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Jim Gates and the symmetry of space and time

Physics professor Jim Gates, AAAS Fellow, uses mathematics to explain how the universe works. | Drew Costley

Jim Gates, physics professor and string theorist at the University of Maryland, began his journey of discovering and attempting to explain the universe when he was 4. His family was living on an Army base in St. John’s, Newfoundland, and he had just watched a movie called “Spaceways” about astronauts, rockets, and countdown launches with his mother.

“From this movie I got the idea that this thing called science was how you got to do that stuff,” Gates said.

He said that after the film he tried to explain how rockets worked to his family, and his parents took note of his newfound interest. Gates’ father bought him four books in the popular Adventure in Space children’s series by German-American science writer Willy Ley, which eventually led him to do pioneering work in string theory and supersymmetry.

“One of the things I got from these books is an understanding that the spots of light in the night sky were not just lights, but they’re places,” Gates said. “That’s when I had what I call my own personal Big Bang between my ears, when I was 8 years old. That’s when I really began to understand something about how big the universe must be.”

Gates’ wonderment about space put him on the edge of what the world knows about the universe. When he was a graduate student at the Massachusetts Institute of Technology (MIT) in the mid-1970s, Gates decided he wanted to work on supersymmetry, but couldn’t find a professor at the university who studied the subject. It was a predictable consequence of his decision to study the subject, which he admits was calculated.

“I decided the appropriate thing to do was figure out what there was on the horizon that looks like it’s going to be important over an extraordinary long time period. So I started making these big lists of what people were doing...and in this survey...I came across one or two papers on this new mathematical idea called supersymmetry,” Gates said.

“I read them and I thought, oh my God, this is mathematics that I’ve never seen before and I was a second or third graduate student at MIT, so I should have seen most of the math that’s going to be important. These papers had ideas that had never appeared before and in reading them I came to understand pretty quickly that if these ideas were correct they were going to be more forms of matter and energy than anyone had ever imagined.”

Supersymmetry is a proposed symmetry of space and time that relates to two elementary particles, bosons and fermions, in which each particle is associated with a particle from the other.

He wrote MIT’s first Ph.D. thesis on the theory, and within the decade, co-authored “Superspace, or One Thousand and One Lessons in Supersymmetry,” the first comprehensive book on supersymmetry.

Surprisingly, the time he spent pioneering this new scientific field was the worst period of his life. “When you’re in your 20s you’re still trying to figure out who you are, you’re trying to figure out what your relationships are to other people, you’re trying to figure out how you’re going to build your life, there’s a lot of uncertainty…. In my life, that went on all through my 20s. I hated that period.”

The most exciting period of his career is now. During the past 20 years his research has focused on what have come to be known as adinkra symbols, which are geometric objects that are diagrammed and encode mathematical relationships between supersymmetric particles, like bosons and fermions.

“These things are kind of like genes. In biology, genes make cells that then make creatures,” Gates said. “In mathematics these little objects that we eventually gave the name adinkras, they were creating the mathematics of this balanced universe.”

The concept of adinkras crystallized for Gates in 2000, when he was at the California Institute of Technology, on a sabbatical from his regular teaching job at the University of Maryland.

Years later, after Gates attempted to talk to several physicists about adinkras but couldn’t get his message across, he assembled an interdisciplinary team of physicists and mathematicians to focus on the new science. “Out of that collaboration the first great discovery that we found was that these adinkras are always related to cubes, not necessarily in our space, but in [fermionic dimensions of superspace],” Gates said. This means that adinkras can show, when based on four-dimensional hypercubes, or tesseracts, how a particle in our dimensions relate to a particle in this other dimension.

Insights like this one gleaned from adinkra diagrams, Gates wrote in a piece for Physics World in 2010, have allowed scientists to better understand nuclear matter.

The next discovery that the team made was that adinkras have built-in error correcting codes, which check transmitted data for errors and corrects them as soon as they are found. Gates said that was the “most stunning” discovery of his work so far. But the most recent discovery, led by Charles Doran, a member of Gates’ team and a professor of mathematics at the University of Alberta, is that a certain number of copies of any single adinkra can be “glued” together, preserving the alignment of the open and closed nodes and the colored links to form a Riemann surface. A Riemann surface is a geometric representation of a function of complex variables in which a multiple-valued function is displayed as a single-valued function on multiple planes, some of which are connected at some of the points, at which the functions take on two or more values.

“The thing that’s amazing about that to me is that Riemann surfaces are actually the basis of string theory,” Gates said. String theory is a theoretical framework in which point-like particles, particles that have zero-dimensions, are replaced by one-dimensional objects called strings. The theory, which attempts to answer several questions in fundamental physics, describes how these strings propagate through space and interact with each other.

The scientific discoveries that Gates and his interdisciplinary team are working on might not have practical application today or tomorrow, he said, but he pointed out that James C. Maxwell’s equations describing how electricity and magnetism are related, which serve as the basis of WiFi, were made in the 1860s.

Adinkras, Riemann surfaces, strings, and how they can contribute to our understanding of the universe, still leave Gates awestruck. He said the importance of Riemann surfaces in string theory is that they are used to find properties and predictions made from superstring theory when the effects of quantum behavior are included.

“So we’ve found some kinds of objects that are more primitive than strings that ultimately I expect are going to be the ‘genes’ of string theory, too. So we’ve found some fundamental mathematical objects…[that, if supersymmetry is real] are going to be controlling the math that describes our universe,” Gates said.

“And, for me, that’s amazing because when I was young I always wondered if I could find a magical piece of mathematics that was also an accurate description of nature. And so if supersymmetry is discovered, I would have done exactly what I set out to do when I was younger.”

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<p>Physics professor Jim Gates, AAAS Fellow, uses mathematics to explain how the universe works. | Drew Costley</p>
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