Lerninhalte |
The goal of this seminar is to discuss some of the most important questions with regard to the foundations of quantum mechanics. Topics will be prepared by the students based on provided references (usually between one and three easy to read papers or book chapters), as well as own literature research, and presented to the course. The grade will be based on this presentation.
Due to the COVID-19 pandemic the seminar will be offered as an online course. Presentations should be recorded and made available for all attendees in a format suitable for the presented topic, for example PowerPoint slides with recorded audio narration, video, podcast (audio only), PDF slides with audio file or transcript etc. (NOTE however that this is NOT a class on video editing or similar. Although students with the technical capabilities and time to present their work in a high quality format are encouraged to do so, grades will be based on content and the general structure/style of the presentation, as would be expected in a live talk, taking the special circumstances of the current situation into account.)
Please contact andre.grossardt@uni-jena.de to pick a topic. Topics will be assigned on a ”first come, first served” basis.
List of topics:
- The quantum measurement problem
What is the “measurement problem” of quantum mechanics? Why is quantum mechanics said to be incomplete? References: - J. S. Bell: “Against 'measurement'” - T. Maudlin: “Three measurement problems”
- Decoherence
How does the interaction of a quantum systems with its environment result in quasi-classical states, and why is this not the (complete) solution of the measurement problem? Reference: - Giulini and others (ed.): “Decoherence and the Appearance of a Classical World”, Chapter 3. E. Joos: “Decoherence Through Interaction with the Environment”, pages 35-47 and 54-61.
- von Neumann’s “no hidden varibales” proof
In his 1932 book “Mathematische Grundlagen der Quantenmechanik” von Neumann presents an argument why the statistical character of quantum mechanics cannot be avoided by introducing “hidden variables”. However, flaws in von Neumann's arguments were pointed out already in 1935 by Grete Hermann and independently by Bell three decades later. Present the von Neumanns argument and its flawed assumption. References: - J. S. Bell: “On the Problem of Hidden Variables in Quantum Mechanics” - N. D. Mermin and R. Schack: “Homer Nodded: Von Neumann's Surprising Oversight”
- Bohmian mechanics
Bohm's approach to quantum mechanics not only provides a possible solution to the measurement problem but also gets rid of the statistical interpretation of the theory at the cost of introducing “hidden” variables. Present the basics of Bohm's theory. How do its predictions relate to standard quantum mechanics and what are its caveats? References: - A. S. Sanz: “Bohm's approach to quantum mechanics” - D. Dürr, S. Goldstein, N. Zanghi: Quantum Physics Without Quantum Philosophy, sections 2.1-2.3
- Nonlinear Schrödinger equations and causality
A crucial element in the measurement problem of quantum mechanics is the linearity of the Schrödinger equation. One can, therefore, question whether nonlinear modifications can help with its solution. Review an argument by Gisin that such nonlinear modifications of quantum mechanics result in faster-than-light signalling. What possible loopholes are there in Gisin's argument? References: - A. Bassi and K. Hejazi: “No-faster-than-light-signalling implies linear evolutions. A re-derivation” - A. Kent: “Nonlinearity without superluminality”
- Collapse models Collapse models solve the measurement problem by modifying the linear evolution of the Schrödinger equation into a nonlinear stochastic dynamical law. Through this modification, the collapse of the wave function during measurement becomes an immediate consequence of the dynamics. Present the basic idea and consequences of these models.
Reference: - A. Bassi and G. Ghirardi: “Dynamical reduction models”, sections 5.1 – 6.5
- Everett/many worlds interpretation
If one rejects both nonlinear modifications of quantum mechanics (as in collapse models) and additional variables (as in Bohmian mechanics) one is forced to make sense of measurements as part of the orthodox formulation of quantum mechanics. This is the idea of Everett's “relative state” formulation of the theory – in its modern variations more commonly referred to as the “many worlds” interpretation. What is the mathematical and philosophical concept behind this reinterpretation of the laws of quantum physics, and which are the reasons for the more critical attitude of some physicists towards these ideas? References: - H. Everett, III: “'Relative State' Formulation of Quantum Mechanics” - B. S. DeWitt: “Quantum mechanics and reality” - L. E. Ballentine and others: “Quantum-mechanics debate” - T. Maudlin: “Three measurement problems”, pages 11-12
- Bell’s theorem / EPR
In 1935 Einstein, Podolsky, and Rosen presented their famous paradox, showing that quantum mechanics predicts a perfect correlation between certain measurements over arbitrarily large distances, concluding that quantum mechanics must be incomplete. It was only with Bell's work three decades later that the consequences were fully understood: quantum mechanics violates an inequality that should be satisfied by any theory that respects locality. Present Bell's theorem and its consequences. References: - A. Einstein, B. Podolsky, and N. Rosen: “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” - J. S. Bell: “On the Einstein Podolsky Rosen paradox” - J. S. Bell: “Bertlmann's socks and the nature of reality”
- experimental violation of Bell’s theorem
By stating his inequality, Bell showed (with few assumptions) that the theory of quantum mechanics is incompatible with a local and causal reality. However, it was only the experimental violation of said inequality that provided the evidence that there are indeed nonlocal correlations in our universe (and, in this regard, quantum mechanics is correct). Present the early Bell tests by Freedman and Clauser (1972) as well as Aspect, Dalibard, and Roger (1982); in the process, introduce the derivation of the CHSH inequality which is the basis for most modern Bell tests. Choose one of the more modern tests to explain some of the loopholes that have been discussed with the earlier experiments (e.g. the BIG Bell Test or the measurement by Rauch and others using light from distant quasars). References: - J. F. Clauser and others: “Proposed experiment to test local hidden-variable theories” - S. J. Freedman and J. F. Clauser: “Experimental Test of Local Hidden-Variable Theories” - A. Aspect, J. Dalibard, and G. Roger: “Experimental Test of Bell's Inequalities Using Time-Varying Analyzers” - BIG Bell Test Collaboration: “Challenging local realism with human choices” - D. Rauch and others: “Cosmic Bell Test Using Randim Measurement Settings from High-Redshift Quasars” - See also Wikipedia article “Bell test experiments” and references therein for a comprehensive list of experimental tests.
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