Updated Notes (May 10)

I have added more to the notes at the end of the "Spontaneous Collapse Theories" section and at the end of the whole document and some stuff on narratability. I won't change the notes any more before the final exam.

Questions to Think About

Your most important task is to list the pros and cons of Everett interpretation, the 3 versions of GRW, 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 Bell's inequality to the EPR argument?
• What is the narratability problem with relativistic QM?
• Does relativity prohibit non-local signaling? What is the potential problem?
• What is Maudlin's argument that the violations of Bell's inequality do not generate a causal loop problem?
• Why can't superluminal particles explain 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 is natural for the Everett interpretation to say about non-locality and violations of Bell's inequality?
• What aspect of relativity does QM seem to conflict with? To what extent and in what way are the two compatible?

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 was a kind of amalgam of different views and is not Bohr's view of quantum mechanics.

Assignment 4

Your assignment is to pick one of the following two topics and write about 1500 words (minimum 1000, maximum 2000).

1. The first is an article hot off the presses, "An experimental test of non-local realism" (also on Course Reserves) claiming that they have experimentally ruled out a significant class of non-local hidden variable theories. Write your paper criticizing the article in whatever way you deem reasonable. Obviously the better focus is on the conceptual issues. (E.g., Were the concepts of locality and reality constructed properly? Is it really right that the reality one is the one that needs giving up? Is the reality condition really important philosophically?)

2. The second is to discuss whether the correlations involved in quantum non-locality should constitute faster-than-light causation as opposed to something weaker. You should address Maudlin's argument as well as others that you can research. Brown briefly discusses the issue in the excerpt we're reading.

The due date for Assignment 4 is now Tuesday May 1 at 4:30.

Answers to Assignment 3

The last change to the answers was at 3:04 PM on April 16.

Assignment 3 on Relativity and Non-Locality

Now available.

Answers to Mid-term Exam

I've got some sample answers to the mid-term to show you what would have been good enough. I didn't do the last two, but I may add answers there later as I get a chance.

6. Entanglement: Many of you were not being clear enough in your explanations. Entanglement is not merely one entity depending on another; that happens classically. Nor is it strictly speaking the state of two entities not being decomposable into the individual properties of each; that's classical too, e.g., the state of the solar system is not only the properties of the planets but also their relations (at least their distances from one another). But at least this second idea is very close to the truth--that what is novel about entanglement is that--so far as we can tell--in QM, the state of the whole cannot be decomposed into the state of its parts plus relations among the parts.

9. A big element that was missing in just about every answer was the old-fashioned thought that QM requires a division of the world into observer and observed, a belief that still lingers. This idea was prominent in Bohr's belief that the quantum properties of things existed only relative to classically defined experimental setups. There was this idea that classical physics applied to macroscopic objects and QM to microscopic objects, so that QM was not a complete theory.

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.

Things to Think about for the Mid-term Exam

Make sure you have the latest version of all the notes. (I haven't changed them for the past two weeks.)

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?

Assignment 2

Here is the second assignment: Discuss and criticize either David J Baker's Measurement Outcomes and Probability in Everettian Quantum Mechanics or Peter Lewis's Uncertainty and probability for branching selves. Try to show how the Everett-advocate can sustain a defense against the arguments in these papers. The paper should be about 1800 words (minimum 1200, maximum 2200). The due date is Friday March 9, 4:30 PM. You can turn in the paper in class on Thursday or put it in my department mailbox. If there are last minute printing problems, email me your paper before the deadline and then turn in a written copy as soon as feasible.

I am not looking for a comprehensive discussion but an analysis that focuses on at least some the most important claims of the paper you select. Also, you don't need to have a conclusion that the Everett theory withstands all the criticisms. Aim to try to determine the best face that an Everett-interpretation can put on its theory and discuss how far that goes.

Answers to Assignment 1

Here are my answers to the first assignment.

Updated Notes (11:10 AM Thursday)

I updated My Notes, Part 1, by changing the sample homework problems, adding diagrams to make the questions coherent. Due to typesetting issue, the second diagram shows up on the next page, so don't miss it.

I haven't yet added the diagrams towards the end of the notes. I'll get to those this weekend.

Assignment 1

Assignment 1 is now available. It's due on Friday, February 16 at 4:30. You can turn it in earlier to me, or just put it in my departmental mailbox.

Don't forget that when multiplying a vector by itself that one side is complex-conjugated. This means you should always end up with a real number after you've done the calculation.

Also, to calculate the probabilities, you don't always have to figure out the full quantum state. If there is no recombining of beams further downstream, you can use heuristics like 'a left particle has a 50% chance of going through the down exit.'

Course Description

Course Hours: 1:00 PM - 2:20 PM Tuesday and Thursday.

Office Hours: Wednesday 2:00 PM to 4:00 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 28% 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 are two exams, a mid-term and a comprehensive final worth 25%, and 35% 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.