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On the Formal Consistency of Theory and Experiment, with Applications to Problems in the Initial-Value Formulation of the Partial-Differential Equations of Mathematical Physics

Curiel, Erik (2005) On the Formal Consistency of Theory and Experiment, with Applications to Problems in the Initial-Value Formulation of the Partial-Differential Equations of Mathematical Physics. [Preprint]

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    Abstract

    The dispute over the viability of various theories of relativistic,
    dissipative fluids is analyzed. The focus of the dispute is
    identified as the question of determining what it means for a theory
    to be applicable to a given type of physical system under given
    conditions. The idea of a physical theory's regime of
    propriety is introduced, in an attempt to clarify the issue,
    along with the construction of a formal model trying to make the
    idea precise. This construction involves a novel generalization of
    the idea of a field on spacetime, as well as a novel method of
    approximating the solutions to partial-differential equations on
    relativistic spacetimes in a way that tries to account for the
    peculiar needs of the interface between the exact structures of
    mathematical physics and the inexact data of experimental physics in
    a relativistically invariant way. It is argued, on the basis of
    these constructions, that the idea of a regime of propriety plays a
    central role in attempts to understand the semantical relations
    between theoretical and experimental knowledge of the physical world
    in general, and in particular in attempts to explain what it may
    mean to claim that a physical theory models or represents a kind of
    physical system. This discussion necessitates an examination of the
    initial-value formulation of the partial-differential equations of
    mathematical physics, which suggests a natural set of
    conditions---by no means meant to be canonical or exhaustive---one
    may require a mathematical structure, in conjunction with a set of
    physical postulates, satisfy in order to count as a physical theory.
    Based on the novel approximating methods developed for solving
    partial-differential equations on a relativistic spacetime by
    finite-difference methods, a technical result concerning a peculiar
    form of theoretical under-determination is proved, along with a
    technical result purporting to demonstrate a necessary condition for
    the self-consistency of a physical theory.


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    Item Type: Preprint
    Keywords: physical theory; initial-value problem; relativistic physics
    Subjects: General Issues > Models and Idealization
    Specific Sciences > Physics > Relativity Theory
    Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
    General Issues > Structure of Theories
    Depositing User: Dr. Erik Curiel
    Date Deposited: 10 Jun 2011 07:26
    Last Modified: 10 Jun 2011 07:26
    Item ID: 8660
    URI: http://philsci-archive.pitt.edu/id/eprint/8660

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