Curiel, Erik
(2005)
On the Formal Consistency of Theory and Experiment, with Applications to Problems in the InitialValue Formulation of the PartialDifferential Equations of Mathematical Physics.
[Preprint]
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 partialdifferential 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
initialvalue formulation of the partialdifferential equations of
mathematical physics, which suggests a natural set of
conditionsby no means meant to be canonical or exhaustiveone
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
partialdifferential equations on a relativistic spacetime by
finitedifference methods, a technical result concerning a peculiar
form of theoretical underdetermination is proved, along with a
technical result purporting to demonstrate a necessary condition for
the selfconsistency of a physical theory.
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