This course offers an elementary introduction to some foundational problems in quantum mechanics. An excellent description of the basic problem treated in this course can be gleaned from the back cover of Jeffrey Barrett's The Quantum Mechanics of Minds and Worlds: "The standard theory of quantum mechanics is one of the most successful physical theories ever, predicting the behavior of the basic constituents of all physical things; no other theory has ever made such accurate empirical predictions. However, if one tries to understand the theory as a complete and accurate framework for the description of behavior of all physical interactions, it becomes evident that the theory is ambiguous, even logically inconsistent."

The core of the theory's ambiguity is captured by the so-called measurement problem (aka Schrödinger's cat paradox), which will be a central concern in this class. We will try to understand what exactly the problem is and study several proposed ways of solving it. Another focus of the course will be what physicists recently voted the most beautiful physics experiment of all times as it illustrates one of the most puzzling features of quantum mechanics, its non-locality, and the related Einstein-Podolsky-Rosen (EPR) paradox.

Accessibility. I intend the course to be self-contained. Early in the course, we will go through much of the technicalities necessary to understand foundational questions in quantum mechanics. In particular, I will assume you can follow the formalism developed in chapter 2 of David Albert's textbook, plus whatever little extra I do in lecture. What that means is that you'll need to understand the very basic linear algebra introduced by Albert (most of which is really not that hard). That said, some of the articles we will read use calculus, algebra, and probability theory. So if papers with the occasional derivative, integral and velocity in it cause you panic, then perhaps this course is not for you.

News: I will offer additional office hours on Friday, 13 March, 10:00am to 12:00pm, in my office. Chris Suhler will offer additional office hours on Thursday, 12 March, from 3:00 to 5:00pm in his office, HSS 8029.

Chris Suhler, csuhler "at" ucsd "dot" edu, office hours: Thursdays 2-3 p.m. in HSS 8029 (or by appointment)

Note (added 25 Feb 2009) concerning change of order of readings: please read the material on Everett and many worlds before the materials on Bohm, not after.

Course materials such as lecture notes, handouts, etc will be made available as they will be used in class.

• Syllabus
• Lecture 1: Organization
• Lecture 2: The early history of quantum mechanics
• Lecture 3: Superposition
• Lecture 4: Formalism
• Lecture 5: Bohr, Einstein, and the EPR experiment
• Lecture 6: Bell`s theorem and nonlocality
• Paper prompt for midterm paper
• Grading rubric for midterm paper
• Lecture 7: Copenhagen and complementarity
• Lecture 8: Measurement problem
• Lecture 9: Collapse
• Study guide for the final exam
• Lecture 10: Dynamics by itself, Everett, and many worlds
• Lecture 11: Bohm`s theory
• Lecture 12: A philosopher looks at quantum mechanics (twice)

• Textbook: David Albert, Quantum Mechanics and Experience. The book is available at the Price Center Bookstore.
• A number of readings for this course are available from e-reserves: Link to this course`s e-reserves page

Note: These additional materials will not be tested in exams with exception of Barrett`s article on Everett. They serve to give you some background or to offer some additional food for thought.

The Stanford Encyclopedia of Philosophy (SEP) is an excellent source for academically serious, yet relatively accessible survey articles on many, many topics in philosophy. You may also wish to consult the following SEP article as background reading for this course.

• Jenann Ismael: Quantum Mechanics
• Jan Faye: Copenhagen Interpretation of Quantum Mechanics
• Giancarlo Ghirardi: Collapse Theories
• Sheldon Goldstein: Bohmian Mechanics
• Jeff Barrett: Everett's Relative-State Formulation of Quantum Mechanics
• Carl Hoefer: Causal Determinism

There are numerous online papers and internet sites dedicated to the topics discussed in this class. Please let me know if you come across something that strikes you as particularly interesting.

General Comments

What matters is not the absolute number of your scores, but your performance relative to everybody else in the class. That is whay it`s important for you to know where you stand with respect to the class average, and that`s why I have given the class averages of those who did the assignment for all assignments below.

I grade to the curve. That means that the top 25-30% of the students in this class (including all who take it for a letter grade or a P/NP, but not including the withdrawals W) will get a grade in the A range (A+, A, A-), the next 25-35% a grade in the B range (B+, B, B-), the next 25-30% a grade in the C range (C+, C, C-), and the remaining 5-25% a D or an F. This is the minimum I guarantee; if the class has worked very well and no one deserves a D or an F, I will not give up and adjust the curve upwards, accordingly.

Right now, i.e. including the first five quizzes and the midterm paper, the class average (mean) of the total points is 23.12. This includes withdrawals (Ws), since I will only be told who withdrew from the course in Finals Week.

Quiz 1

Question 1

The most common problems on Question 1 were (1) not explicitly mentioning that, to determine the state of the universe at a time of our choosing from our knowledge of its state at a particular time, we need to know the dynamical laws and (2) thinking that determinism meant the (erroneous) assumption that classical physics was essentially complete.

Question 2

A common problem was mentioning the importance of frequency but not the corpuscular structure of light.

Question 3

There was a lot of, er, uncertainty on Question 3, where many people seemed to be looking for an empirical discovery rather than a theoretical one (namely, non-commutativity). This may have led quite a few people simply to state Heisenberg's uncertainty principle rather than the (theoretical) discovery that led to it, which is what the question was asking for.

Question 4 and 5

The responses to Questions 4 and 5 were generally good.

Quiz 2

Question 1

The responses to Question 1 were generally good. The most common reason people didn't get full credit was not mentioning that the vectors that make up the orthonormal basis have to be of length 1.

Question 2

The main problem here was not showing the multiplication of at least one of the vectors by the hardness operator.

Question 3

A common error was only saying that the Schrodinger dynamics are deterministic/predictable (sans measurement) without explaining what that means in terms of state vectors.

Question 4

Among people who didn't leave the question blank or run out of time, the main issue was giving a general explanation of collapse without relating this to the Schrodinger dynamics. In other words, people didn't explain in sufficient detail why the linear evolution of the Schrodinger dynamics can't account for the experimental results (basically, it predicts a superposition state rather than a determinate state, which is what we actually get when we make a measurement).

Quiz 3

Question 1

The responses to this question were pretty good. The most common errors were defining some aspect of the formalism other than Hermitian operators or not mentioning that the eigenvectors of Hermitian operators have real eigenvalues.

Question 2

An extremely common error was not adjusting the expansion coefficients so that the vector representing the post-measurement state has unit length.

Question 3

A frequent error was defining the Principle of Correspondence rather than the Principle of Complementarity.

Question 4

Most people got full credit on this question.

Question 5

The responses here were generally good. The main reason some people didn't get full credit on this question was that they didn't state the positions of both Bohr and Einstein.

Quiz 4

Question 1

Most people got full credit on this question.

Question 2

Most people got at least 1 point for correctly describing the basic conflict between Bell's inequality (which states that the probability that the same color flashes is greater than or equal to 5/9) and the second type of data from Question 1 (where the probability that the same color flashes is 1/2). To get the other point, you needed to show (in terms of the combinations of instruction sets and detector settings) where the 5/9 prediction of Bell's inequality comes from.

Question 3

The responses to this question were generally good. The main reason people didn't get full credit was not writing out the mathematical representation for the expectation value.

Question 4

The responses here were generally good.

Quiz 5

Question 1

A handful of people described the general measurement problem rather than the specific one the question was asking for (Maudlin's "problem of outcomes"). Among those who didn't make this error, most correctly stated the three claims Maudlin takes to be mutually inconsistent. This was enough to get some credit, but to get 2.5 or 3 points, you had to explain the reasons for the inconsistency in some detail and/or discuss the interpretations that correspond to the rejection of each of the three claims.

Question 2

(a) A common reason people got only partial credit here was that they wrote the mixture and superposition states but didn't explain the difference between them. (b) A lot of people didn't get any credit on this question, for instance because they gave an answer that focused on how measurement will collapse the system rather than explaining that the two theories yield identical predictions and thus can't be empricially distinguished.

Midterm paper

The average score on the midterm was 19.63 out of 30, although that's only moderately informative because it masks a lot of variation (the standard deviation was 8.11).

Given the diversity of topics and responses, these comments will necessarily be general.

One problem was not explaining terms, concepts, arguments, experiments, etc. in sufficient detail. Although your actual audience (me) knows the details of, say, the structure of the EPR argument, one goal of the paper was for you to demonstrate that you understand the issues, which requires explanation.

Another problem was providing only an incomplete or superficial discussion of the implications and/or strengths and weaknesses of the arguments, positions, debates, etc. that you discussed.

Finally, many people stuck very closely to the readings/lectures. You didn't have to provide anything groundbreaking to get a decent number of "originality" points, but you at least needed to show that you had thought about and wrestled with the issues independently to get more than 2 or 3 points.

Quiz 6

Question 1

Most people got full credit on this question.

Question 2

A lot people got half credit on this question because their answers hinted at what the preferred basis problem is but also bordered on simply restating the question. To get full credit, you had to provide additional details/explanation beyond just saying that it's problematic to determine which basis should be used.

Question 3

The answers to this question were generally good.

Question 4

This was by far the toughest question. A number of people left it blank or gave very short answers that earned little or no credit. Among those who gave longer answers that were at least headed in the right direction, common reasons for losing points were (1) giving, in effect, an EPR-style explanation of how locality could be maintained and (2) describing Albert's setup accurately but not making clear how it relates to or preserves locality.

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