four categories: epistemology, natural philosophy, emergent simplicity, and unfinished business.

Symmetry abounds in the Standard Model. Credit: Peeter Viisimaa/iStock

1. Reductionism Works : The premise of reductionism is that you can understand how things work by breaking them down into constituent parts with simple properties and interactions and then building back up. As a strategy for understanding the physical world, it’s been brilliantly successful! Matter as we know it, in all its richness, can be represented as vast numbers of identical copies of a few ingredients whose properties and interactions we can describe quite fully and accurately. It appears that we have achieved, following the reductionist program, a foundation in fundamental physical law for all applications of physics to chemistry, biology, materials science, engineering in general, astrophysics, and major aspects of cosmology.

2. The Surface Appearance of the Physical World is Quite Different from its Deep Structure : In general, quantum theory presents a picture of the world that appears quite different from the everyday world of experience. There is still considerable work to be done, I think, to show convincingly how observed macroscopic “classical” behavior follows from the underlying quantum equations, with their indeterminacy and discreteness, even at the level of mundane low-energy physics. The specifics of the Standard Model make this strangeness even stranger. We find that the familiar, effective building blocks of low-energy physics, i.e. protons, neutrons, electrons, and photons, are themselves complicated objects when expressed in terms of more truly fundamental entities. Protons and neutrons are complex bound states of quarks, antiquarks, and gluons. Quarks, antiquarks, and gluons obey simple mathematical equations, while protons and neutrons don’t—but protons and neutrons are what we get to see. Even “structureless” electrons arise, in the basic equations, from mixtures of massless particles. It is those more basic entities, not the emergent electron, whose properties are ideally simple.

Natural Philosophy

3. Relativity (Poincare Symmetry), Quantum Mechanics, and Local (Gauge) Symmetry Rule : It might have been the case that the basic recipe for nature would be like the basic recipe for a human being (i.e., the human genome) or the software that runs a complex program like Word—a long list of instructions, containing many logically independent modules and accidental details. That is not what we find. Instead, there are three powerful principles that can serve as axioms, allowing us to formulate the Standard Model deductively. Two of these guiding principles, special relativity and quantum mechanics, date from the early twentieth century. The third, gauge symmetry, only came to full fruition in the 1970s, though its roots go back decades further. Gauge symmetry is (even) more abstract and mathematical than relativity and quantum mechanics, and perhaps for that reason it is less well known to the general public. I will not be able to remedy that situation here, though I’ll be attempting it in a forthcoming book (“The Beautiful Question”). Let me just advertise, as an illustration of its power, that gauge symmetry is what allowed David Gross and me to predict the existence of gluons and their detailed properties prior to their observation.

The Standard Model is best understood not as a list of particles, but as a realization of principles. That nature’s basic operating system can be so understood, in detail, marks a profound revolution in natural philosophy.

4. The Distinction between “Matter” and “Light” is Superficial : Like light, the building-blocks of matter are essentially massless, and they can be created and destroyed. Conversely, as its wavelength shortens, “light” as we ordinarily sense it is on a continuum with the sorts of gamma rays that leave tracks at the LHC, which are manifestly particles.

5. “Empty Space” is a Substance : What we perceive to be “empty space” is actually filled with pervasive condensates and also exhibits spontaneous activity. Both the condensates, and the fluctuating activity (“virtual particles,” vacuum polarization) radically alter the qualitative properties of particles moving through space.

6. Nature Loves Transformations : Superficially, the Standard Model seems to contain dozens of independent ingredients—for instance, quarks with different colors and flavors and gluons galore. But many of these particles are related to one another by symmetry and can physically transform into one another. Thus the unwieldy account using dozens of degrees of freedom becomes the story of a much smaller number of underlying ur-substances and their transformations.

Emergent Simplicity

7. The Behavior of Matter at High Energy Simplifies and Reveals Its Deep Structure : Flows of particles we can observe at accelerators follow patterns we can calculate using fundamental equations directly. The observed flows are found to be organized into narrow jets: If we turn down the resolution and lump observed particles moving in the same direction into units, adding their energy and momenta, then those units obey the equations of quarks and gluons. In that very strong sense, they are quarks and gluons.

It is like an impressionist painting where you have to blur the resolution to see the shapes.

Because the fundamental equations themselves are much easier to work with than the complicated “solutions” we find embodied in everyday (low-energy) matter, it is profoundly correct to say that the behavior we see at the Large Hadron Collider is simpler than the behavior we study in an undergraduate chemistry laboratory.

8. The Early Universe is Open to Rational Reconstruction : At the extremely high energy density of the Big Bang, the equations for matter simplify dramatically, as we just discussed. This allows us to make serious, scientifically grounded models for what happened in the very early Universe and to draw observable conclusions from them. Moreover, by reproducing those extreme conditions on a small scale at accelerators, we can check our equation.

Unfinished Business

9. We’ve Got Vexing Family Problems : When the muon—a more massive, unstable version of the electron—was discovered in 1934, I.I. Rabi famously asked, “Who ordered that?” Since then, the discovery of the tau lepton (1973) has given the electron a yet heavier, more unstable brother and the up and down quarks have also sprouted triplets. When we expand the Standard Model to describe the properties of these unexpected kin, its elegant core grows an oversized appendix, uncomfortably like the “long list of instructions” we were happy to avoid. This is where the Standard Model, otherwise remarkably beautiful and tight, gets sloppy.

There is one bright spot. An adequate account of it would require a separate post, but to make a long story short, we can fix the worst of our family problems by postulating the existence of a new particle, the axion . Axions are predicted to be Higgs-like particles, but much lighter and much more weakly interacting. If they exist at all, they will contribute a large fraction of the astronomical “dark matter.” Difficult but promising experiments to search for axions are in progress.

10. Unification Looks Good, and Suggests Supersymmetry : The standard model contains three (mathematically) similar but distinct forces and neatly accommodates a fourth—gravity, in the form of general relativity. It also contains, even after we count particles that transform into another by symmetry as the same and ignore the family triplication, five distinct ur-particles. We would like to build a more economical description, without so many independent parts. And in fact we can transcend the standard model, by pushing its ideas further. If the gauge symmetries that lead to the different forces are all part of a larger, better hidden but more encompassing symmetry, then the different forces are not truly independent, but instead are merely different aspects of a single basic force. Remarkably, then, the different ur-particles turn out to be different aspects of a single basic particle, too.

Unification dynamics can work as a quantitative idea and explain the relative strength of the different forces (including gravity). But for this to work in detail, we need to augment the standard model. The most convincing idea in that direction is supersymmetry . Supersymmetry, too, deserves a post of its own, and here I will only mention its most immediate, testable consequence—namely that for every particle we currently known there must be a heavier superpartner with different spin (and of course mass) from its conventional mate, but sharing other properties like electric and strong color charges. Hopes are high that the next round of LHC experiments, at higher energy, will uncover some of the new particles supersymmetry requires.

Bonus Item, for our baker’s list of 10:

The standard model, as we currently understand it, does not account for the astronomical dark matter. On the other hand, that dark matter appears to be composed of some kind of relic gas of particles, surviving from the earliest moments of the Big Bang. Axions are a good candidate to be that particle, as are possible stable superpartners.

Go Deeper
Editor’s picks for further reading

CERN: The Standard Model
Discover the Standard Model in this brief primer from CERN.

Science: Does Dark Matter Consist of Weird Particles Called Axions?
In this video archived from a 2013 live chat, Frank Wilczek and Gianpaolo Carosi, spokesperson for the Axion Dark Matter Experiment team, discuss axions and how physicists hope to detect them.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.