Relativity

Physics Memories

I recently read a history of Einstein's theory of general relativity. Among the names of many scientists who made important contributions to the theory were those whose books and papers I read during my career. In some cases, I had seen these physicists in person and attended their talks. Although physics was my life before retirement, I've now left it almost completely behind. Reading about the development of general relativity evoked strong memories of my own intellectual journey, made me briefly nostalgic about my former life, and motivated this autobiographical post.

How I loved relativity theory! Relativity was my specialty. Relativity was the reason I chose to make physics my profession. The initial spark was struck by something my father said during a big family dinner when I was a boy. We sat around my Polish grandmother's dining room table admiring a huge steaming bowl of homemade pierogies. My father, who must have been reading a popular article about relativity, said, "If we could understand time, we could understand everything." For some reason this pronouncement captured my attention and started my life-long quest to study time. Later, when I learned Einstein's theory of relativity held the key to understanding time, I wanted to learn this theory. I also heard the myth that very few people were smart enough to understand relativity. Learning about relativity, I thought, would not only bring me a deeper understanding of time, it would also be a test of my intellectual capacity.

So I took lots of math and physics courses in college. My initial encounter with relativity during sophomore physics yielded only shallow understanding. By senior year, however, I had learned enough mathematics and solved enough problems to gain some intellectual maturity. I began studying relativity on my own. Between regular classes and assignments I spent every spare minute in the library studying tensor analysis and introductory general relativity. I had switched my major from electrical engineering to physics, and did my senior research project in general relativity working with Dr. Ronald Gautreau helping him investigate the meaning of certain solutions to Einstein's equations. It was intoxicating to know I was the only undergraduate at my college working in general relativity.

In graduate school I continued the quest. Gautreau recommended Temple University where I could work with the resident relativity expert, Dr. Peter Havas. At Temple I was in a bigger league, but really a minor league, like AAA baseball. Princeton, the major league, had rejected my grad school application. That was a good thing because I would not have survived at Princeton. Honestly, I wasn't smart enough for Princeton. It's not that I didn't try. I spent years filling page after page with calculations trying to find solutions to Einstein's equations. My work resulted in stacks of paper a few meters high. This is no exaggeration. When I eventually discarded these calculations, they filled more than one garbage can to full height! Einstein's equations, the basic equations of general relativity, are ten, simultaneous, coupled, nonlinear, partial differential equations virtually impossible to solve without simplifying assumptions. I tried my hand at making clever original assumptions. None of my assumptions worked. It was exhilarating to be working with such high powered theory, but disappointing to have so little success.

The original plan was to work with Havas at Temple, but I found him to be intimidating and unapproachable. He had swept back silver hair and a German accent. His favorite game was destroying colloquim speakers with devastating remarks at the talk's conclusion. Havas would say things like: "Vell, from ze first  sentence of your talk I can see zat you don't even understand Newton's First Law!" Havas knew I was interested in relativity, and he knew I wanted to work with him, but if we approached each other head on in a hallway, he would not acknowledge my existence. If we happened to be in the men's room alone together, he would not even nod or say hello. I couldn't imagine working with such a cold mentor. (Imagine my anxiety when he was appointed to my thesis committee and when he participated in my oral exam.) Instead, I worked with Dr. Mael Melvin who researched cosmological applications of general relativity. Melvin was a bit eccentric, but, compared to Havas, Melvin was friendly, patient, and sometimes encouraging.

Melvin set me working on my doctoral thesis, an investigation of possible universes filled only with neutrinos. The actual universe is filled with matter and energy, and its evolution is described by the equations of general relativity. I investigated an imaginary model universe filled only with neutrinos, a situation that might have been relevant at some time in the past. Melvin suggested using a relatively obscure mathematical formalism that expressed general relativity in terms of three-dimensional vectors and dyadics instead of the usual four-dimensional tensors. Three years of laborious calculations later I produced a thesis titled: Homogeneous Cosmologies with Strong Neutrino Fields, a title that often provokes laughter.

Sometime during my final year in grad school Melvin took me to a talk at Princeton. After the talk we went to a conference room and sat around a table with relativity geniuses on Mount Olympus. There I sat for an incredible hour in the inner sanctum of relativity. I was introduced to the famous John Wheeler, who had worked with Niels Bohr and taught Richard Feynman. Wheeler shook my hand. He graciously asked me a question about my thesis. I mumbled some reply. I was completely overwhelmed by the high-powered intellects present and could barely speak. That was the zenith of my career as a general relativity researcher.

I learned a lot in grad school. Along with a deeper understanding of the mathematical structure of relativity theory I also learned my place in the intellectual pecking order: I was smart enough to understand and appreciate relativity theory, smart enough to work with the mathematics, but not smart enough to make important original contributions to research. I was smart enough to appreciate genius, but not smart enough to be a genius myself.

In grad school I learned theoretical physicists working in general relativity were not in high demand. A more practical career path, a more employable specialty, would have been experimental physics focused on properties of materials. But I was completely, utterly, uninterested in the properties of molybdenum, so I stayed with my first love, relativity.

In grad school I learned how survival at a research university requires constant publication, continual cultivation of reputation, and repeated acquisition of funding through research grants. Strong self-confidence and persistent salesmanship are required in order to obtain research grants. Important people must be impressed enough to award money, employment, and opportunities. Grant proposals are really elaborate ways of proclaiming, "I'm wonderful, and the spectacular work I do is fundamentally important." To me, this seemed like bragging. It conflicted with my personality. Aggressive self-promotion and immodesty are unseemly to me.

Fortunately, in grad school I also discovered some talent for teaching. So, instead of following the usual route of postdoctoral research appointments after grad school, I applied for teaching positions at small colleges. It was a brutal job market for new PhD's at the time. Thank goodness I was lucky enough to find a position at Randolph Macon Woman's College (now Randolph College). It was exactly the right place for me, although I was a one person department, completely overwhelmed preparing and teaching almost every course in the undergraduate physics curriculum and running the college observatory as well.

During my first few years at Randolph Macon Woman's College I tried to keep working on general relativity. I published a paper based on my thesis and studied gravitational waves over the summers. Gravitational wave calculations produced more stacks of paper several inches high. In December, 1980 I had a revelation at the 10th Texas Symposium on Relativistic Astrophysics in Baltimore, MD. While attending talks there I realized I didn't know a single person at the meeting. I was completely outside the loop. At one particular talk the empty seat beside me was suddenly occupied by the famous Kip Thorne, one of John Wheeler's genius students and a distinguished expert on black holes. A bolt of insight hit me as I glanced at him. Kip Thorne and his fellow relativity geniuses were not only much more talented than I, they were also not teaching five courses a semester like I was. They were working year round with high-powered colleagues. I could never keep up with them or hope to compete on their level. In that moment I understood I was an undergraduate physics teacher, not a relativity researcher. I gave up any hope of original research in relativity and devoted the rest of my career to teaching.

Through years of teaching I learned more about relativity than ever before. My conceptual understanding increased greatly because I had to craft clear explanations for students. Two of my strong students did senior honors projects in general relativity under my guidance. It was nice to visit my old intellectual stomping grounds with these students. After retirement my long, slowly diminishing dance with relativity came to an end.

During this long dance I gained profound insights:

• I can still feel the wonder of first understanding the relation of gravity to reference frame acceleration. It was similar to hearing Chopin's Prelude 13 for the first time.
• It was a thrill to understand how the fundamental nature of gravity is not its value at a single point, but how it varies from point to point.
• I was astounded to learn how application of the Principle of Relativity to quantum mechanics led to the incorporation of particle spin and the prediction of the existence of antimatter. Antimatter actually exists!
• It was great working through the mathematical description of black holes. These exotic objects were predicted by general relativity, and they actually exist!
• Gravity governs the overall evolution of the universe, and general relativity is our best description of gravity. General relativity predicted the observed expansion of the universe.
• I spent many hours thinking about time travel and exploring the amusing paradoxes it can include. Time travel to the future is actually possible and has been observed! Time travel to the past is another story.
• Near the end of my career I came across a profound insight: time is not an observable in quantum mechanics! There's something very deep here, but I'm not the one to figure it out.

My dance with relativity is definitely over. At this point my burnt out brain is a smoldering, smoking ruin. I'm no longer able to run a 5-minute mile, see clearly without glasses, or do any work in general relativity. But I still remember what it was like.

Here's a very brief, incomplete, and very superficial look at Einstein's famous general relativity field equation:

This equation, written on one line, is really shorthand notation hiding a mountain of complex mathematics. The Greek letter subscripts, called indices, can each take on 4 different values. So Einstein's equation is really a shorthand way of writing 16 different equations, ten of which are independent. Also, most of the symbols themselves are shorthand names. For example, the R symbol, called the Ricci Tensor, describes the curvature of spacetime. It is defined in terms of other symbols as follows:

The symbols after the last equal sign on the right, called Christoffel Symbols, are, in turn, defined in terms of the metric tensor, the g symbols, as follows:

Perhaps you can see how writing out all the terms on the left hand side of Einstein's equation would quickly spread across many sheets of paper. In fact, the entire left hand side of Einstein's equation can ultimately be expressed in terms of the g symbols. Solving Einstein's equations means solving for the g symbols. This is the mathematical jungle I staggered through for many years.