# Quantum Foundations

### Seminar series on the foundations of Quantum Mechanics

### Fall 2012

Quantum Theory is an enormously successful theory from a practical point of view. It correctly predicts both non-relativistic and relativistic phenomena to extraordinary precision and has driven major technological developments such as the laser, superconductivity and micro-circuitry. Recent experimental advances show coherence and entanglement of quantum systems routinely. And yet, even after more than a century, nobody seems to understand quantum mechanics. What are the properties that distinguish quantum systems from classical systems? Is the quantum-mechanical description complete? What does it describe?

**This seminar series is not intended to explain quantum
mechanics, but rather to expose the difficulties. There will be three
themes: the building blocks of quantum mechanics, the difference
between quantum and classical systems, and questions of
interpretation.**

### Place

The seminars will take place Thursdays at 15:15 in Signalen, and take (nominally) one hour. Any changes in this will be announced. Let me know if you want to receive such announcements by email.

**The seminars will contain** (subject to change):

- (20 Sept) Basic notions, black-body radiation, the photoelectric effect, quantization, matrix mechanics, undulatory (wave) mechanics
- (27 Sept) More on matrix mechanics, complex amplitudes, harmonic oscillator, the canonical commutation relation, derivative operators, equations of motion, comparison with wave mechanics
- (4 Oct) The Born rule, Dirac's notation (modern QM), uncertainty relation(s), complementarity
- (11 Oct) The Einstein-Bohr debate on consistency, completeness and the Einstein-Podolsky-Rosen argument
- (18 Oct) von Neumann's impossibility theorem, Bell's theorem, local hidden variables, entanglement, quantum "nonlocality", experimental tests and their problems
- (1 Nov) Contextual hidden-variable models, existence of properties as separate entities, joint measurability, the Kochen-Specker theorem, Gleason's theorem
- (8 Nov) Entanglement, Greenberger-Horne-Zeilinger, quantum teleportation, quantum bomb-testing, quantum Zeno effect
- (15 Nov) The measurement problem, von Neumann's measurement paradigm, generalized measurements, decoherence models, the quantum-classical "cut", dynamical collapse models, Ghirardi-Rimini-Weber
- (6 Dec) The recent experiment that rules out the fair sampling loophole for entangled photons
- (24 January) de Broglie-Bohmian mechanics, non-local hidden variables, Everett, the many-worlds interpretation, the problem of probability therein, quantum Bayesianism, subjective quantum states

Since I know that there will be participants with little formal knowledge of quantum mechanics, I will explain the needed theory as we proceed. Some knowledge of probability theory, linear algebra, and complex numbers will be enough to follow most of the discussion.

### PhD-level course on the foundations of Quantum Mechanics

This seminar series can be used as a course for PhD students, at a nominal size of 6 hp. The examination would consist of reading, presenting and discussing a recent (or important) paper in the field. Contact me for details.

### Examination assignments

The assignment is to read and present a paper, say a fifteen-twenty-minute presentation followed by discussion. Some suggestions (some are really good papers, some are not):

- Heisenbergs response to EPR, unpublished 1935, (English translation) preprint, 2011, for a planned book '"The Einstein Paradox": The debate on nonlocality and incompleteness in 1935'.
- Aspect's experiment(s), Aspect et al, PRL 1981, PRL 1982a, and PRL 1982b.
- Testing noninvasive measurability, Leggett and Garg, PRL 1985
- How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, Aharonov, Albert, and Vaidman, PRL 1988
**Jonathan Fors (31 January):**Bell Inequality for Position and Time, Franson, PRL 1989 and Aerts et al, PRL 1999**Eduardo Antunez de Mayolo (21 March, 10:15):**Laser cooling and trapping of neutral atoms, RMP 1998**Jens Ogniewski (7 March):**A Heisenberg microscope for correlated photons, Dopfer, PhD Thesis (in German), Ch. 4, 1998**Anna Orlof (7 February):**Wave-particle duality of C_{60}molecules, Arndt et al, Nature 1999**Christopher Tholander (28 February):**Measuring the speed of quantum information, Scarani et al, PLA 2000**Hans Lind (28 February):**Nonlocal Hidden-Variable Theories and QM: an incompatibility theorem, Leggett, Found. Phys. 2003 and Gröblacher et al, Nature 2007- Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement, Ozawa, PRA 2003
- Single-Particle Diffraction and Interference at a Macroscopic Scale, Couder and Fort, PRL 2006
**Daniel Edström (31 January):**Paradox in Wave-Particle Duality, Afshar et al, Found. Phys. 2007**Muhammad Ajmal (14 February):**Information causality as a physical principle, Pawlowski et al, Nature 2009**Aysajan Abidin (21 March, 10:15):**No extension of quantum theory can have improved predictive power, Colbeck and Renner, Nature Comm. 2011**Alexander Lindmaa (14 February):**On the reality of the quantum state, Pusey et al, Nature Physics 2012

More may appear. You are free to suggest papers yourselves.

### Extra reading

## Jan-Åke Larsson

## Contact:

Department of Electrical Engineering

Linköping University

+46(0)13 281468

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Page responsible: Jan-Åke Larsson

Last updated: 2013-03-07