Teaching
Feynman famously wrote that “I think I can safely say that nobody understands quantum mechanics. ... Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.” But that seems like a perfect question for philosophers – and some physicists – who want to know what quantum mechanics is (or isn’t) telling us about the world: how can it be like that? For instance, is Schrodinger’s cat really ‘dead and alive’? And what does it mean for it to ‘become’ dead or alive when we ’observe’ it?
To tackle this question, we will study the foundations of quantum mechanics. We start by understanding the ’bare formalism’ of quantum mechanics at a conceptual and logical level, and the crucial experiments in support of this formalism over the classical picture. We then consider three questions at the core of this formalism: the measurement problem, the Einstein-Podolsky-Rosen argument for non-locality, and Bell’s theorem. We will then study ’the standard picture’ to quantum mechanics: the so-called Copenhagen interpretation, and an emphasis on measurement and instrumentalism, diagnosing some conceptual worries with this picture. We then turn to three robust families of proposals for approaching quantum mechanics and its ontology: the Ghirardi-Rimini-Weber (GRW) theory, Bohmian mechanics, and the many-worlds interpretation. In so doing, we engage with philosophical questions about locality, determinism, the dimensionality of fundamental space, underdetermination of theory by data, scientific realism, the arrow of time, the meaning of quantum probabilities, among others.
There is no formal prerequisite for the course, though a high school or undergraduate background in physics will be extremely helpful. A tolerance for math is important, however, as we’ll dive into physics. Every effort will be made to present the math and physics as cleanly and accessibly as possible. Students without technical backgrounds can and do thrive in this course, so long as math anxiety is left behind.
Space and time are probably intuitive concepts to many of us. Clocks tick down, trees grow taller. Things were here, now they are there. We have memories of the past, of things back then, but not of things in the future. But despite their familiarity, space and time do not seem to be the same sort of stuff as tables or chairs. So what are they, really? Are they “real"? Is there a sense in which space and time are substantial ‘stuff’ at all? If they are, are they the same kind of stuff? Can we travel through time, like traveling through space? Could we live in a world where space and time are not ‘really’ there, where they are merely emergent? Can influences travel across
arbitrary large spatiotemporal regions instantaneously?
Some of the greatest thinkers in history have considered these questions, from the Presocratics and Aristotle, to Newton, Leibniz, Kant, Poincare, and Einstein. These are also questions which continues to occupy many philosophers and physicists today. This course will introduce you to some of the ways one can conceptualize, and question, the nature of space and time. The first half of the course will take us through a brief tour of the history of philosophy of space and time, from the Presocratics to Einstein’s theory of relativity. The second half will sample some contemporary topics in the philosophy of space and time.
A traditional standard for knowledge requires certainty. With that standard in mind, Socrates responded that the only thing he knows is that he knows nothing. Meanwhile, confidence men will happily tell you they know the answers to all your problems. Where should we stand? What we know is probably somewhere in between, and the question is: where's the line between the known and the unknown, and how do we draw it? This course will help you trace your own line between the known and the unknown, by taking you through various epistemological, metaphysical, and methodological problems with the search for knowledge. Hopefully, along the way, you can make up your own mind about what you can confidently say you know, and what you are prepared to commit to the flames.
The first half of the course will introduce you to some traditional problems of philosophy, concerning our knowledge -- and the reality -- of certain mundane things: of the external world, of the self, of personal identity, of consciousness, of other minds, and of time. The second half of the course begins with a question of what it means to be a realist about these things, and the world in general, and considers a standard, popular, response: science. We then turn to understanding the nature of science, if there be such a thing. We will look at various problems at the foundations of science: the problems of induction, whether the laws of nature are true, whether there is a principled set of necessary and sufficient conditions to demarcate ``science" from ``pseudo-science", whether we should think it likely that our current science is false because of the so-called pessimistic meta-induction, whether inductive risk threatens the idea of a value-free science, and, finally, the broader relationship between knowledge and society.
Space and time are probably intuitive concepts to many of us. Clocks tick down, trees grow taller. Things were here, now they are there. We have memories of the past, of things back then, but not of things in the future. But despite their familiarity, space and time do not seem to be the same sort of stuff as tables or chairs. So what are they, really? Are they “real"? Is there a sense in which space and time are substantial ‘stuff’ at all? If they are, are they the same kind of stuff? Can we travel through time, like traveling through space? Could we live in a world where space and time are not ‘really’ there, where they are merely emergent? Can we really know the structure of spacetime in our universe?
Some of the greatest thinkers in history have considered these questions, from the Presocratics and Aristotle, to Newton, Leibniz, Kant, Poincare, and Einstein. These are also questions which continues to occupy many philosophers and physicists today. This course will introduce you to some of the ways one can conceptualize, and question, the nature of space and time. The first half of the course will take us through a brief tour of the history of philosophy of space and time, from the Presocratics to Einstein’s theory of relativity. The second half will sample some contemporary topics in the philosophy of space and time.
The word “epistemology" stems from the Greek words “episteme” and “logos”, translated roughly as “knowledge", and “reason" or “argument", respectively. In short, epistemology is the branch of philosophy which focuses on the study of the various aspects of knowledge, asking questions like “what can we know?", “how do we know?", “what are the conditions for knowledge?", and “what are we justified in knowing?", among other questions.In this course, we will focus on the study of scientific knowledge. Interestingly, the word “science" stems from the Latin “scientia", which also translates roughly to “knowledge". After all, a paradigm of contemporary human knowledge is scientific knowledge. We frequently appeal to and rely on scientific knowledge: our GPS works because of general relativity, our semiconductors are designed with quantum-mechanical principles in mind, and we take vaccines because we think the science behind it is trustworthy, etc. But what is scientific knowledge? How do we acquire scientific knowledge? These two questions will be the driving questions of our course for the next five weeks, and I hope you will walk away from this course with at least some tentative answers to these big questions.