by Nelson Christensen
The participation of undergraduates in scientific research is important for a number of reasons. First and foremost, undergraduates can make significant contributions to the science. In addition, research by undergraduates is now recognised to be an extremely important part of the educational process for these students. LIGO and Virgo have provided wonderful opportunities for undergraduates to experience the joys of physics research. With guidance, students across the undergraduate physics spectrum can find a project suited to their level of expertise and their interests.
Professor Nelson Christensen, who has conducted research and published with numerous undergraduates over the years.
Over the years at Carleton College I have had the thrill of seeing many students make real and significant contributions to LIGO and Virgo’s research efforts. When the students take their success from the classroom to research their joy for physics really springs out. But it should be noted that research is not a sure success for all undergraduate physics majors. I have seen “A” students who could never make the connection to the independent and original work required with a research project; that’s okay, research is not for everyone. On the other hand, I have worked with students who earned B’s and C’s in their physics classes, yet exploded with the opportunity of research; the applied nature of the physics motivated them, and consequently, often encouraged them to become better students in the classroom as well. Continue reading
The road from Dunsink to the exceptional symmetries of M-theory
By Leron Borsten and Alessio Marrani
Our journey starts in the fall of 1843 at the Dunsink Observatory, presiding from its hill-top vantage over the westerly reaches of Dublin City, seat to the then Astronomer Royal Sir William Rowan Hamilton. In the preceding months Hamilton had become preoccupied by the observation that multiplication by a complex phase induces a rotation in the Argand plane, revealing an intimate link between two-dimensional Euclidean geometry and the complex numbers ℂ. Fascinated by this unification of geometry and algebra, Hamilton set about the task of constructing a new number system that would do for three dimensions what the complexes did for two. After a series of trying failures, on October 16th 1843, while walking from the Dunsink Observatory to a meeting of the Royal Irish Academy on Dawson Street, Hamilton surmounted his apparent impasse in a moment of inspired clarity: rotations in three dimensions require a four-dimensional algebra with one real and three imaginary units satisfying the fundamental relations i2 = j2 = k2 = ijk = -1. The quaternions ℍ were thus born. Taken in that instant of epiphany, Hamilton etched his now famous equations onto the underside of Broome bridge, a cave painting illuminated not by campfire, but mathematical insight and imagination. Like all great mathematical expressions, once seen they hang elegant and timeless, eternal patterns in the fixed stars merely chanced upon by our ancestral explorers.
Leron Borsten (left) and Alessio Marrani (right) stood before Hamilton’s fundamental relations, Broome bridge Dublin. Leron is currently a Schrödinger Fellow in the School of Theoretical Physics, Dublin Institute for Advanced Studies. Alessio is currently a Senior Grantee at the Enrico Fermi Research Centre, Roma.