Becoming An Empiricist Theorist
With this first post I wish to set the tone for my blog by explaining and exploring my perspective on science. Concurrently, I wish to introduce myself beyond my website's content, relate my scientific influences and interests, and preview topics about which I might write. This post is notably more personal than I anticipate subsequent posts to be.
As I proclaim on my website's homepage, I am a theoretical physicist with empiricist inclinations. What do I mean by empiricist inclinations? (I assume that you already know all about theoretical physicists!) To answer this question, I will present my perspective on science, elaborate on how I came to this perspective, and illustrate the application of my perspective. I will not proffer a detailed philosophical position: I am not particularly interested in enunciating and defending such a position; I am far more interested in the lessons for physics that my perspective affords. Moreover, strict empiricism as a philosophy of science no doubt has its pitfalls, and I make no claim to be a strict empiricist. Rather, the word empiricist captures and conveys my perspective relatively well (and nicely complements the word theorist). Let me now begin to expound upon my empiricist inclinations by highlighting some key elements of my perspective on science.
First and foremost, observation and experiment ground science. This seemingly uncontroversial statement is, unfortunately, not universally accepted among scientists, theoretical physicists notably included. Second, scientists develop approximate descriptions of their observations and experiments, namely scientific theories. These descriptions do not necessarily provide explanations of these observations and experiments. (Genuine explanations do exist within scientific theories; however, whether or not such explanations entail explanations of observations and experiments is an entirely separate question. For instance, the general theory of relativity provides an explanation for the equivalence of gravitational and inertial mass; this explanation does not necessarily entail the equivalence (within experimental bounds) of what experimental physicists identify as gravitational and inertial mass in their experiments.) Third, two (or more) scientific theories might describe the same set of observations and experiments. If one of these theories possesses further descriptive power, then one should prefer this theory. When neither theory possesses more descriptive power, many scientists would like to employ simplicity as a criterion to adjudicate between such theories; unfortunately, simplicity, for the most part, is in the eye of the beholder. Fourth, I do not consider myself a scientific realist: the content of scientific theories does not necessarily reflect an underlying reality. That said, if our scientific theories allowed for a straightforward, unambiguous interpretation in terms of an underlying reality, then that would be fantastic. I do not believe that current scientific theories, particularly quantum mechanics, allow for such an interpretation; furthermore, I see no compelling reasons to believe or hope that such an interpretation will be forthcoming.
Regarding the practice of science, I advocate a pragmatic approach founded upon intellectual honesty and constructive criticism. Science is a social enterprise in which scientists convey their ideas in written and spoken word, in which scientists debate each other's ideas and results to make progress. Unbiased, frank interaction is essential. This interaction starts with one's own work and presentation thereof. In the communication of science, I highly value conceptual explanation and conceptual understanding. Indeed, I value conceptual over mathematical clarity despite the fact that science—particularly theoretical physics—requires a certain degree of mathematical rigor. In the communication of science, I also highly value precision and ingenuity.
I have no idea how prevalent amongst scientists—or, more specifically, theoretical physicists—is a perspective like my own. My perspective must not be too prevalent as there are many arguments, explanations, folklores, and the like that would benefit from the clarification, elucidation, and illumination afforded by my perspective. Accordingly, my perspective on science—on theoretical physics, in particular—motivates this blog. I plan to bring my perspective to bear on these many arguments, explanations, folklores, and the like. As I emphasized above, my interests lie not in expounding my perspective but in applying my perspective. Accordingly, I will not actively attempt to convince readers of my perspective; rather, through my subsequent posts I hope that my perspective provides useful insights into physics.
As I detail below, I have (of course) not always been a theoretical physicist, and I have certainly not always harbored empiricist inclinations. Ernst Mach, a noted empiricist, wrote in The Science of Mechanics that
The historical investigation of the development of a science is most needful, lest the principles treasured up in it become a system of half-understood prescripts, or worse, a system of prejudices. Historical investigation not only promotes the understanding of that which now is, but also brings new possibilities before us, by showing that which exists to be in great measure conventional and accidental. From the higher point of view at which different paths of thought converge we may look about us with freer powers of vision and discover routes before unknown.
To lay bare my own prejudices—as well as accidents and conventions—I will recount how I came to embrace the scientific perspective espoused above. This history intimately intertwines with the evolution of my interests in physics. In telling this history, I also illustrate the application of my perspective in two contexts, an approach to quantum gravity (that I research) and the quantum measurement problem. I begin with the origins of my interest in physics, and I return to the theme of Mach's statement shortly.
My interest in physics developed early in middle school, undoubtedly influenced by my newfound obsession with Star Trek: The Next Generation and my reading popularizations of The Feynman Lectures on Physics. I had been drawn to science for as long as I can remember. My early childhood interest in dinosaurs—so typical at that age but possessing more serious intent than outright enthusiasm—gave way to a profound interest in human origins. Throughout elementary school I had my heart set on becoming a paleoanthropologist (in the vein of my then idol Louis Leakey). Why then did physics captivate me, entice me away from such definite dreams? Reflecting on the formation of my interest in physics, I believe that one realization proved critical: physicists address the most fundamental scientific questions. (I do not now wish to enter into a prolonged discussion of the meaning of fundamental. Although my younger self most likely thought otherwise, I would contend that my above statement is largely a matter of definition: physics aspires to be the science that underlies all other science. Furthermore, in no way do I mean to belittle any other scientific investigations. Scientific questions outside of the foundations of physics are certainly no less important, no less valuable.) Pursuing answers to the most fundamental scientific questions resonated with me as nothing else had previously, not even excavating our ancestors' remains in Africa's Rift Valley. I still follow developments in our understanding of human origins, but I never looked back on my paleoanthropological plans. I was intent on becoming and remain intent on being a physicist.
Through high school and into college my enthusiasm for physics intensified. I read widely—from John Gribbin's In Search of Schrodinger's Cat to Brian Greene's The Elegant Universe to my first downloads from the arXiv. (After a public lecture I even asked Greene for further suggestions.) I took all of the physics courses that my high school offered. When I exhausted these offerings, I created an independent study. This independent study nurtured an interest in the historical development of our scientific theories. Specifically, I came to view an understanding of the development of our physical theories as a means to deepen my own understanding of these theories. (I had not yet read Mach's book.) I carried this viewpoint into college, where I spent one January term studying Maxwell's original works on electrodynamics and another January term studying the founding papers of quantum mechanics.
My first tastes of research came during this time. I spent the summer after my junior year of high school in Lyman Page's cosmology group, mostly soldering circuit boards and routing cooling tubes, and I spent the summer after my freshman year of college in Tiku Majumdar's atomic physics group, mostly aligning laser beams and establishing thermal contacts. I became quite proficient at soldering but not aligning. The summer after my sophomore year of college, I worked with Bill Wootters on my first project in theoretical physics: analyzing the temperature dependence of mutual information in classical and quantum harmonic chains. These experiences definitively convinced me of what I had tentatively suspected: that I wanted to become a theoretical physicist.
The summer before my senior year of college, my longstanding curiosity about the physical nature of time came to the fore. At the time I was beginning to work on my senior thesis under Wootters' guidance. We spent the first few weeks of summer discussing and investigating potential topics. I soon latched onto his research with Don Page, pioneered in their paper (with the Wheelerian title) Evolution without evolution, in which they propose a method for recovering dynamics within globally stationary quantum states using select subsystems as internal clocks. Their proposal is often called the Page-Wootters approach to or the conditional probability interpretation of the problem of time in quantum gravity. (This line of research has seen renewed interest in the past few years.) Wootters and I set the ambitious goal of understanding how the second law of thermodynamics might arise within the Page-Wootters approach.
That same summer I discovered and devoured three books: Julian Barbour's The End of Time, Huw Price's Time's Arrow and Archimedes' Point, and Lee Smolin's Three Roads to Quantum Gravity, all drawn from David Park’s bookshelves. The first has proved most influential, the second intermittently nags at the back of my mind, and the last directed me down the road to quantum gravity. As best as I could judge at the time, research in quantum gravity was a nexus for the foundational questions that had come to most interest me—or at least researchers in the field of quantum gravity, like Smolin, were deeply interested in these questions. I truly thought that by studying quantum gravity I would achieve deeper insight into the fundamental natures of space and time. I would write as much on my graduate school applications. (I searched for the original language, but it must be lost on a now ancient hard drive.) Indeed, at the height of the string wars, still very much influenced by researchers like Smolin, I would write that I had more interest in loop quantum gravity than string theory; perhaps that explains my many letters of rejection. (I do not now hold any general bias against either loop quantum gravity or string theory; indeed, I wish that I understood both of these research programs more thoroughly.)
Upon graduating from college, I embarked upon a two-year fellowship at the University of Cambridge. In my first year I studied pure mathematics with an eye towards a future in theoretical physics. I quickly learned, however, that I could not sustain an interest in mathematics in and of itself. In my second year I completed a masters in history and philosophy of science. While I enjoyed immensely working with philosophers Jeremy Butterfield and Peter Lipton, I confirmed that physics, not philosophy, was my calling. The summer between my two years, I lived and worked with Barbour at his farmhouse in the Cotswolds.
I arrived at graduate school still intent on researching quantum gravity, and, as planned, I joined Steven Carlip's group. I began working on a project of his suggestion: understanding the relationship between bulk and boundary unitary evolution within the anti-de Sitter--conformal field theory correspondence. We were primarily motivated to understand the nature of the resolution of the black hole information paradox in this context. Needless to say, I did not make much progress. This relationship remains an outstanding problem within the anti-de Sitter—conformal field theory correspondence; though, the last few years have witnessed some notable progress.
Another of Carlip's students, Rajesh Kommu, had recently coded the first independent implementation of causal dynamical triangulations, and one of my classmates, Michael Sachs, had begun to study the spectrum of geometric perturbations on spacelike 2-spheres within this approach to quantum gravity. Accordingly, our weekly group meetings witnessed considerable discussion of causal dynamical triangulations. With my initial research project floundering, I gradually fell into working on causal dynamical triangulations. At first, to be honest, causal dynamical triangulations did not hold much appeal as an approach to quantum gravity—I had never been interested in computational research, and I questioned its assumption of causality—but I sorely needed to make progress on a project. As I continued to work on causal dynamical triangulations, its appeal continued to mount.
Why did—and why does—causal dynamical triangulations appeal? I discovered that causal dynamical triangulations is an approach to quantum gravity in which one can—indeed, must—directly ask and address questions of physical import, moreover, using a relative minimum of mathematical formalism. Computer simulations generate (representative samples of) numerical representations of spacetimes contributing to the gravitational path integral from which one must extract and analyze physically meaningful information to determine and assess the predictions of causal dynamical triangulations. This challenge appealed to my emerging empiricist inclinations. (Of course, there are caveats: for instance, computer simulations run post Wick rotation, so one asks and addresses questions in the Euclidean domain, the connection back to the Lorentzian domain being not yet clear.)
Still, when I headed to a postdoctoral fellowship in Renate Loll's group, I was not convinced that I wanted to continue working on causal dynamical triangulations. Loll encouraged me to think much more deeply about renormalization in the context of causal dynamical triangulations. This line of inquiry led me to explore much more deeply the theoretical underpinnings of causal dynamical triangulations. As I scrutinized these underpinnings, I came to appreciate the constraints and motivations that led Loll and her collaborators to formulate causal dynamical triangulations, and I came to accept the approach’s causality condition as a compromise enabling the rigorous exploration of nonperturbative quantum gravity via standard computational techniques.
Is causal dynamical triangulations the end all and be all of quantum gravity? This question is entirely premature for not only causal dynamical triangulations, but also every other approach to quantum gravity. We simply cannot address this question without comparing the approach's predictions to observational or experimental findings. Causal dynamical triangulations has yet to yield any results that I would categorize as predictions capable of being compared to observation or experiment. (Replace causal dynamical triangulations with string theory, loop quantum gravity, or any other approach to quantum gravity, and the previous sentence rings just as true.) Observations and experiments potentially requiring (nonperturbative) quantum gravity for their description are also lacking, though not for lack of effort.
My work on this one approach to quantum gravity notwithstanding, I no longer believe that studying quantum gravity will lead to an understanding of the fundamental natures of space and time; heck, I do not even believe in space or time as fundamental entities. My hopes now rest on our (eventually) making predictions of genuine quantum-gravitational phenomena and in experimentalists (eventually) attempting to perform observations of these phenomena. (I fully acknowledge that theoretical physicists have made predictions of quantum-gravitational phenomena and that experimentalists have attempted to perform observations of these phenomena. To my knowledge, however, none of these predictions follow directly from a nonperturbative approach to quantum gravity like causal dynamical triangulations.) Despite the remote prospects for such observational and experimental predictions and findings, quantum gravity, including its less directly empirical aspects, continues to hold my interest above all else. My interest in other areas of physics has grown, but I still maintain that quantum gravity ranks amongst the most fundamental problems currently facing theoretical physics, and I still cannot resist those most fundamental scientific questions.
As a first-year graduate student, I organized a reading group on the foundations of quantum mechanics. My interest in quantum foundations originated with my reading popularizations of quantum mechanics, and my interactions with Wootters heightened my interest. I did not intend to conduct research in quantum foundations, but I wanted to feed my interest and expand my understanding. While initially well-attended, the group rapidly reduced to two stalwarts: myself and philosopher Paul Teller. We maintained this reading group through all six years of my graduate schooling, meeting every two weeks to discuss quantum mechanics (and, occasionally, other topics in the foundations of physics). Our discussions were truly a highlight of my graduate experience. I now attribute these interactions with Teller to nurturing my nascent empiricist inclinations. I do not know that Teller would describe himself as an empiricist, but his dogged pragmatism about physics effected a gradual, notable change in my outlook. In particular, Teller had studied Niels Bohr's writings, and their influence on his thinking about physics was often in evidence. I have not (yet) read Bohr's writings, but I strongly suspect that I would largely agree with many of his perspectives.
Within the foundations of quantum mechanics, the quantum measurement problem has long fascinated and intrigued me. Initially, the potential for interpretations of quantum mechanics to solve the measurement problem held considerable interest. I distinctly recall favoring the Everett interpretation, also known as the relative state or many-worlds interpretation. (Everett's relative quantum states figure prominently in the Page-Wootters approach.) Surely, the idea of ever-branching, parallel existences enchanted my naive, Star Trek-obsessed self while the argument that quantum mechanics needs no additional structures—neither the collapse postulate nor the Born rule—for its implementation and interpretation appealed to my thoughtful self. Now, however, I do not grasp what one gains from the Everett interpretation (unless you count, for instance, David Deutsch's insights into quantum computation, which, I understand, he partially attributes to the perspective afforded by this interpretation). I would argue that any and all experiments and observations—even cosmological—performed thus far are perfectly consistent with and interpretable within Bohr's framework, the much maligned Copenhagen interpretation. Moreover, I remain unconvinced by supposed derivations of the Born rule within the Everett interpretation. Still, some small fragment of myself sometimes agrees with John Wheeler's quip about subscribing to his graduate student's interpretation every other day of the week.
Despite my disinterest in interpretations of quantum mechanics, the quantum measurement problem still holds my interest. I am now largely convinced of its insolubility within the framework of quantum mechanics. Accordingly, the nature of my interest has changed: I seek solutions that invoke physics beyond quantum mechanics such as spontaneous collapse and superdeterministic models. While no particular spontaneous collapse or superdeterministic models enamor me, I appreciate the intent of these attempts. Still, some small fragment of myself sometimes hopes that one can resolve the measurement problem wholly within quantum mechanics, and some other small fragment of myself sometimes sympathizes with the claim, recently espoused with characteristic clarity by David Mermin, that there is no quantum measurement problem.
There you have it—highlights from my journey to becoming an empiricist theorist. I hope to have reasonably conveyed the nature of my empiricist inclinations and to have piqued your interest in what I plan to write about here. My empiricist inclinations will undoubtedly become abundantly apparent through my subsequent blog posts. I hope that you stay tuned.
