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.

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.

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

• Topic 0: Organization
• Topic 1: The early history of quantum mechanics
• Topic 2: Superposition
• Topic 3: Formalism
• Topic 4: Bohr, Einstein, and the EPR experiment
• Topic 5: Bell's theorem and nonlocality
• Topic 6: Copenhagen and complementarity
• Topic 7: Measurement problem
• Topic 8: Collapse
• Topic 9: Dynamics by itself, Everett, and many worlds
• Topic 10: Bohm's theory
• Topic 11: A philosopher looks at quantum mechanics (twice)

Click here for the study guide for the final.

Paper prompt for midterm:

• Midterm paper topics (due 14 February 2013)
• Grading rubric

Information concerning plagiarism and guides on how to write a smashing philosophy paper can be found in the sidebar of the top page of the teaching section. The leaflet concerning plagiarism is absolutely mandatory reading.

The following materials are mandatory for this course:

• 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 (password is 'cw146')

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. For this course, the following articles are relevant:

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

At Scientific American, you can find a recent short movie playfully explaining some of the features of entanglement that we will be going over. The video can be found here.

As a part of his 2010 UCSB PhD, Aaron O'Connell constructed the first 'quantum machine', i.e. a macroscopic device which is claimed to be visibly in a superposition state. Here is a link to a short movie where he explains his work. If you find a movie where one can actually see the superposition, let me know!

Here is not a superposition, but a macroscopic system apparently exhibiting wave/particle duality.

Nature published a news piece on a recent survey polling experts in quantum physics on foundational questions of interpretation which can be found here.

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 or valuable.

Quiz 1: The average was 3.57, pretty high for a first quiz! Some comments concerning specific questions follow.

Question 1

• Look up the definition if you didn't get it right.
• Importantly, this led to Planck's recognition that energy is quantized.

Question 2

• Be fairly precise; and if you didn't get it, look it up!

Question 3

• You absolutely have to mention 'non-commutativity' and say between what and what.

Question 4

• Two frequent mistakes (though I was lenient about them):
• First, correlation was often equated with perfect correlation.
• Second, only a 50/50 distribution was considered correlation-free--but distribution of properties can be anything!

Question 5

• This should be explained in a contrastive manner, about two possible experimental set-ups and what is observed in both cases: with and without color box in the middle.

Quiz 2: The average was 2.14, too low for my taste! The quiz wasn't easy, I admit, but still would have expected a higher mean.

Question 1

• Look up the definition if you didn't get it right.

Question 2

• Make sure to actually show the multiplication.

Question 3

• The question is about the linearity of the dynamics, not of operators, although there is of course a connection.
• It doesn't mean that the evolution is deterministic, although I did give some partial credit for that--go look up the definition if you didn't get it right.

Question 4

• Cf. Barrett, pp. 28-30.
• We will come back to that in class.

Quiz 3: The average was 2.74, quite a bit better than for the second quiz. Still, I want to see the mean rise above 3 points!

Question 1

• Hermitian operators have real eigenvalues and are thus taken to correspond to measurable properties.

Question 2

• Notice that the coefficients of the surviving terms must be adjusted to... well, figure it out!

Question 3

• A number of you confused this with the Principle of Correspondence. Go look it up if you didn't get it right!

Question 5

• Here I want to hear something about completeness and locality.

Quiz 4: The average was 2.86, a bit better still. It should be added, however, that the distribution is unhealthily bimodal!

Question 1

• Data 2 concerns all runs, not just those with different settings.

Question 2

• State exactly how the inconsistency arises. Do that in some detail--the question is worth two points, and I expect a correspondingly more substantive answer.
• The answer can be found in Topic 5, slides 9 and 10.

Question 3

• Make sure to state the complete definition, as it can be found in Topic 5, p. 12.

Question 4

• The answer is essentially given on p. 20 and 24 of Topic 5; basically, I expect you to say something about non-locality.

Midterm paper: The class average was 16.77, with a rather large variation.

• 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 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.

Quiz 5: The average was 2.98, a bit better once again.

Question 1

• Often, people have conflated 'determinate' with 'deterministic'--an evolution can be deterministic, but outcomes ought to be determinate.
• You absolutely have to get this right. If you didn't, go look it up!

Question 2

• Make sure to write the states down and explain the difference.

Question 3

• The solution can be found in Topic 8: Collapse, p. 7, and in Albert, p. 86.

Quiz 6: The average was only 1.86, the lowest for this class. The median would be lower still, as there were a very small number of high-scoring outliers, and most students scored only around 1 point! On the up side, this also means that most of you didn't lose many points against the class average...

Question 1

• Again, people have conflated 'determinate' with 'deterministic'--an evolution can be deterministic, but outcomes ought to be determinate.
• Please note assuming that there is no collapse (as Everettian approaches indeed do assume) does not solve the measurement problem yet! In fact, this leads quite directly to it. So you also need to say that these approaches reject that there must be determinate measurement outcomes.

Question 2

• Look it up if you didn't get it right!

Question 3

• Don't just state that by making infinitely many measurements on identically prepared systems, one recovers the correct statistics, but explain how this is achieved.

Question 4

• No doubt this was a hard question. Very hard. Perhaps the hardest you saw so far on any quiz. But I did say in class (and state on the slides (p. 33)) that you should have a close look at this. You should have believed me! Anyway, the answer can be found on pages 131 and 132 of Albert's textbook.