###### By Don Lincoln, Fermilab

## On June 1, 1947, a group of distinguished physicists converged on Shelter Island, a small island just east of Long Island, New York. They had assembled for a conference on the Foundations of Quantum Mechanics. Talks were presented on the theory of quantum mechanics, as well as a number of measurements.

### Measuring the Magnetic Moment of Electron

There was a measurement presented at Shelter Island and this was a precise measurement of the magnetic moment of the electron. Austrian-American Isidor Isaac Rabi was one of the attendees of the Shelter Island conference and he announced a measurement of the magnetic moment of the electron. Rabi was the group leader of one of the most productive physics research groups at the time at Columbia University.

The scientist who actually made the measurement was German-born American physicist Polykarp Kusch. He measured the magnetic moment of the electron, but that is equivalent to measuring the *g* factor. The classical quantum mechanics predicted that *g* should equal 2, but that’s not what Kusch measured.

He found that the experimental value of *g *was 2.00238. Now, of course, 2.00238 is very close to 2, but we also need to understand the measurement’s uncertainty. Kusch’s uncertainty was 0.00010, which means that the correct answer was somewhere between 2.00228 and 2.00248. But the number 2 doesn’t fit in that range, which means that the measured value of *g *wasn’t 2.

### Anomalous Magnetic moment of the Electron

Now, physicists didn’t want to report the *g* number for clarity reasons. Instead they wanted to divide the measured *g* by the prediction which was 2. This way of presenting the data can tell you the percentage by which the measurement disagreed with the prediction.

And, dividing 2.00238 by 2 gives 1.00119 with an uncertainty of ± 0.00005. And, if we just mentally and temporarily round that number to 1.001, we can say that what Kusch found was that the actual magnetic moment of the electron was 0.1% different from the prediction. If the estimated uncertainties are right, we can conclude that something else is going on in the magnetic properties of the electron which is called the anomalous magnetic moment of the electron.

*This article comes directly from content in the video series The Evidence for Modern Physics: How We Know What We Know. Watch it now, on Wondrium.*

### Precision of the Measurement

And, of course, over 70 years later, we know that Kusch was right. The actual *g* factor for the electron isn’t two. It’s off by 0.1 percent. Furthermore, we know that the origin of the shift is the virtual cloud of photons and electrons and positrons in the vicinity of the actual electron.

We have measured the anomalous magnetic moment of the electron to incredible precision—12 digits of accuracy. The current value (as this is being written) is 1.00115965218073 with an uncertainty of 28 in that last 73 number. The rest of the numbers are completely accurate, with no chance that they are wrong.

### Theoretical Prediction

While the precise numerical prediction is amazing, the theoretical prediction turns out to be a challenging calculation. It requires the theory of quantum electrodynamics proposed by Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga, which is built around the idea of these virtual particles jumping in and out of existence in the vicinity of an electron. If you do the calculation, you get a number that is nearly identical to the measurement.

The current best prediction for the anomalous moment of the electron is 1.001159652181643 with an uncertainty of 764 in that 1643. This agrees digit for digit for 12 digits. Any time you can make a prediction with that level of accuracy, you know you’re on to something. And, in this case, the thing that we’re on to is the inescapable conclusion that there is a cloud of virtual particles surrounding every electron. Data and theory wouldn’t agree so well without the contribution due to them.

### Magnetic Moment of the Muon

There’s another exciting aspect to magnetic moments and it is a comparable measurement of the magnetic moment of the muon, which is the electron’s heavier cousin. Muons live for a very short time, just 2 microseconds, but researchers can measure their magnetic properties.

The theory and measurement are similarly precise to the electron, but there is a very slight disagreement between the two.

One could try to claim that the disagreement meant that the idea of virtual particles around a muon is wrong, but the two measurements don’t disagree that much. After all, they still agree to 12 digits of accuracy. But they disagree a little too much for comfort in the 13th. The agreement means that the virtual particle idea is still solid, but the disagreement is exciting. It might mean that looking at these very precise determinations of the properties of muons might lead us to a discovery.

So, the determination of the magnetic properties of the electron and muon are excellent evidence for the existence of virtual particles, at least in the vicinity of subatomic particles.

### Common Questions about Magnetic Moment

**Q: Who measured the magnetic moment of the electron? What did he find?**

The magnetic moment of the electron was measured by the German-born American physicist Polykarp Kusch. He found that the experimental value of *g *was 2.00238. Now, of course, 2.00238 is very close to 2, but we also need to understand the measurement’s uncertainty. Kusch’s uncertainty was 0.00010, which means that the correct answer was somewhere between 2.00228 and 2.00248.

**Q: What is anomalous magnetic moment of the electron?**

Polykarp Kusch found that the actual magnetic moment of the electron was 0.1% different from the prediction. If the estimated uncertainties are right, we can conclude that something else is going on in the magnetic properties of the electron which is called the anomalous magnetic moment of the electron.

**Q: What is the measurement of the anomalous magnetic moment of the electron?**

The anomalous magnetic moment of the electron has been measured to incredible precision—12 digits of accuracy. The current value (as this is being written) is 1.00115965218073 with an uncertainty of 28 in that last 73 number. The rest of the numbers are completely accurate, with no chance that they are wrong.