Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Description

Quantum mechanics-even in the ordinary, non-relativistic, "particle" formulation that will be the primary focus of this course-has been a staggeringly successful physical theory, surely one of the crowning achievements of 20th century science. It's also rather bizarre-bizarre enough to lead very intelligent and otherwise sensible people to make such claims as that the universe is perpetually splitting into many copies of itself, that conscious minds have the power to make physical systems "jump" in unpredictable ways, that classical logic stands in need of fundamental revision, and much, much more. In this course, we intelligent and sensible people will attempt to take a sober look at these and other alleged implications of quantum mechanics, as well as certain stubborn problems that continue to trouble its foundations. Doing so will require learning some math: not the heavy-metal differential equations and approximation techniques that you need to actually start making predictions with the theory, but rather the simple, elegant linear algebra that lies behind the way physical states are represented in quantum mechanics, and that leads in a surprisingly direct fashion to most of the interesting problems that we will discuss. So, after mastering what we need of this mathematical formalism (with no prior exposure to either it or quantum physics required), we will turn to the most famous foundational issues associated with quantum mechanics: the problem of coming up with an adequate account of measurement, the question of whether quantum mechanics can and should be replaced by a "deeper" theory which posits "hidden variables", quantum logic, and (time permitting) some seldom discussed problems associated with the quantum mechanical treatment of composition and identical particles. In addition, we may (again, time permitting) take a look at recent claims that quantum mechanics will make possible faster-than-light communication, or teleportation, or massive improvement in the computational power of computers.

Along the way, we will take plenty of time out to discuss philosophical questions about science that quantum mechanics raises in new and interesting ways: e.g., what it means to attribute probabilities to physical events, what the aims of scientific inquiry are (does it aim at something true, or merely at something useful?), what the role of observation is in constructing a scientific theory, what it means to say that there is an "objective" physical world, whether something as basic as logic can be viewed as an empirical discipline, whether there can be meaningful scientific questions whose answers cannot possibly be settled by experiment, and more.

Assignments

You will have weekly homework assignments, which will sometimes involve 2-3 pages of writing (1 page = 300 words), and will sometimes take the form of problem sets. Don't even think about turning them in late, unless you have some massively good excuse that you tell me well ahead of time; I won't accept them. There will be 12 weekly assignments in all; you are required to do 10 (your choice, mostly; in a few cases the weekly assignment will be non-optional). If you do more, I will pick the ten best in determining your grade. You are free to revise any of the writing assignments-provided you notify me right away that you want to do so, and turn in the revision no more than two weeks after the given assignment was handed back to you. Occasionally, I may replace the weekly assignment by an in-class quiz; the probability that I will do so will be inversely proportional to my degree of confidence that everyone is doing the reading. There is no final exam, and no mid-term.

Grading

The weekly homework assignments will contribute 70% of your grade, and class participation 30%. To make it easy for you to keep track of how you're doing, I will score the assignments on a scale of 1 to 7; I will also give you regular feedback on how well you are holding up your end of class discussion. (A rough guide: think of a day's participation as being scored on a 2-point scale. Score of 0: you didn't show up to class. Score of 1: you showed up, but sat there like a lump. Score of 2: you showed up, and participated in discussion in a way that demonstrated that you had done, and thought about, the reading. Score of 3 (yes, 3): you showed up, and made all our lives richer by your scintillating, insightful discussion of the day's topics.)