David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The QET has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s. However, we point out that this criticism does not apply to the actual QET, a correct statement of which does not appear in these papers, but to a different (indeed weaker) statement. Furthermore, we formulate a stronger statement of normal typicality, based on the observation that the bound on the deviations from the average specified by von Neumann is unnecessarily coarse and a much tighter (and more relevant) bound actually follows from his proof.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
J. B. Kennedy (1995). On the Empirical Foundations of the Quantum No-Signalling Proofs. Philosophy of Science 62 (4):543-560.
Jan von Plato (1982). The Significance of the Ergodic Decomposition of Stationary Measures for the Interpretation of Probability. Synthese 53 (3):419 - 432.
John Hamilton, Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category.
Meir Hemmo & Orly Shenker (2006). Von Neumann's Entropy Does Not Correspond to Thermodynamic Entropy. Philosophy of Science 73 (2):153-174.
Michael Stöltzner (2002). Bell, Bohm, and von Neumann: Some Philosophical Inequalities Concerning No-Go Theorems and the Axiomatic Method. In. In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer. 37--58.
Lon Becker (2004). That Von Neumann Did Not Believe in a Physical Collapse. British Journal for the Philosophy of Science 55 (1):121-135.
Leah Henderson (2003). The Von Neumann Entropy: A Reply to Shenker. British Journal for the Philosophy of Science 54 (2):291-296.
Sheldon Goldstein & Roderich Tumulka, On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems.
Added to index2009-07-04
Total downloads26 ( #68,119 of 1,102,882 )
Recent downloads (6 months)9 ( #24,605 of 1,102,882 )
How can I increase my downloads?