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.