If you were writing a book whose draft is currently 2,310 pages long (with a table of contents that spans 22 pages) and you had spent 15 years doing so, would you give it away on the Web for free?
If you happen to be Alex Dragt ’58, an internationally known physicist, perhaps you would. The official title of the effort is Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics. The book details the use of Lie-algebraic techniques in the design of accelerators.
Dragt said of his book, “I’m nearing the point of saying, yes, it’s done. People are already using it in their research, so that’s the important thing.”
In the late 19th century a Norwegian mathematician named Sophus Lie (pronounced “Lee”) discovered a new kind of algebra now called Lie algebra. His initial discoveries blossomed to become a major part of 20th century mathematics.
Toward the end of the 20th century physicists learned that elementary particles (e.g. electrons, protons, quarks and the like), as they were being discovered, fell into patterns. Remarkably, these patterns turned out to be the same as some of those encountered in the classification of Lie algebras. Thus, what began as pure mathematics has now become fundamental to our understanding of matter. One of the amazing feature of the universe is that it seems to give evidence of many areas of what once was only known as pure abstract mathematics.
While a University of California–Berkeley theoretical physics graduate student, Dragt learned about Lie algebras in the context of elementary particle physics. Some years later, while a physics professor at the University of Maryland and on sabbatical leave outside Paris and subsequently at Los Alamos, Dragt realized that Lie algebras could also be used to describe and compute particle orbits in accelerators.
His work was recognized by the 2013 Particle Accelerator Science and Technology Award, given to individuals who have made outstanding contributions in this field. Dragt is also a recipient of Calvin’s Distinguished Alumni Award, having been honored by his alma mater in 1985.
Accelerator physics has a long history of important achievements. One application is to produce two beams of very energetic particles (as in protons traveling at nearly the speed of light) and to cause these beams to collide head on. When this is done, their energy of motion is sometimes converted into new kinds of matter. In effect, the famous Einstein relation E=mc2 describing how mass can be converted into energy is turned around to become m=E/c2 thereby describing how energy can be converted into mass (matter).
“In research such as this, the desire to understand is the primary motivator. Whether in the future there will be practical applications of this research is hard to know, but past experience suggests there will be. The results of the research on electricity and magnetism carried out in the 19th century provide the basis of much of our current civilization,” Dragt said.
The technology used to produce particle accelerators and detectors has already had other applications including the now familiar X-ray, CAT, PET and MRI scans.
The major facility in the world devoted to the production and study of new kinds of matter is the Large Hadron Collider (LHC) located just outside Geneva, Switzerland. It is the largest laboratory project in the world and is the work of more that 7,000 scientists and engineers drawn from all nations. The immediate research goal is to produce conditions (temperatures and particle densities) that are comparable to those thought to have occurred in the early universe shortly after the Big Bang. The Lie-algebraic methods developed by Dragt and his Maryland research group were among the tools used in the design of the LHC.
A critically acclaimed documentary film called Particle Fever is making the rounds of movie theaters and is also available through Web viewing sources including Netflix. It describes the start-up of the LHC and discusses the potential scientific gains of expected research. “Imagine being able to watch as Edison turned on the first light bulb, or as Franklin received his first jolt of electricity,” touts the publicity for the film.
“I encourage Calvin alumni to track down this film and take note of the significance of the incredible work being done,” said Dragt.
