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Brian Hayes

Science is often portrayed as a kind of tennis match between theory and experiment. This description is nowhere more apt than in the study of a physical constant known as the g factor of the electron and the muon. For more than 50 years g has been batted back and forth by theorists and experimenters striving always to append another decimal place to the known value. The game depends on having well-matched players on either side of the net, so that what's predicted theoretically can be checked experimentally. In this case the players are very good indeed. The g factor of the electron has been both calculated and measured so finely that the uncertainty is only a few parts per trillion. The current experimental value is 2.0023193043718 ± 0.0000000000075.

Measuring a property of matter with such extraordinary precision is a labor of years; a single experiment could well occupy the better part of a scientific career. It's not always appreciated that theoretical calculations at this level of accuracy are also arduous and career-consuming. Getting to the next decimal place is not back-of-the-envelope work. It calls for care and patience and for mastery of specialized mathematical methods. These days it also requires significant computer resources for both algebraic and numerical calculations. Only a few groups of workers worldwide have the necessary expertise. My own role in this tennis game is purely that of a spectator, but I have been watching the ball bounce for some time, and I would like to give a brief account of the game from a fan's point of view, emphasizing the action on the theoretical side of the net.

The study of g is not just an exercise in accumulating decimal places for their own sake. The g factor represents an important test for fundamental theories of the forces of nature. So far, theory and experiment are in excellent agreement on the g factor of the electron. But for the muon—the heavier sibling of the electron—the situation is not so clear. Calculations and measurements of the muon g factor have not yet reached the precision of the electron results, but already there are hints of possible discrepancies. Those hints could be early signs of "new physics." Or they could be signs that we don't understand the old physics as well as we think we do.

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