Recent years have seen a growing consensus in the philosophical community that the grandfather paradox and similar logical puzzles do not preclude the possibility of time travel scenarios that utilize spacetimes containing closed timelike curves. At the same time, physicists, who for half a century acknowledged that the general theory of relativity is compatible with such spacetimes, have intensively studied the question whether the operation of a time machine would be admissible in the context of general relativity theory or theories that attempt to combine general relativity and quantum mechanics. A time machine is a device which brings about closed timelike curves—and thus enables time travel—where none would have existed otherwise. The character of this project makes it inevitable that its content is of a rather technical nature. The purpose of this project, among others, is to convince philosophers that they should nevertheless be interested in this literature because the topic leads to a number of interesting foundational issues in classical and quantum theories of gravity. Furthermore, philosophers can contribute to the topic by clarifying what it means for a device to count as a time machine, by relating the debate to other concerns such as the fate of determinism in general relativity theory, and by eliminating a number of confusions regarding the status of the paradoxes of time travel. This is a joint project with John Earman (Pittsburgh, History and Philosophy of Science) and Chris Smeenk (University of Western Ontario, Philosophy).

Papers:

• Earman and I have already written an entry for the Stanford Encyclopedia of Philosophy, see here.
• I have written an article for a collection in German, see here. When I get to it, I will post an English translation of this article.
• A joint paper by all three of us is currently under review. For a preliminary preprint of this article, go here.
• Chris Smeenk and I are currently working on a paper on this topic for the Oxford Handbook in the Philosophy of Time, edited by Craig Callender, to be published by Oxford University Press presumably in 2009.

This related project is a collaboration with Hajnal Andréka and István Németi (Rényi Institute of Mathematics, Budapest), two Hungarian logicians interested in the foundations of general relativity. We investigate rotating black holes and other generally relativistic spacetimes where rotation of matter might induce closed timelike curves, thus allowing for a 'time traveller' who might take advantage of this spacetime structure. Interestingly, some kind of 'counter-rotational phenomenon' occurs here in the following sense. If a potential time traveller wants to use a Kerr-Newman black hole for travelling into her past, she will have to orbit along the closed timelike curve in the direction opposite to that of the rotation of the black hole. We analyze whether this phenomenon occurs generically in spacetimes with closed timelike curves.

Papers:

• The first paper arising from this collaboration is forthcoming with General Relativity and Gravitation, see here.
• We have started working on a second paper, to be made available in due course.

While my dissertation examines the fate of singularities in modern quantum gravity, this historical project focuses how singularities emerged as a crucial issue in the classical theory. More particularly, it studies the role of Göttingen mathematician Felix Klein in the debate among Albert Einstein, Willem de Sitter, and Hermann Weyl about whether de Sitter's static solution to Einstein's field equations was free of singularities. In particular, this project argues that the reason why Klein—unlike his fellow interlocutors—immediately recognized the coordinate character of the singularity at stake is to be found in his familiarity with related problems in projective geometry and in his genuinely geometrical—as opposed to purely algebraic—approach to the problem. It also studies possible explanations for Einstein's and Weyl's curious failure to discern that the alleged singularity is really a mere coordinate effect.

Papers: A draft will be made available soon.

This project has been presented at the First International Conference of the Ontology of Spacetime in 2004 in Montreal. Its aim is to suggest a fruitful connection between the philosophical debate of endurantism vs. perdurantism on the one hand and theories in fundamental physics on the other hand. More specifically, the project studies the relation between Lagrangian and Hamiltonian formulations of classical and quantum mechanics, as well as of classical and quantum general relativity and harvests the results of this study for the benefit of the metaphysical debate regarding persistence. Thus, this project explores the disciplinary borderland between philosophy and physics.

Papers: An extended abstract can be found here.

Steven Orzack and Elliott Sober (2001) have formulated a method for quantitatively testing models in optimality theory, the so-called 'method of controlled comparisons.' Motivated by the similarity of the challenges of testability faced by optimality theory and by evolutionary game theory, I propose a mathematical framework common to both theories. This will enable the application of the method of controlled comparisons to models in evolutionary game theory. I discuss the strengths and the limitations of this application.

Papers: A draft will be made available soon.

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. This project investigates the possibility of finding a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This project is at a preparatory stage.