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Physics + MathPhysics & Math

Smaller than Small: Looking for Something New With the LHC

In this excerpt from his new book, Don Lincoln describes the quest for new fundamental particles.

ByDon LincolnThe Nature of RealityThe Nature of Reality

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From The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind , an insider’s account of the LHC’s operational history and the search for the Higgs boson, by Don Lincoln. Published by Johns Hopkins University Press. Reprinted by permission of the publisher.

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The Victorian era mathematician Augustus de Morgan wrote:

Great fleas have little fleas upon their backs to bite
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on.

This oft-quoted passage is a parody of Jonathan Swift’s 1733’s On Poetry: A Rhapsody , which was written about poetry. However, scientists have taken those lines as a metaphor for the natural world. As one learns about the microworld, one is quickly faced with the observation that all matter is made of molecules. Molecules are in turn made of atoms which are themselves made of electrons and atomic nuclei. The nuclei are made of protons and neutrons and these are composed of quarks.


However, as far as we know, quarks and electrons are it. That’s the end of the line as far as structure goes. Unlike the atom or proton, which have a rich structure with complex interactions between their components, the quarks and electrons are currently believed to have no internal structure at all. Both theoretically and physically, they are considered to be mathematical points.

Of course anyone with an ounce of imagination can’t help saying, “Now just hold on a minute. Why couldn’t the quarks and leptons themselves have an internal structure?” Well there’s only one possible answer and that is “they could.” The quarks and electrons (and, by extension, all leptons) could be made of even smaller objects. Or they (rather improbably) may indeed be fundamental (i.e., have no smaller parts, in other words, structureless).

Before we proceed further, let’s consider the sizes involved. Everything in the microworld is small. A single molecule is so small that you could place a million of them side by side in a single millimeter. They are so small that you can’t use ordinary light to see them. And yet, such smaller objects are enormously large: a billion times larger than the research frontier.

Molecules are composed of atoms, which are about a tenth the size of molecules. The mental picture of an atom as a little solar system, with the sun as a nucleus and planetary electrons, is flawed and yet it is not without merit. It highlights the fact that an atom consists of mostly empty space, with the electrons swirling frenziedly far from a small, dense nucleus. The radius of the nucleus is about 10,000 times smaller than the atom and takes up but a trillionth of the volume.

The nucleus of the atom consists of protons and neutrons, packed tightly together. My mental picture of the nucleus is a mass of frog eggs or marbles after being handled by a toddler with very sticky fingers. Each proton or neutron is about 10 -15 meters wide, and you would need a trillion laid end-to-end to span a single millimeter. That’s small.

Protons and neutrons contain within them quarks and gluons. The simplest way to think of a proton is that there are two up quarks and one down quark stuck in a force field of gluons. Think of three numbered plastic balls in one of those air-blown lottery machines and you get the basic idea.

But the mental picture of quarks as plastic balls has one major flaw. The balls are not much smaller than a lottery machine. Quarks are small. Maybe a better mental picture of the proton is three little flecks of Styrofoam in the same machine.

So what do we know of the size of quarks? Earlier I said that they have no size, and that’s certainly how the current theory treats them. However, as an experimenter, I’m more concerned with measurements. You the reader must be curious as to what measurements have revealed the size of a quark to be. And now the answer . . . a drum roll please . . . they haven’t. This doesn’t mean we know nothing about their size. We’ve studied this question rather thoroughly, and we know precisely how good our equipment is. If quarks (and electrons) were larger than about ten thousand times smaller than a proton, we’d have seen that they have a size. In all of our experiments, we’ve never seen even the slightest believable hint of a size. We therefore conclude that, while we can’t say what the size of a quark or electron actually is, we can safely say that if quarks have size at all, they are smaller than one ten-thousandth the size of a proton.

If this idea is hard to understand, let’s consider how small an object you can see with your eyes. You can easily see a grain of sand. With very considerable effort, you might be able to see the smallest bit of flour in your cupboard. But that’s about it. With your bare eye, you can’t see anything smaller. Thus when you decide to look at a germ with your eye, you could conclude that it has no size, but the strictly correct conclusion you should draw is that germs are smaller than a tiny fleck of flour.

With better equipment, say a powerful microscope, one can see that germs actually do have a measurable size. So once you’ve hit the limitation of your equipment, you simply need to get a more powerful microscope. The microscope that is the LHC and its two primary detectors will observe the size of quarks if they are no less than 20 or 30 thousandths of the size of a proton . . . or they will set a limit that is about two or three times smaller than currently thought.

While observations, intuition, and de Morgan’s ditty may be enough to support a casual suspicion that other levels of matter may occur at ever smaller sizes—a whole new layer or set of layers in the cosmic onion—there are more scientific reasons as well. For instance, consider the periodic table. While Mendeleev intended it to be an organizational scheme, with the formulation of the theory of the nuclear atom and quantum mechanics in the first few decades of the twentieth century, it became clear that the periodic table was actually the first indication of atomic structure, half a century before we truly understood the table’s message.

While the story told by the periodic table clearly hinted at atomic structure, the story of nuclear radiation also suggests the structure of the nucleus. For instance, cesium ( 137 55 Cs, with fifty-five protons and eighty-two neutrons) emits an electron and becomes barium ( 137 56 Ba, with fifty-six protons and eighty-one neutrons).

Let’s take these historical examples and apply the reasoning to the modern world. We realize that historical lessons do not always apply. But sometimes they do.


Our “periodic table” of particles is shown in the image above. Its organization is different from the chemical periodic table. In the figure, there are six types of quarks. The up, charm, and top quarks all have +⅔ charge (in a system where the charge of a proton is +1) and the mass of the charm quark exceeds that of the up quark, which in turn is surpassed by the top quark. Similarly, the down, strange, and bottom quarks all have electric charge -⅓, with the mass increasing as one goes toward the right.

In the modern periodic table, the “chemically similar” units are the rows, in contrast to the columns of Mendeleev’s table. We see that there are three “generations” or carbon copies of the same quark and lepton pattern. This is highly reminiscent of the hints that the chemical periodical table was giving us in the latter half of the nineteenth century.

There is another historical similarity to consider. Just like the various atomic nuclei could decay into other nuclei, so too can the quarks and leptons. A top quark can decay into a bottom quark and a W boson. Likewise, the muon can decay into an electron and two neutrinos. Other types of quark and lepton decay are also possible. In fact, all particles in the second and third generations eventually decay into the particles of the first generation. One crucial clue is that the only force that can change one quark or lepton into another (we say “change the quark or lepton’s ‘flavor’”) is the weak force. Further, specifically only the electrically charged W boson can do the job.

There is no hard evidence that the presence of quark and lepton generations indicate that quarks and leptons are themselves composed of smaller (thus far undiscovered) particles. However, the historical analogy is powerfully suggestive and certainly warrants closer attention. The fact that, by emitting a W boson, one can change the quark or lepton flavor is an extremely valuable clue that is screaming something important at physicists.

I just wish that I had the wits to understand what it was saying.

However, even without the crucial insight that cracks the conundrum wide open, we can speculate intelligently on the subject and (much more important) sift through our mounds of data, looking for additional clues. As with all searches for new physical phenomena, you have to make an educated guess about what to look for and then look for it. So, what are the likely experimental signatures of quark structure?

Historically, one of the best places to look has been the most violent collisions. You smash two objects together and see how many collisions there are at each level of violence. Specifically, you look at the amount of “sideward violence.” Technically we call this transverse momentum , which means perpendicular to the beam. There are technical reasons for this choice, but mostly it is because you have to hit something hard for it to go sideways from its original direction.

Today, most physicist take a “wait and see” attitude, preferring to see what hints the universe will give us. Even so, names have been proposed for these objects smaller than quarks, with the most popular being “preon” (for pre-quark). However, each theoretical physicist who has devised a theory has invented his or her own name, with subquarks, maons, alphons, quinks, rishons, tweedles, helons, haplons, and Y-particles all having been suggested. I kind of like the names quinks or tweedles myself.

What will be the next big discovery? I have no idea. It may well be one of the topics mentioned here. Or, even more exciting, it may be something utterly unexpected; something that just hits us out of the blue. As they say, time will tell.

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.