In response to “The Standard Model” (Vol. 4, No. 1).

To the editors:

Sheldon Lee Glashow’s essay is a wonderful overview of the historical development of the Standard Model of particle physics. Not surprising, perhaps, given that he is one of the key players in that development. Glashow shared the 1979 Nobel Prize with Steven Weinberg and Abdus Salam for their work unifying two of the four fundamental forces in nature, the so-called weak force, and the more familiar force of electromagnetism.

The story of the development of the Standard Model is anything but linear. As I wrote in The Greatest Story Ever Told… So Far, the actual development followed a long period of frustration, during which much of the physics community were busily chasing their own tails, even as the key insights were actually already out there in plain view for anyone who chose to look in the right direction.

Too often we present the history of science as a series of logical steps, one inevitably following the other. In hindsight it is easy to see the connections that allow for such a progression. At the time, however, these connections and the next steps are often much more elusive. If they weren’t, anyone could make profound discoveries at the cutting edge.

To tell the full story of the historical development of the Standard Model would require an entire book. In this essay, Glashow has much more limited space. Nevertheless, with a clarity and historical precision that I have yet to see in a short popular piece on the subject, he has captured the key physical and mathematical insights that allowed physicists, over a period of twenty-five years, to produce what I believe will be viewed as one of the greatest scientific revolutions of the twentieth century, comparable in significance to more well-known developments such as quantum mechanics and relativity.

Glashow, a particle physicist, begins his story by describing the particles that were known early in the twentieth century—protons, photons, and electrons. As long as we confine ourselves to phenomena observable on human scales, these appeared to be all that was necessary to fully describe nature. Needless to say, it didn’t take long for physicists to discover that this is not the case. With the exception of photons and electrons, which are both observable and, as far as we currently can say, are both truly fundamental, the building blocks of nature correspond to objects we cannot detect and observe directly in the physical processes that govern biology or chemistry.

By the time Glashow’s essay is complete, we find that we live in a world that at its fundamental scales contains a zoo of exotic and foreign particles: quarks, mu and tau leptons, neutrinos, W and Z bosons, gluons, and the famous Higgs particle. As Glashow notes, these particles, along with electrons and photons, allow for a mathematically elegant, and more importantly, testable and accurate description of the universe—known as the Standard Model—at all the scales we have yet been able to probe directly in laboratories.

The world we observe, with massive particles like electrons, protons, and neutrons making up atoms, which make up all the materials we measure on Earth and which comprise the material of the stars, interacting via electromagnetic and gravitational interactions is, in this sense, largely an illusion. At a fundamental scale, not only are the elementary particles that make us up actually massless, but the nature of the forces that govern their behavior is vastly different than we perceive on human scales. So much for the notion of a universe that is finely designed for life! Our own existence, and the existence of everything we see in the universe today depends on a set of cosmic accidents, including the freezing of a vast invisible field—the Higgs field—in the earliest moments of the Big Bang.

Seen in this way, the broader historical intellectual significance of the Standard Model may, in fact, be far greater than that implicitly alluded to in Glashow’s essay—not surprising perhaps because he was intimately involved in its development.

In 1955, we correctly understood only one out of the four known forces in nature as a fully relativistic quantum theory. No candidates for a mathematically consistent theory of the other two forces of relevance on laboratory scales were known. Just two decades later, all of the ingredients were in place to understand three of the four forces in terms of a single type of mathematical theory known as a gauge theory, of which electromagnetism is the simplest known example. Even gravity, for which we do not yet have a fully workable quantum theory, is classically described using the same mathematics of gauge theories.

It will be up to historians of the twenty-second century and beyond, who will have greater historical perspective and distance from current developments, to judge the significance of the remarkable physical developments of the twentieth century. Nevertheless, in terms of its scope and the manner in which it completely altered our picture of fundamental processes, the two decades between 1955 and 1975 may represent the most revolutionary period of physics in that century, rivaling the period 1910 to 1930, which witnessed the development of quantum mechanics and general relativity.

There are three other aspects of Glashow’s essay that I would like to elaborate on, in order to provide a slightly different perspective on some issues he raises.

The first concerns his cogent discussion of the problem of so-called vacuum, or zero-point energy in quantum field theory. Taken at face value, the energy of space in its ground state is, according to quantum mechanics, infinitely large.

This potentially infinitely serious problem is actually not a problem at all if one ignores gravity. After all, only gravity is sensitive to the absolute energy of a system. All other forces are only sensitive to energy differences. In an atom, what matters for the generation or absorption of electromagnetic radiation is the energy difference between the ground state configuration of the atom and an excited state of the atom. Thus, when ignoring gravity, which we can do in considering the physics of individual atoms or elementary particles because the gravitational force is so weak on the scale of atoms and elementary particles, we can simply ignore the infinite ground state energies of systems and calculate energy differences between the ground state and excited states.

This idea is at the heart of the mathematical methods that form the basis of renormalization, described by Glashow when he discusses the numerous divergences that arise in quantum field theory. There is another physical basis for ignoring these infinities. The source of these infinities comes from extrapolating the mathematical algorithms that allow one to perform calculations with the theory down to arbitrarily small scales. But there is no reason to assume that no new physics will be encountered on ever-smaller scales—physics that would require one to change the nature of the calculations at small scales. Theories that make sense are therefore theories that are insensitive to changes associated with possible new physics on arbitrarily small scales—so-called renormalizable theories. In such theories one can discard the arbitrary infinities that arise from unknown effects at arbitrarily small scales with impunity.

As both Glashow and I have suggested, all of these arguments ignore gravity. If the vacuum carries energy of any amount, that energy should gravitate. Clearly then, given our existence, the vacuum does not possess infinite energy. Until 1998, most physicists had assumed that when we possessed a fully consistent quantum theory of all the forces in nature, including gravity, we would then find that the energy of the vacuum is in fact zero—the simplest and most physically satisfying assumption.

It was in 1998 that astronomers discovered that the expansion of the universe was itself accelerating. This could only be the case of empty space having a very small, but non-zero energy, since the energy of empty space actually produces a gravitational repulsion rather than an attraction.1 To date, the only natural values for the energy of empty space that our theories suggest is either zero or infinity. Nothing prepared us for a non-zero value, moreover a value that is, within the context of the typical scales one might expect in particle physics, about 120 orders of magnitude too small. It is fair to say that this problem, inherent in the Standard Model, and indeed in all of our physical theories, is perhaps the biggest unsolved problem in fundamental physics today.

The second issue relates to the unobservable nature of quarks—again as central precept of the Standard Model, driven by observation. As Glashow suggests, the presumption that quarks are confined into color-neutral objects played a central role in the viability of the theory. But two aspects of this are worth providing a little more emphasis than was given in Glashow’s essay. While computer calculations strongly suggest confinement is a property of quantum chromodynamics (QCD), no first-principles proof of confinement yet exists for the theory. Equally important was the discovery of asymptotic freedom mentioned by Glashow. This discovery was more surprising than it may at first appear, as it suggests that the strength of the force between quarks gets weaker the closer the quarks are to each other. Exactly the opposite is true for electromagnetism, and it is fair to say that the discovery of asymptotic freedom in QCD was both surprising and profound. Not only does it allow one to perform calculations with the theory that allow its predications to be compared with experiment, but it also suggests that the strength of the force grows with distance. This, in turn, provides a physical motivation to assume that confinement is also a property of QCD, even though the mathematical calculations required to demonstrate this large distance property of the theory are currently beyond our abilities.

Glashow ends his essay with a brief discussion of the disappointing history and hyperbolic claims associated with string theory, which was based on the attempt to incorporate gravity as a quantum theory along with the other known forces in a unified framework.

Glashow is absolutely correct in his statement that string theory has thus far failed to fulfill any of the grand claims made for the theory early on, or even answer any of the outstanding puzzles associated with the Standard Model.2 It is worth noting that string theory is at least well motivated, and several components that are required for the theory to work, although their possible manifestation in nature does not imply the validity of the entire string theory edifice, are in fact motivated by solving some of the problems of the Standard Model.

In particular, a new symmetry known as supersymmetry has been proposed as an extension of the Standard Model in order to stabilize the mass of the Higgs particle. Physicists have been disappointed that there is thus far no evidence of supersymmetry in phenomena observed at the Large Hadron Collider, meaning that many of the simplest supersymmetric model theories are ruled out. If supersymmetric partners of ordinary particles are one day observed at the LHC, or in a future accelerator, this will not only help us understand the stability of the Higgs, but it will imply that at least one of the ideas underlying string theory is relevant to the real world.

I am quite taken by Glashow’s concluding statement: “Things are as they are, but why they are as they are, the theory does not say.” It is important to point out that this is not a property that is peculiar to the Standard Model. Science never really deals with why questions. Instead, it deals with how questions. General relativity tells us that space curves in the presence of matter and energy, but it doesn’t tell us why it has to be that way. As far as the laws of nature are concerned, they are the way they are, and the job of physics is to discover how things are, not why they are.

More generally, why questions presume purpose, but a key aspect of science is that it doesn’t presume purpose in the universe. When we ask “Why is the sky blue?” what we really mean is “How do the laws of nature operate so that the sky appears blue?” While the Standard Model has left open a variety of puzzles about the universe, this should not be taken as a failing of the theory. It is puzzles and mysteries that drive us forward, and the remarkable developments of the twentieth century do not herald the end of physics, but rather the possibility of a new century of discovery.

Lawrence Krauss

Sheldon Lee Glashow replies:

I first encountered Lawrence Krauss in 1980 at a Scottish summer school at St. Andrews where I was a lecturer and he a student. We have been friends, colleagues, and occasional collaborators ever since. Krauss is now an accomplished theoretical physicist, a successful author, and a powerful voice for science. I heartily agree with most of his remarks about my article. How could I not? But I do have a few minor quibbles, more about tone than substance.

Supersymmetry (SUSY) is decidedly not a new symmetry. It was devised and applied to hadronic physics nearly a half century ago. If nature were supersymmetric, every known fermion would have a spinless superpartner, every known boson a spin-1/2 superpartner. Particles and their partners would have the same mass. At best, SUSY is a badly broken symmetry because no superpartner has yet been seen. Even as a broken symmetry, SUSY is theoretically attractive and phenomenologically useful. Evidence for supersymmetric particles has been sought at accelerator laboratories throughout the world and by several generations of high-energy experimentalists. No trace of SUSY has been detected, not even at today’s most powerful particle collider, the LHC at CERN. It appears that the energy scale associated with any still viable SUSY scheme is likely too high for the theory to fulfil its several assigned tasks: stabilize the Higgs boson mass, provide a dark matter candidate, and enable the coupling-constant convergence predicted by grand unification. Perhaps the time has come for experimenters to peer beyond their supersymmetric chimera.

The observed value of the dark energy density of the universe is surely tiny… as it must be for us to be here to observe it. Its value can be expressed as an energy to the fourth power. That energy is roughly one milli-electron volt, only a bit smaller than the rest energies of neutrinos, the heaviest of which is no more than a trillionth of the top quark mass. Is it mere coincidence? Can neutrino masses and the cosmological constant, both once thought to vanish, share a common origin? And why is the Planck mass, an inverse measure of the strength of gravitational forces, some seventeen orders of magnitude greater than the top quark mass? In 1937, Paul Dirac remarked that ratios of fundamental quantities “are so enormous as to make one think that some entirely different type of explanation is needed for them.”3 Similar thoughts continue to plague us.

Johannes Kepler didn’t ask why there are planets, but now that we know most stars to have them, it has become a sensible question with “Why?” having the sense “How did it come to be?” Kepler did ask why there were just five planets in the solar system and why their orbital radii were as they are. His answers, in terms of nested Platonic solids, now seem silly. So do his questions. The details of our solar system are simply accidents of its birth. “Why” questions can certainly imply purpose: Niels Bohr and his cohorts explained why the periodic table works. The purpose of the charmed quark was to expunge strangeness-changing neutral currents. Makoto Kobayashi and Toshihide Maskawa explained why nature needed even more quark flavors. I think it was Steven Weinberg who first suspected that many of the questions physicists ask, perhaps most of them, are like Kepler’s questions. String theory, in its current guise, has come to just that conclusion. The countless universes comprising the string landscape include all imaginable variations of our standard model. The dozens of parameters appearing in our parochial picture of fundamental physics are only accidents of the birth of our particular universe. Please let it not be so!

Lawrence Krauss is Foundation Professor of the School of Earth and Space Exploration at Arizona State University and director of its Origins Project.

Sheldon Lee Glashow is a Nobel Laureate and the Metcalf Professor of Mathematics and Physics at Boston University.

  1. In the interests of full disclosure, there were inklings as early as 1995, argued by myself and colleagues, that this energy existed well before it was directly detected via the accelerating expansion of the universe. 
  2. As another Nobel Laureate, Frank Wilczek, has put it, string theory is promising… and promising, and promising… but so far that is all. 
  3. Paul Dirac, “The Cosmological Constants,” Nature 139 (1937): 373.