Physics standout Stephen Walborn '98 hangs ten on quantum mechanics
"Here's this water, and this thing propagating through water, pushing you along," he says. His voice grows stronger, cutting through the din of lunchtime conversations in the Reed commons. "It's incredible that it's even possible, and the fact that people can even do aerials and carve around a wave is even more amazing, if you really stop and think about it."
Walborn does stop and think about it: physics engages him in an everyday way, and right now it is foremost on his mind as he completes a Reed senior thesis that his adviser, Howard Vollum Professor of Science David Griffiths, calls "one of the very finest thesis projects I have ever supervised."
His project focuses on quantum mechanics, which is the basis of our contemporary understanding of atomic, nuclear, and subnuclear processes. While classical mechanics allows for limitless accuracy of measurement, quantum mechanics in principle shows that all physical quantities cannot simultaneously be known with complete accuracy. Physicists must rely on probability.
Attempting to illustrate the concept of probability, Walborn picks up a salt shaker from the table and calls it a particle.
"This salt shaker has a great probability of being here," Walborn says, setting it down in the middle of the table, "but it also has a tiny, tiny, tiny possibility of being over here." He slides the shaker to the edge of the table.
Walborn is studying a method in quantum mechanics called perturbation theory. Griffiths explains that every physics student studies perturbation theory ("but they hope to god they don't have to use it"). It is an involved way of approximating the answer to a hard-to-solve problem by working off the exact solutions to a slightly different problem. "You can piggyback off the exact solution," says Griffiths.
Walborn is studying the theory at its second order, a further refinement of the initial approximations. Each successive order brings the physicist closer to the true answer.
What Walborn is looking at is not a discovery, but a rediscovery.
Logarithmic perturbation theory, the specific approach he is studying, was developed in 1926. Walborn stresses that the theory has been written about periodically since that time, although few physicists know about it. "Frankly, the process is so elegant that I am astonished it's not in the books," Griffiths says. A lot of his colleagues feel the same way. This can't be true, they say; why haven't we been doing this for years?
The reason it is interesting to physicists is that the traditional perturbation theory requires a lot of information and is difficult. Logarithmic perturbation theory is, says Walborn, "a clever little tricky way that requires less information."