Observations on hyperplanes: I State reduction and unitary evolution


This is the first of two papers responding to ‘recent’ commentary on various aspects of hyperplane dependence by several authors. In this paper I focus on the issues of the relations of HD to state reduction and unitary evolution. The authors who’s comments I address here are Maudlin and Myrvold. In the second paper of this set I focus on HD dynamical variables and localizable properties and measurements and address comments of de Koning, Halvorson, Clifton and Wallace. Each paper ends with some reflections on the implications of HD for the ontology of Minkowski space-time. To set the stage for my responses, I begin this paper with some general position statements designed to correct what seem to be widespread and erroneous construals of some of my views. Two central points are argued for in this first paper. First, dynamical evolution occurs not only within foliations of Minkowski space-time. Rather the transition from the physical state of affairs on any one hyperplane to any other, whether the hyperplanes intersect or are parallel, is always an instance of dynamical evolution between them, generated by some active combination of boost-like transformations and/or time-like translations and/or state reductions and ‘reconstructions’. This point gives rise to a generalized conception of a history of dynamical evolution, allowing for the use of parameterized families of hyperplanes that multiply cover some portions of space-time. Nevertheless, and this is the second central point, for any two generalized histories, H and H’, the quantum states for a system on all the hyperplanes of H from the asymptotic past up to some hyperplane, h, determine the quantum states for the system on all the hyperplanes of H’ from the asymptotic past up to any hyperplane, h’, such that h’ lies to the past of all those state reduction regions that lie to the future of all hyperplanes of H that are ‘earlier’ than h. Consideration of these results should defuse concerns that have been voiced about the coherence and consistency of HD. A position closely related to the second point has already been argued for by Myrvold



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Gordon N. Fleming
Pennsylvania State University

Citations of this work

A Quantum-Theoretic Argument Against Naturalism.Bruce L. Gordon - 2011 - In Bruce L. Gordon & William A. Dembski (eds.), The Nature of Nature: Examining the Role of Naturalism in Science. Wilmington, DE: ISI Books. pp. 179-214.
Relativistic Invariance and Modal Interpretations.John Earman & Laura Ruetsche - 2005 - Philosophy of Science 72 (4):557-583.
Chasing Chimeras.Wayne C. Myrvold - 2009 - British Journal for the Philosophy of Science 60 (3):635-646.
Bloch's paradox and the nonlocality of chance.Brian A. Woodcock - 2007 - International Studies in the Philosophy of Science 21 (2):137 – 156.

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References found in this work

On relativity theory and openness of the future.Howard Stein - 1991 - Philosophy of Science 58 (2):147-167.
On peaceful coexistence: is the collapse postulate incompatible with relativity?Wayne C. Myrvold - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (3):435-466.

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