Nearly fifty years ago, physicists determined the value of one of the fundamental fixed values of physics, the fine structure constant, using quantum electrodynamics theory-or did they? Through an interplay of laboratory experiment and theoretical work, physicists have improved on the value of the fine structure constant seeking ever increasing accuracy. According to Cornell physicist Toichiro Kinoshita, there is still room for further improvement.
Quantum electrodynamics is the basic theory of physics that explains how electrons interact through the electromagnetic force, which is transferred by photons. Electrons absorb and emit photons during their interactions. The probability that this will occur is expressed by the value of the fine-structure constant. "This constant plays an important role in the theoretical structure of physics and is also important to metrology, the science of weights and measures," Kinoshita explains. His method of measuring this constant is based on the study of a subtle change of the magnetic moment of the electron due to its interaction with photons (the electron anomaly).
Updates to the calculation of the fine structure constant have moved to higher and higher order as experimental techniques in the lab and the speed of the computer have improved. When experimentalists push forward in the accuracy of their measurement systems, theoretical physicists follow in hot pursuit trying to outperform the experimentalists relying only on the first principles of physics. Kinoshita uses the numerical integration method for this purpose. His computational efforts often set the stage for analytic solutions. Once an analytic solution (the ultimate goal of the effort) has been confirmed, the challenge moves on to a finer scale.
Kinoshita's effort has resulted in the most accurate numerical estimates of the value of the fine structure constant to date. Using the IBM RS/6000 Scalable POWERparallel Systems (SP) supercomputer at the Cornell Theory Center (CTC), he has achieved a numerical solution for the fourth order term of the electron anomaly with great statistical confidence.
The first order term in the equation used to describe the electron anomaly is proportional to the fine structure constant. The original calculation of this term was done by hand in 1947. "A physics graduate student needs about 30 minutes for the calculation," says Kinoshita. "The solution fits on one page of an exam notebook."
Moving up in accuracy entailed solving the second order term (proportional to the square of the fine structure constant) and adding it to the original value. This required a few years of hard work using paper and pencil. The exact solution was announced in 1957. Kinoshita contributed a numerical solution for the third order term (proportional to the cube of the fine structure constant), reporting a crude initial solution in 1972, and finally a highly accurate value in 1995. The analytical solution for this term was determined the next year by a team of Italian physicists.
Kinoshita already had more than fifteen years invested at the next level of accuracy. His first crude solution for the fourth order term was proposed in 1981. "Its precision has improved steadily with the development of more and more powerful computers," he says. Based on Kinoshita's electron anomaly work, the fine structure constant is now known to eight digit precision. Its value is 1/137.035 999 93.
Numerical integration requires that an enormous number of integrals be calculated to achieve a final answer. "Computation is an essential tool at this fundamental level of physics," comments CTC director Malvin H. Kalos, "allowing researchers such as Kinoshita to press against the very fabric of our understanding looking for gaps." Moving a decimal point further in the accuracy of the known value of the fine structure constant required several hundred times more work than the numerical integrations for the third order term. Kinoshita uses 32 to 64 nodes of the SP to run parallel calculations for as much as a hundred hours per run. Then he painstakingly tests the results through further calculations requiring an order of magnitude more computing time.
Updates to the estimates of the fine structure constant are published every ten years in the Adjustment of the Fundamental Constants of Physics. The next edition is due in 1996. Because of its high statistical confidence, Kinoshita's result stands out from the other values vying for acceptance as the next standard. But pushing a decimal point in accuracy is not Kinoshita's only goal; he is looking for places where theory breaks down. So far, it hasn't; although the answers do get more subtle and complex. "I am digging at the roots of physics to see whether there is some treasure there," says Kinoshita with a grin.
CTC is one of four high-performance computing and communications centers supported by the National Science Foundation. Activities of the center are also funded by New York State, the Advanced Research Projects Agency, the National Center for Research Resources at the National Institutes of Health, IBM, and other members of CTC's Corporate Partnership Program.