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 |
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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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