Image: Laser apparatus
F. Reiser and A. Antognini / Paul-Scherrer-Institute
This laser apparatus, used in 2010 to measure the size of the proton, found that the particle's radius is about 4 percent smaller than previously thought.
By Contributor
updated 1/24/2013 6:59:20 PM ET 2013-01-24T23:59:20

How many protons can dance on the head of a pin? The answer is nowhere near as straightforward as one may think — and it might offer new insights into one of the most well-tested theories in physics. 

An international team of scientists recently tried to find out the actual size of a proton, one of the ingredients (along with neutrons and electrons) of the atoms that make up our bodies and the world around us.

Reporting this week in the journal Science, the researchers found that the particle's radius is 0.84087 femtometers. A femtometer is a millionth of a billionth of a meter, or so small that the wavelength of gamma radiation is 100 times longer. The new measurement is about 4 percent smaller than the currently accepted radius of 0.8768 femtometers, and that small difference presents a puzzle.

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If the smaller size is correct, then there's something missing in physicists' understanding of quantum electrodynamics, which governs how light and matter interact.

Proton error?
Aldo Antognini, a physicist at the Swiss Federal Institute of Technology and first author of the paper, told LiveScience the difference could mean one of three things.

First, that there is some error in the earlier work, though that isn't likely given how many times various experiments were repeated.

The second possibility is that some piece of the calculations for the proton's size is missing. "Maybe we don't understand fully proton structure," Antognini said.

The third explanation is that the current theories of quantum electrodynamics are wrong, though the chances of that seem slim, given that the theory works very well and it has been tested many times. [Wacky Physics: The Coolest Little Particles in Nature]

This result isn't the first time a discrepancy has shown up. In 2010, Antognini, working with an international team led by Randolf Pohl of the Max Planck Institute of Quantum Optics in Garching, Germany, found the proton radius seemed to be 0.84185 femtometers.

How to measure a proton
To find the size of a proton scientists have used three methods. One is electron scattering: firing negatively charged electrons at positively charged hydrogen nuclei (protons) and measuring how they are deflected. The scattering pattern can then give an idea of how big the region of positive charge is.

The second method is to measure how much energy it takes to get an electron to move to different orbital regions around a nucleus. Electrons usually stay in regions that are a certain distance from the nucleus. Increase their energy and they become excited, and move to a different region, called an orbital. The electrons then fall back into their unexcited states and emit a photon. By looking closely at how much energy it takes to move an electron from one orbit to a higher-energy one, and the wavelength of the photon emitted when the electron drops back to its lower-energy orbital, it's possible to estimate a proton's size.

Last, the method used in the latest set of experiments, involves muonic hydrogen, which is a proton with a muon, rather than an electron, orbiting around it. Like electrons, muons are negatively charged, but they are 207 times heavier. That means they fly closer to the proton, and it takes more energy to move them to higher-energy orbitals. The greater energy differences make measuring them easier. Firing a laser at the muonic hydrogen excites the muon, moving it to a different orbital. The muon then falls back to its lower-energy state, emitting an X-ray photon.

The first two methods, used over decades, had come up with the larger value for the proton's radius. The latter method, which scientists say has a smaller uncertainty, found the smaller one. These calculations, though, are quite complex.

New proton measure
Antognini's team, carrying out experiments at the Paul Scherrer Institute in Switzerland, not only did the muonic hydrogen experiment a second time, they also took steps to ensure a more accurate measurement. The discrepancy remained. "Maybe there is something in [proton] structure only highlighted by muons," Antognini said. [Weird: Top 10 Unexplained Phenomena]

That's why the new value is proving such a mystery. Quantum electrodynamics (QED) is probably right, and it's also not likely that the earlier experiments were that far wrong due to simple errors, experts say.

"There might be some missing terms in the calculations," said Helen Margolis, a research scientist at the National Physical Laboratory in the U.K., who was not involved in the research. "QED has been tested to incredible levels so far, but the mathematical foundation is not as secure as you might like."

Chad Orzel, an associate professor of physics and astronomy at Union College and author of "How to Teach Physics to Your Dog" (Scribner, 2010), said the results are good for physics generally, because of the questions they raise. "It's really boring when all the measurements and theory agree with each other. This kind of disagreement gives us something to talk about that isn't the Higgs boson."

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Explainer: What’s a hadron? Tour the particle zoo

  • Image: Elementary particles

    The Standard Model of particle physics is one of science's most successful theories, enabling the development of devices ranging from light bulbs, to microwave ovens and television, to quantum computing devices. The Standard Model is also one of the oddest theories, because it lays out a dizzying menagerie of hundreds of subatomic particles. At its heart are 16 types of elementary particles ... plus at least one more mysterious particle that scientists are spending billions of dollars to detect.

    Click on "Next" to get the full rundown.

  • Quarks

    Image: Quarks and gluons
    Berkeley Lab

    Six "flavors" of quarks have been detected: up and down, charm and strange, top and bottom. Quarks are almost always found in different combinations, bound together by gluons (more on those later). Particles built up from quarks and gluons are called hadrons. The Large Hadron Collider is so named because it's a large collider that smashes hadrons together.

    Three-quark combinations fit in the category of baryons. The best-known baryons are the proton (with two up quarks and one down quark) and the neutron (with two down quarks and one up quark).

    Particles that have one quark and one antiquark fit in the category of mesons. For example, the pion, or pi meson, contains an up quark and an anti-down quark.

  • Leptons

    Image: Single electrons in helium
    Brown University

    Six "flavors" of leptons have been detected: The negatively charged electron is the best-known lepton — along with its antimatter counterpart, the positron. This photo shows the path of single electrons passing through liquid helium, in an experiment devised by Brown University researchers.

    The muon is also negatively charged, but it's about 207 times as massive as the electron. ("Who ordered that?" physicist Isidor Rabi reportedly asked.) The negatively charged tau particle is even bigger — 3,477 times as massive as the electron — but it decays into other particles in less than a trillionth of a second.

    Each of those leptons has a neutrino associated with it: the electron neutrino, the muon neutrino and the tau neutrino. Neutrinos interact only weakly with other particles, and they zip through our planet virtually without a trace. Physicists only recently determined that they have mass, but there's still a great deal of mystery surrounding the ghostly particles.

  • Force carriers

    Image: Graviton

    The Standard Model sets aside a category for particles that are associated with force fields. The effect of a field can be viewed as involving an exchange of such force-carrying particles.

    Four elementary force-carrying particles have been detected. The best-known force carrier is the photon — which plays a part in the electromagnetic spectrum, including visible light. The gluon binds quarks together through the strong nuclear force. The weak nuclear force involves the exchange of W and Z bosons. The W boson can carry a positive or a negative charge, while the Z boson is neutral.

    If gravity could be incorporated into the Standard Model, the force-carrying particle would be called the graviton (shown here in an artist's depiction). However, gravitons have not yet been detected, and at least for now, such particles are not accounted for in the Standard Model.

  • Bosons vs. fermions

    Image: Bosons vs. fermions
    Rice Univ. via AIP

    All force-carrying particles are bosons, but not all bosons are force carriers. The difference has to do with a property known as particle spin. Particles with a fractional spin value (for example, electrons, protons and neutrons) are fermions. Two identical fermions cannot occupy the same quantum state. This is a property that keeps electrons from collapsing into a jumble, and thus makes chemical reactions possible.

    All particles with a whole-integer spin value are classified as bosons, and such particles can occupy the same quantum state even if they're identical. The photon is the best-known type of boson.

    Even atoms can be classified as fermions and bosons. This photo shows how atom clouds of lithium-7 (bosons) and lithium-6 (fermions) behave at low temperatures. The bosons collapse into a compact cloud, while the fermions can't squeeze that closely together.

  • The mysterious Higgs

    Image: Higgs as seen by CMS
    Ianna Osborne / CERN / CMS Collection

    The Higgs boson is the only particle predicted by the Standard Model that has not yet been detected. The Higgs is the main quarry for physicists at the Large Hadron Collider. This image is a simulation of the Higgs' signature as it might appear in one of the LHC's detectors.

    The Higgs boson, named after Scottish theorist Peter Higgs, is thought to be associated with a field that endows some particles (such as the weak nuclear force's W and Z bosons) with mass, while leaving the electromagnetic force's photons without mass.

    This Higgs field may have played a role at the very beginnings of the universe: Physicists believe that at the highest energies, the electromagnetic and weak nuclear forces were unified, but something led to "electroweak symmetry breaking" as the infant cosmos cooled. That would be why the electromagnetic force and the weak nuclear force are distinct in the current universe. The Large Hadron Collider could shed new light on this mysterious Higgs mechanism.

  • Why so complicated?

    Image: Particle zoo
    Tim Jones / McDonald Observatory / HETDEX

    Hadrons and leptons? Baryons and mesons? Fermions and bosons? Sometimes it seems as if particle physicists set up these classifications just to keep outsiders totally confused. But for researchers, these occasionally overlapping categories are useful for figuring out how different types of particles interact with each other.

    In a sense, it's as if we've been talking about the game of chess but have gotten only to the point of naming the different pieces on the board: black pieces and white ones, pawns and knights, bishops and rooks, kings and queens. The real meaning of the game comes out when you start studying how the pieces perform and interact.

    To delve into the deeper meaning of the Standard Model, you can visit The Particle Adventure at Lawrence Berkeley National Laboratory, "A Subatomic Venture" at CERN, or Particle Physics UK.


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