Research

Essential Content of Physical Theories: The foundation of my research in philosophy of physics is my views on the essential content of physical theories. The "essential" content is those parts of a theory that actually matter for the predictive success of the theory. For example, what does a formula such as Newton's second law (F=ma) really tell us? The most straightforward answer is: "the quantity of force equals the product of mass and acceleration". But is this talk of entities and properties such as forces and masses in fact what makes the theory predictively successful? Or is the part of the theory that matters perhaps the structure of the theory? Or something else? In my dissertation, I argue that the essential content of physical theories is not a description at all (whether of entities, properties, or structures). Rather, the essential content of these theories is their prescriptions for how to construct certian theoretical quantities from local experimental data. What makes the theory successful is not what it says about what there is, but rather what it tells us about what to do.

Relation between theory and world: How are theoretical terms of a successful theory related to unobservable objects of reality? Some philosophers suggest that the entities or properties in the theory must directly refer to or represent entities and properties in the world. Others say that the structure of the theory must resemble the structure of the world. But none of these approaches seem to hold up in the face of the history of science. Niels Bohr's model of the atom, for instance, is excellent at predicting a whole host of phenomena in single-electron systems, but its entities (little charged grains of dust) and the properties it attributes to them (swirling around a nucleus) are completely wrong, at least if quantum mechanics is correct. So what made Bohr's theory so successful? I argue that this success has to do with its prescriptions for how to assign dynamical states to the system. Therefore, it is the states that must somehow connect to unobservable reality, not entities or properties or structures. But states have a much more sophisticated relationship to reality: they do not refer to or represent or resemble the true states, but rather track them in a precise, mathematical sense. The cool thing about tracking is that it is referentially opaque, meaning it doesn't commit us to saying that the ontology of Bohr's theory must correspond to reality in order for it to be successful. Unlike reference, representation, and resemblance, which are static relations, tracking is a dynamical relation, which must take into account not only what state the system is in, but also how this state evolves.

Theoretical Equivalence: When are two physical theories equivalent to each other? For example, why do physicists say that Hamilton's theory of mechanics is equivalent to Lagrange's, despite the fact that each has models that the other lacks? Some philosophers say that to be equivalent, two theories must be intertranslatable, which indicates a one-to-one correspondence between the sentences of the two theories. Others look for a one-to-one match-up between the structures of one theory and those of another. Yet others appeal to more abstract mathematical constructs like "category theory" to explicate equivalence. What all of these approaches have in common, though, is that they take the theory to be fixed, meaning they assume the theory is the same pre-ordained set of statements or models in every application of the theory. But if I'm right and theories are prescriptions for constructing theoretical quantities from local data, then they must be partly open-ended, because at any point new data might indicate a new model we had not considered before. One cannot list the statements or models of a theory once and for all. Thus, there can be no such thing as a one-to-one match-up of any kind between them. Part of my project is to define a new notion of equivalence which is based on the sameness of the fixed parts of theories, and thus allows two equivalent theories to have non-overlapping models (due to the open-ended part).

Realism or anti-realism? How should we explain the wide-ranging and impressive success of our physical theories in making predictions? Is it because the theory is in some sense approximately true? Does it mean that the ontology of the theory corresponds to reality? Philosophers of science fall into two distinct camps regarding this question. Realists claim that the enormous success of the theory would be an inexplicable miracle unless the theory is some kind of a window to unobservable reality, allowing us to read off the ontology of the world from the theory. Anti-realists, on the other hand, find the realist's claim problematic because of its poor historical track record (see the Bohr example above). So anti-realists go on to claim that successful theories need not be related to truth in any way at all. Both camps are unsatisfactory. If successful theories are windows to reality, then why have all of our past theories been fundamentally wrong? And if they are not related to reality in any way at all, then what allows them to succeed in experiment after experiment, in very wide ranges of conditions? I argue that this is a false dichotomy: physical theories are connected to unobservable reality in a robust and systematic manner (through tracking), so their success is not a coincidence; yet since this connection is referntially opaque, one cannot expect to read off the ontology of the world from the theory. This passes both the explanatory and the historical tests!

History of quantum mechanics: All of the lessons above can be gleaned from the history of the formation of quantum mechanics starting with Niels Bohr's atomic model and ending with Werner Heisenberg's matrix mechanics. Bohr's proposal was very successful in predicting the behavior of single-electron systems like the hydrogen atom or the helium ion, but it failed to track systems that had more than one electron. Twelve years of struggle between 1913 and 1925 led physicists such as Heisenberg to the conclusion that what is hamstringing the theory is the pesky orbits that the electrons are supposed to be following in Bohr's "planetary" model of the atom (like the picture above). By getting rid of the orbits, Heisenberg achieved two goals simultaneously: first, he purged the theory of entities and properties, and kept only the state assignments without saying what these states are states of; second, by removing the orbits, Heisenberg made the theory fully open-ended. This is because in Bohr's theory, one would calculate the orbits from mechanical principles and then use the orbits to predict the probability of an electron transitioning between two given states. By getting rid of orbits, Heisenberg essentially declared that the transition rules must be read off empirical data, rather than imposed from theory. The state assignments give us a framework in which to summarize these transitions, but they cannot dictate the transitions themselves.