I have written on conceptual problems arising in quantum gravity, and have more recently discussed the extent to which in which information-theoretic concepts -- concepts with a semantic flavor like entropy and 'signal' -- are subjective or contextual. I am currently working on multiple time dimensions and on nonlocality in classical (non-quantum) physics.
- The Dimensionality of Time
- This is audio from a talk on the possibility of multiple time dimensions I gave in July, 2006 at the Time and Consciousness conference in Sydney.
Papers and Reviews
- Electromagnetism and time-asymmetry.
- Modern Physics Letters A26 (2011) 815-818. (It is a commonplace to note that in a world governed by special or general relativity, an observer has access only to data within her past lightcone (if that). The significance of this for prediction, and thus confirmation, does not however seem to have been appreciated. In this paper I show that what we regard as our most well-confirmed relativistic theory, Maxwell's theory of electromagnetism, is not at all well-confirmed in the absence of an additional assumption, the assumption that all fields have sources in their past. I conclude that we have reason to believe that there is a lawlike time-asymmetry in the world. Also available at this URL.
- Decoherence without decoherence.
- (It has been claimed that decoherence of open quantum systems explains the tendency of macroscopic systems to exhibit quasiclassical behavior. We show that quasiclassicality is in fact an unremarkable property, characterizing generic subsystems of environments even in the absence of dynamical decoherence. It is suggested that decoherence is best regarded as explaining the persistence of true classicality, rather than the emergence, rather than the emergence of quasiclassicality.)
- Many times (a.k.a. 'Multiple time dimensions').
- 3rd Jury Prize in FQXI essay contest on "The Nature of Time". (The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable evolution--for theories in multiple time dimensions. Though similar in many ways to ordinary, single-time theories, multi-time theories have some rather intriguing properties which suggest new directions for the understanding of fundamental physics.) Also available at this URL.
- On determinism and well-posedness in multiple time dimensions (with Walter Craig).
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 465 (2009), no. 2110, 3023–3046. (We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial hypersurfaces surface of arbitrary space–time signature. We show that, under a non-local constraint, the initial value problem posed on codimension-one hypersurfaces—the Cauchy problem—has global unique solutions in the Sobolev spaces Hm. Thus, it is well-posed. However, we show that the initial value problem on higher codimension hypersurfaces is ill-posed due to failure of uniqueness, at least when specifying a finite number of derivatives of the data. This failure is in contrast to a uniqueness result for data given in an arbitrary neighbourhood of such initial hypersurfaces, which Courant deduces from Asgeirsson’s mean value theorem. We give a generalization of Courant’s theorem that extends to a broader class of equations. The proofs use Fourier synthesis and the Holmgren–John uniqueness theorem.) Also available at this URL.
- Nonlocality without nonlocality.
- Foundations of Physics 39, August 2009, 921-936. (Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all.) Also available at this URL.
- Philosophy Pulls Strings.
- Physics World, Sept. 2007, 18-19. (Non-technical article on string theory, discussing the problem of confirmation and falsification, and the prospects for a theory which does not presuppose a background spacetime.)
- Review: The Structural Foundations of Quantum Gravity (ed. Rickles, French and Saatsi).
- Studies in History and Philosophy of Modern Physics 40, January 2009, 88-89., September 2007, 18-19. Also available at this URL.
- Anthropic reasoning and typicality in mulitverse cosmology and string theory.
- Classical and Quantum Gravity 23, 4231-4236 (2006). (Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle is fundamentally ambiguous. It can be formulated in one of two ways, which we refer to as WAP1 and WAP2. We show that WAP2, the version most commonly used in anthropic reasoning, makes no physical predictions unless supplemented by a further assumption of "typicality", and we argue that this assumption is both misguided and unjustified. WAP1, however, requires no such supplementation; it directly implies that any theory that assigns a non-zero probability to our universe predicts that we will observe our universe with probability one. We argue, therefore, that WAP1 is preferable, and note that it has the benefit of avoiding the inductive overreach characteristic of much anthropic reasoning.) Also available at this URL.
- Superluminal signaling and relativity.
- Synthese 148, 2: 381-399 (January 2006). (Gives a precise criterion for deciding whether a signal has been sent faster than light. Key features include a focus on the act of signalling rather than the signal itself and a contextualist account of signalling media.. Prospects for a 'no-go' theorem are discussed, as is the extension from classical to quantum theory.) Also available at this URL.
- Objectivity, information, and Maxwell's demon.
- Philosophy of Science 70, 5: 1245-1255 (Dec 2003). (This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information-content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.) Also available at this URL.
- Review of Palle Yourgrau's Gödel Meets Einstein: Time Travel in the Gödel Universe.
- Philosophical Review 111, 148-152 (Jan 2002). Also available at this URL.
- Absolute quantum mechanics.
- British Journal for the Philosophy of Science 52, 1: 67-73 (March 2001). (Argues that quantum mechanics and quantum field theory are heavily dependent on an absolute spacetime structure, irreconcilable with relational theories of space and time.) Also available at this URL.
- Gravity and gauge theory.
- Philosophy of Science 66, 3: S146-S155. (Points out that the diffeomorphism group of general relativity is not a gauge group in the sense of standard model particle physics, and argues that ignoring the difference between the two sorts of group is vital to understanding the difficulties involved in quantizing gravity.) Also available at this URL.
- Naive quantum gravity.
- In Physics Meets Philosophy at the Planck Scale, edited by Craig Callender and Nicholas Huggett, Cambridge Univ. Press, Cambridge, 2001. (Examination of the way in which the equivalence principle gives rise to difficulties in defining observables, local and global
energy, and time translation, and sketch of the way in which this leads to difficulty in quantizing the theory.)
- General relativity and quantum theory---ontological investigations.
- In Metadebates, 'Einstein Meets Magritte', edited by Diederik Aerts, Jean Paul Van Bendegem and Gustaaf Cornelis, Kluwer Academic, Dordrecht, 1999. (Survey of the respective ontologies of general relativity, non-relativistic quantum mechanics, and quantum field theory, and discussion of the difficulty in finding a single ontology for the physical world.)
- Time, gauge, and the superposition principle in quantum gravity.
- In The Eighth Marcel Grossmann Meeting on General Relativity, edited by Tsvi Piran, World Scientific, Singapore, 1999. (Discussion of the danger of treating time-evolution as a gauge transformation in quantum theory.)
- Review (jointly with A. Fine) of Lee Smolin's The Life of the Cosmos.
- Journal of Philosophy 95:264-268 (May 1998). Also available at this URL
- Strange couplings and space-time structure.
- Philosophy of Science 63,3: S63-S70 (September 1996). (Presentation and discussion of general relativistic
models with ambiguous geometric structure.) Also available at this URL.
- Synthese 106: 241-251 (February 1996). (Critical examination of the Albert & Loewer "Many Minds" interpretation of quantum mechanics.) Also available at this URL.
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