### Fractional Charge

February 3, 2011

It seems that, given enough passage of time, every fundamental concept of science will be modified or discarded in favor of something else. Newtonian gravitation is one example. It's been superseded by General Relativity. Given enough time, General Relativity will likely be modified, perhaps as a consequence of our getting to know the nature of black holes a little better.

From the time of Millikan, we've known that there's an "elementary" charge, the absolute value of which is a property of both electrons and protons. Millikan, in his oil drop experiment determined an elementary charge close to its presently established value of 1.602176487 x 10-19 coulombs.[1] This was an important result that earned Millikan the 1923 Nobel Prize in Physics.

As an aside to the history of science, the Millikan Oil Drop Experiment should be called the Millikan-Fletcher Oil Drop Experiment, since it was a dissertation project of one of Millikin's graduate students, Harvey Fletcher. Fletcher was somehow convinced to assign full priority to Millikan, perhaps because Millikan had been working on such experiments for more than a decade. Fletcher went on to obtain his Ph.D., and he eventually established his own reputation in physics as Director of Research at Bell Labs. He's well known to electrical engineers for the Fletcher-Munson curve that I referenced in a previous article (Too Loud! October 29, 2010); and as the father of stereophonic sound.

Herbert Pietschmann[1] of the University of Vienna has published an article[2] on the arXiv preprint server that discusses the competing theories of the elementary particles that existed before the idea that there were particles even more fundamental, now called quarks. What interested me most about this paper is the considerable commentary on fractional charge.

The six quarks. Quark charge is +2/3 or -1/3. (Diagram modified from original by "MissMJ.")

As the figure illustrates, there are six quarks, named whimsically, up, down, charm, strange, top and bottom. Their charge, as noted in the figure, is either 2/3 or -1/3. Through a combination of these two charges, we can get our proton charge of +1. Of course, the idea of fractional charge was distasteful to most physicists of the era, possibly because of Occam's Razor. In fact, Murray Gell-Mann wasn't able to publish his quark theory in the usual venues. It ended up in Physics Letters.[4] However, in this case, it turned out that Occam's Razor favored the quarks because their existence simplified our ideas about hadrons.

One outcome of the quark theory was that a lot of people tried to find isolated fractional charges. First, a team from CERN examined 10,000 archived bubble chamber photos, but didn't find any. Another group from the Ecole Polytechnique scanned 100.000 of their heavy-liquid bubble chamber photographs, and found nothing. Four fractionally charged (+2/3) particles were found in cosmic ray tracks in July, 1968. [5-6] Many years later, niobium spheres showed factional charge in a Millikan-type experiment,[7] but the result was not confirmed. Niobium was used since it's superconducting and can be levitated.

Pietschmann, in an earlier book, wrote the following,
"Everything that is predicted by a sufficiently renowned theorist will be discovered, irrespective of its actual existence..."

Of course, experiments of the Millikan type are difficult. Millikan himself labored more than a decade on his experimental apparatus. It's interesting, also, that fractional charges were discovered in a Millikan-type experiment by Felix Ehrenhaft and his students at the University of Vienna. Pietschmann quotes from a letter he received from George Zweig on June 11, 1980. Zweig writes that Felix Ehrenhaft had published a paper in 1938 that included data on charge measurements for 150 selenium spheres. The data show two large peaks at charge 1 and 2/3. Zweig asked whether the specific batch of selenium could be located. Pietschmann did a search, but none was found.[3] Why selenium? The melting point of selenium is 221oC, so a Millikan-type experiment is a little difficult, but quite possible.

Solid state physicists have been acquainted with fractional charges for years in the fractional quantum Hall effect. Robert B. Laughlin, who shared the 1998 Nobel Physics Prize with Daniel C. Tsui and Horst L. Störmer, explained the effect as the result of electrons capturing an odd number of magnetic flux quanta. This resulted in the fractional quantized resistance values with odd denominators observed in semiconductors by Tsui and Störmer. In this case, the fractional charge carriers are not particles, but excitations that act as pseudo-particles.

One interesting consequence of the quantum Hall effect is that we now have a quantum of resistance called the von Klitzing constant. Its value, which is Planck's constant divided by the square of the electron charge, is 25812.807557 ohms.

### References:

Linked Keywords: Newtonian gravitation; General Relativity; black hole; Millikan; elementary charge; electron; proton; oil drop experiment; coulombs; Nobel Prize in Physics; Harvey Fletcher; Bell Labs; electrical engineers; Fletcher-Munson curve; stereophonic sound; Herbert Pietschmann; University of Vienna; arXiv preprint server; elementary particles; quarks; quark charge; up; down; charm; strange; top; bottom; Occam's Razor; Murray Gell-Mann; Physics Letters; hadrons; CERN; bubble chamber; Ecole Polytechnique; cosmic ray; niobium; superconductivity; Felix Ehrenhaft; George Zweig; selenium; fractional quantum Hall effect; Robert B. Laughlin; 1998 Nobel Physics Prize; Daniel C. Tsui; Horst L. Störmer; magnetic flux quantum; resistance; quantum of resistance; von Klitzing constant; Planck's constant; ohms.

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