Unification, decoupling, and identification in the “Palatini formalism”

Unification, decoupling, and identification in the “Palatini formalism”. February 2017.
abstract bibtex

This paper focuses on a couple of philosophical and historical aspects of the “Palatini formalism,” one of the “metric-affine” approaches to general relativity. It is argued here that the history and the conceptual developments of this formalism (mainly in the first two decades after the wake of general relativity), as well as its more recent incarnations, illustrate the interplay of several concepts in the philosophy of science. There are three aims of the present argument. First, the unificatory power of formalism is under scrutiny here: the decoupling of two mathematical structures by taking them as independent variables, followed by a partial structural identification. Second, it is the way we can read off enticing philosophical aspects of General Relativity from its formalism: the relation between the operations of decoupling and identifications (of mathematical structures) and explanation (mathematical explanation, structural explanation, and last but not least, functional explanation) is germane here. Third, this approach complements and augments current discussions on the role and value of variational principles in physics, especially in general relativity. Overall this paper attempts to show how mathematical constructs and assumptions have a role in the ontology of general relativity and some of its “extensions.”

@unpublished{UnificationDecouplingIdentification2017a,
	title = {Unification, decoupling, and identification in the “{Palatini} formalism”},
	copyright = {All rights reserved},
	abstract = {This paper focuses on a couple of philosophical and historical aspects of the “Palatini formalism,” one of the “metric-affine” approaches to general relativity. It is argued here that the history and the conceptual developments of this formalism (mainly in the first two decades after the wake of general relativity), as well as its more recent incarnations, illustrate the interplay of several concepts in the philosophy of science. There are three aims of the present argument. First, the unificatory power of formalism is under scrutiny here: the decoupling of two mathematical structures by taking them as independent variables, followed by a partial structural identification. Second, it is the way we can read off enticing philosophical aspects of General Relativity from its formalism: the relation between the operations of decoupling and identifications (of mathematical structures) and explanation (mathematical explanation, structural explanation, and last but not least, functional explanation) is germane here. Third, this approach complements and augments current discussions on the role and value of variational principles in physics, especially in general relativity. Overall this paper attempts to show how mathematical constructs and assumptions have a role in the ontology of general relativity and some of its “extensions.”},
	language = {5. Philosophy of physics},
	month = feb,
	year = {2017},
	keywords = {Correction to GTR, Decoupling, General Theory of Relativity, Unification},
}

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