Learning too well from Wheeler

Tony Zee’s poignant recollection of his association with John Wheeler (Physics Today, October 2009, page 10 ) included the comment that he learned to “never calculate without first knowing the answer.” Perhaps, like me, he learned that lesson too well—we both missed the opportunity to calculate the beta functions for non-abelian gauge theories.

At the time, the beta functions for all known field theories had a positive sign. It was also known, however, that the scaling observed in deep inelastic scattering would be comprehensible if the field theory of the strong interaction, then still unknown, had a negative beta function.

My thesis adviser, Tom Appelquist, specifically suggested the calculation for non-abelian theories to me more than a year before it was done by the Nobel Prize-winning trio of Frank Wilczek, David Politzer, and David Gross (Physics Today, December 2004, page 21 ). Having had an excellent graduate education at Harvard University, I responded immediately by asking, “Is there any reason to believe that it has the opposite sign?” Of course, no one had any idea then, and unfortunately, it took me about a decade to come up with the physical argument that implies the correct answer without explicit calculation. ¹

Tony has probably suffered even more for having calculated the beta function for every other known case even earlier. So it would seem that at least occasionally, there is also a good argument for calculating even when you don’t know the answer—particularly when there is a discovery waiting to be made.