If you’ve ever struggled with (and failed to solve) a physics problem, UMass Boston professor Maxim Olshanii can empathize. Olshanii recalls taking a course in college in which writing out the solution to a single problem took over two hours. If it weren’t for his training in qualitative methods, Olshanii might never have become a physicist at all.
Qualitative analysis is a physicist’s best friend. It’s really a sophisticated form of estimation, a way of testing a hypothesis before diving in to months of in-depth research.
In his new book, Back-of-the-Envelope Quantum Mechanics, Olshanii offers a series of problem sets designed to introduce undergraduate and graduate students to qualitative methods. With this book, he hopes to introduce students to qualitative methods earlier in their education, and better prepare them for careers in physics.
“The purpose of my book is to give students some exposure to what we [physicists] actually do during the day,” Olshanii said. “We’re not solving beautiful, well-rounded textbook problems. Most of the time, it’s quick and dirty.”
Olshanii explains the value of qualitative methods with a story about another physicist, Enrico Fermi:
Fermi famously asked the question: “Using common sense, find the number of piano tuners in Chicago.” To find the answer, Fermi looked at the number of people in Chicago, the potential number of pianos, the frequency with which pianos needed to be tuned, and more—producing a fairly accurate estimate of tuners. Fermi was using qualitative methods to come up with a workable answer far more quickly than if he’d factored in every single variable.
Estimates help scientists to quickly check whether a problem is worth pursuing.
“When you apply for a new grant, you won’t have three months to test a particular idea,” Olshanii said. “You need to have a way to discard an idea in three minutes. And that’s what qualitative methods do.”
According to Olshanii, physics students are usually presented with “problems that allow a straightforward, relatively simple solution. And they start thinking that the whole field of physics is like that.”
The minute those students step into the world of research, everything is different. Researchers in physics use those “quick and dirty” estimates when setting up problems for their student assistants, and that often surprises students who haven’t yet encountered estimation as a tool for physics research.
“I do believe we have to start research earlier than we do,” Olshanii said. He hopes to develop qualitative analysis as a regular class, preparing students for the tools they need to do great research.
Of course, even with estimation, physics research comes with a lot of head-scratching puzzles.
“A part of our job description is to feel stupid for a long period of time—to really be puzzled,” Olshanii said.