Amit Hagar

Relying on the universality of quantum mechanics and on recent results known as the “threshold theorems,” quantum information scientists deem the question of the feasibility of large‐scale, fault‐tolerant, and computationally superior quantum computers as purely technological. Reconstructing this question in statistical mechanical terms, this article suggests otherwise by questioning the physical significance of the threshold theorems. The skepticism it advances is neither too strong (hence is consistent with the universality of quantum mechanics) nor too weak (hence is independent of technological contingencies). *Received June 2009; revised August 2009. †To contact the author, please write to: Department of History and Philosophy of Science, College of Arts and Sciences, Indiana University, Bloomington, IN 47405; e‐mail: [email protected].

In the chapter “The Geometry of Visibles” in his ‘Inquiry into the Human Mind’, Thomas Reid constructs a special space, develops a special geometry for that space, and offers a natural model for this geometry. In doing so, Reid “discovers” non-Euclidean Geometry sixty years before the mathematicians. This paper examines this “discovery” and the philosophical motivations underlying it. By reviewing Reid’s ideas on visible space and confronting him with Kant and Berkeley, I hope, moreover, to resolve an alleged impasse in Reid’s philosophy concerning the contradictory characteristics of Reid’s tangible and visible space.

Hugh Everett III died of a heart attack in July 1982 at the age of 51. Almost 26 years later, a New York Times obituary for his PhD advisor, John Wheeler, mentioned him and Richard Feynman as Wheeler’s most prominent students. Everett’s PhD thesis on the relative state formulation of quantum mechanics, later known as the “Many Worlds Interpretation”, was published (in its edited form) in 1957, and later (in its original, unedited form) in 1973, and since then has given rise to one of the most radical schools of thought in the foundations of quantum theory. Several years ago two conferences held in Oxford and in the Perimeter Institute celebrated the occasion of 50 years to the first publication of Everett’s thesis. The book Many worlds? grew out from contributions to these conferences, but, as its editors emphasize, it is more than mere conference proceedings. Instead, an attempt was made to assemble an impressive collection of papers which together illustrate the promise of the many worlds interpretation and the obstacles it faces. 23 papers divided into six sections follow an introduction by Simon Saunders, one of Oxford’s fiercest Everettians. The first four sections cover two thorny issues that have been flagged by contemporary opponents to the many worlds interpretation, namely, the problem of ontology and the problem of probability, while the fifth discusses alternatives to Everett such as Bohmian mechanics and information–theoretic approaches to quantum theory. The sixth section seems to be a wild card, hosting several papers unrelated to each other, including one of the most interesting contributions to this volume on the history of Everett’s thesis and his (some may say all too) short academic career. Each section concludes with transcripts of the discussion session that took place after the talks, thus giving an additional emphasis to the points of contention. Apart from general comments on the volume, in what follows I would like to concentrate on few papers I found especially illuminating. Start with ontology..

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical resources required to reach a physical state from another.

We present a brief history of decoherence, from its roots in the foundations of classical statistical mechanics, to the current spin bath models in condensed matter physics. We analyze the philosophical import of the subject matter in three different foundational problems, and find that, contrary to the received view, decoherence is less instrumental to their solutions than it is commonly believed. What makes decoherence more philosophically interesting, we argue, are the methodological issues it draws attention to, and the question of the universality of quantum mechanics.