Topics to Think about for the Final Exam

Your most important task is to be knowledgeable about all the interpretations of QM we have discussed, including Everettian interpretations, the 3 versions of GRW, and Bohm's interpretation. Evaluate the strength of each of these with regard to conceptual coherence, ad hoc-ness, potential for being included in an improved physics, compatibility with a reasonable scientific conception of how the world could be.

• Explain what the EPR paper tried to show.
• What was the relevance of violations of Bell's inequality to the EPR argument?
• Does relativity prohibit non-local signaling? What is the potential problem non-local signally poses?
• Why can't superluminal particles explain violations of Bell's inequality?
• How does the contextuality of spin measurements in Bohmian mechanics relate to Bohr's explanation of the EPR thought experiment? What is Maudlin's criticism of Bohr's explanation?
• What is Bell's relative time invariance?
• What is the distinction between fundamental and observable Lorentz-invariance?
• How do GRW-mass-density, Bohmian mechnics and GRW-flash differ with regard to how they approach explaining the Bell correlations? In what ways does each fit with the spirit of relativity?
• What aspects of relativity does QM seem to conflict with? To what extent and in what way are the two compatible?

Assignment 4

Discuss whether Everettian (and generally Many-Minds) interpretations are really local theories of quantum mechanics. Consdier Brown's argument posted on the course reserves.

Your paper should be approximately 700-1500 words, though I will not place any strict limits on the size.

Assignment 3

The third assignment for the course is posted on OCRA.

Mid-Term

The exam is on March 25, 2010. The questions will be focused on the range of interpretations we have discussed, primarily the spontaneous collapse interpretations, the Everettian interpretations, and Bohm's interpretation.

It would be advisable for you to outline all the interpretations we have discussed and mention the problems they intend to solve, challenges to them that have been posed, and any challenges that have been resolved.

Study questions:

What is the practical problem and the epistemic problem for Everettian interpretations?

What are "subjective uncertainty" approaches to the practical problem?

Explain the kind of contextuality exhibited by Bohmian mechanics.

Enumerate the various versions of spontaneous collapse interpretations. What are their relative merits and disadvantages.

Albert argues that on the one hand the many-minds interpretation and Bohmian mechanics are empirically equivalent to each other and on the other hand that they are (in a radical sense) empirically incommensurable. Explain what he means.

What is the 'tails' problem?

Assignment 2

Present an explanation of Gomatam's interpretation of Bohr's interpretation of quantum mechanics. You do not need to include your own interpretation of Bohr or evaluate whether Gomatam is getting Bohr's view correct. But you should articulate the conception of reality offered Gomatam's Bohr. In doing so, you should make clear whether Gomatam's Bohr solves the measurement problem and to what extent his account makes sense.

Your paper should be approximately 1000-2500 words, though I will not place any strict limits on the size.

Course Description

Course Hours: 2:30 PM - 3:50 PM Tuesday and Thursday.

Office Hours: Tuesday and Thursday 12:10 PM to 1:10 PM.

Textbooks: David Albert, Quantum Mechanics and Experience. Tim Maudlin, Quantum Non-locality and Relativity.

The goal of this course is to analyze a wide range of philosophical issues that are informed by quantum mechanics. The primary issue will be evaluating various interpretations for the theory. How to best understand what the quantum mechanical formalism tells us about the world is still very controversial.

There are no formal prerequisites for this course, but mathematics will be used in the course. I will presuppose that you understand differential calculus, vectors, matrices, and complex numbers. No prior knowledge of quantum mechanics will be assumed. Two of the homework assignments will involve mathematical problems, and you will be expected to be able to solve some simple problems, but the vast majority of the course will not require mathematical problem-solving ability.

Tasks and Evaluations

Your grade for the course will be determined by these factors:

 1. There will be two homework assignments worth a total of 16% of your final grade. The goal of these assignments will be for you to demonstrate understanding of how simple quantum mechanics/relativity problems are solved.

2. There will be two homework assignments worth a total of 32% of your final grade. The goal of these assignments will be for you to write expositions of theoretical and philosophical issues that arise in quantum mechanics. You will be attempting to write articles of the kind a sophisticated science journalist would write, pitched at an educated adult audience.

3. There is a mid-term and exam and a comprehensive final worth 22%, and 30% of your final grade, respectively. It will involve criticism of existing textbook and popular presentations of various aspects of quantum mechanics, as well as analysis about the range of philosophical interpretations of quantum mechanics and related phenomena like non-locality. I will provide study questions before the exam.

Links to Additional Papers

If you are interested, here are a couple of papers about the Copenhagen interpretation. A paper from 1958 by Hanson, "Copenhagen Interpretation of Quantum Theory" gives you a pretty good idea of the both the hostility (among a segment of physicists) to the goal of getting clear about what your theory says and as well as exhibiting its own serious misconceptions.

Don Howard's "Who Invented the "Copenhagen Interpretation"? A Study in Mythology" gives you a fuller picture of what I was hinting at when I mentioned that the Copenhagen Interpretation might be seen as a kind of amalgam of different views and is not Bohr's view of quantum mechanics.

List of Interpretations

Brief account of the interpretations:

• Classical "Orthodox" Interpretations
  • Bohr's Interpretation (Insistence on Indeterminism, No Extra Variables, Contextuality of Measurement) Read the Howard Who Invented the "Copenhagen Interpretation"? A Study in Mythology for more detail.)
  • von Neumann Collapse Interpretation
  • Wheeler Collapse
  • Wigner Collapse
• Many Worlds Interpretations
  • deWitt's Literal Many Worlds
  • Many Minds
  • Everett/Decoherence-based Many Worlds (Two kinds of explanations for how to understand probability: Subjective Uncertainty about one's subjective experiences and a Caring Function expressing how future branches ought to be weighed in utility calculations.
• Bohmian Mechanics
  • World-particle + Wave function Ontology
  • Particle (in 3D physical space) Ontology with the wave function being considered a physical "condition", not taken seriously as an independent physical field.
• Spontaneous Collapse Interpretations (Can read Peter Lewis: GRW: A Case Study in Quantum Ontology for a nice review of some of the issues.)
  • GRW0: Bare wave function ontology
  • GRWm: Wave function + mass-density field (in 3D space)
  • GRWf: Wave function + Flash ontology (points in 3D space corresponding to the centers of the wave function collapses)
    • (Version 1: With real collapse) The wave function really collapses at the flash points and the probability for future collapses depends just on the current wave function.
    • (Version 2: Without collapse) The probability for future flashes is only given by the current wave function plus the totality of all past collapses, not the current wave function alone.

Topics to Think about for the Mid-term Exam

Create an exhaustive categorization of all the interpretations (including sub-variants).

Consider the relationships among them them regarding (1) how they solve the measurement problem, (2) what assumptions they make about the mind-body connection, (3) what their ontology is, (4) what the standard objections are against them, (5) how they account for Born's rule.

20-25% of exam involves QM calculations. Practice a few simple calculations using polarizers, recombiners, and particle detectors. Be sure that you are calculating wave function collapses efficiently (collapses at the time the particle position is "measured". (You won't need to renormalize any spin states for the recombiners. I'll make sure you can just add the spins. I will provide the matrices that correspond with standard spin properties and states.)

Be able to explain why interference effects go away when you "measure" where the particle is. It is different on different interpretations.

Understand what was initially so philosophically revolutionary (challenging to our ordinary conceptions) about QM. How have the initial worries been addressed?

What are the arguments for and against understanding the wave function as a "real" physical field?