Deb Aronson

Rethinking an Axiom

First appeared in Arts & Sciences newsletter of Washington University in St. Louis in December 2007 under Profiles

Physics professor Carl Bender embodies that good old Missouri saying, “show me.” His knack for questioning things often taken for granted has led to exciting results.

Quantum physics is formulated in terms of a set of axioms that are physical and have an experimental basis. All axioms, it turns out, except one.

The axiom, that a crucial component of quantum mechanics had to be Hermetian, meaning the numbers must be real — (i.e. whether positive, negative, rational or irrational, they can be found on a number line) — was, says Bender, more an “axiom of convenience, a mantra. It really bothered me because it was not physical at all, it doesn’t sound like physics; it was purely mathematical.”

About nine years ago Bender suggested a more physical, alternative axiomatic framework , allowing for complex numbers that lie outside the real number line. This new framework is based on PT symmetry (i.e. the universe is symmetrical if reflected in space and time). He describes this new framework as “more beautiful and interesting, very simple and easy to understand.”

In recognition of his achievements, Bender, who has been with Washington University since 1977, is being installed as the Wilfred R. and Ann Lee Konneker Distinguished Professor of Physics.

Although he grew up on the East Coast and first taught at the Massachusetts Institute of Technology, Bender is a confirmed Midwesterner.

In addition to the ease of life in St. Louis, he appreciates the high caliber of the Washington University students. “The undergraduates here are really, really good,” he says. “They are the smartest students I’ve ever met. They also are nice kids and a lot of fun to teach.”

Bender treats many of these students as colleagues, co-authoring several papers with them.

One of the biggest thrills of his research, he says, is how many people have advanced their own work using his theory.

“Physics is a very combative field. If you want to convince physicists you have to have a very big fight and that is how it should be. The first reactions were shock and horror, but what has happened is that hundreds of people all around the world have joined in and I’m, well, basically I’m the leader,” he says with delight.

“You can’t imagine how fantastic it is to go to an international conference where every single paper presented is in this new field. I’ve done lots of work in my lifetime, but this is the first time something this cool has happened to me.”