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On Two Slights to Noether's First Theorem: Mental Causation and General Relativity

Pitts, J. Brian (2022) On Two Slights to Noether's First Theorem: Mental Causation and General Relativity. Rethinking the Concept of Laws of Nature: Natural Order in the Light of Contemporary Science.

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Abstract

It is widely held among philosophers that the conservation of energy is true and important, and widely held among philosophers of science that conservation laws and symmetries are tied together by Noether's first theorem (that rigid symmetries yield conservation). However, beneath the surface of such consensus lie two slights to Noether's first theorem.

First, there is a 325+-year controversy about mind-body interaction in relation to the conservation of energy and momentum, with occasional reversals of opinion. The currently popular Leibnizian view, dominant since the late 19th century, claims to find an objection to broadly Cartesian views (and non-epiphenomenalist property dualism) in their implication of energy non-conservation. Here energy conservation is viewed as an oracle, an unchallengeable black box. But Noether's first theorem and its converse show that conservation and symmetry of the laws stand or fall together. Absent some basis for expecting conservation in brains that has a claim on the Cartesian (whose view implies the absence of law symmetries in brains), the objection is circular. An empirically based argument is possible, but is a different argument with little force except insofar as it is rooted in neuroscience.

Second, General Relativity has a 100+-year-long controversy about whether gravitational energy exists and is objectively localized. The usual view is that gravitational energy exists but is not objectively localized, though some deny its existence. Without positive answers to both questions, generally applicable conservation laws do not exist: energy is not conserved. This conclusion is startling in itself and a problem for conserved quantity theories of causation. Yet Noether's first theorem applies to General Relativity, which has uncountably many symmetries of its laws and so has conservation laws, indeed uncountably many of them. Many authors downplay these laws due to their quirky properties; some authors even attempt to explain the laws' supposed nonexistence in terms of an absence of symmetries of the geometry, which is a distraction. Thus Noether's first theorem is widely ignored, left uninterpreted, or distorted in relation to General Relativity. Taking the theorem seriously seems possible, however, restoring the conservation of energy, or rather, energies.

How do these controversies relate? One sometimes finds claims that General Relativity's supposed lack of conservation laws answers Leibniz on behalf of Descartes. Taking seriously the superabundance of formal conservation laws in General Relativity, however, suggests that General Relativity resists (not facilitates) mind-to-body causation. This conclusion can be proven apart from interpretive controversies. The resistance is, however, finite and tends to be swamped by larger world-view considerations.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Pitts, J. Brianjbp25@cam.ac.uk0000-0002-7299-5137
Keywords: conservation laws, Noether's first theorem, philosophy of mind, dualism, Cartesianism, interactionism, gravitational energy
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Psychology > Evolutionary Psychology
General Issues > Causation
Specific Sciences > Neuroscience > Cognitive Neuroscience
Specific Sciences > Physics > Fields and Particles
General Issues > Laws of Nature
Specific Sciences > Neuroscience
Specific Sciences > Physics
Specific Sciences > Psychology
Specific Sciences > Physics > Relativity Theory
General Issues > Science and Religion
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr. Dr. J. Brian Pitts
Date Deposited: 11 Mar 2022 02:11
Last Modified: 11 Mar 2022 02:11
Item ID: 20294
Journal or Publication Title: Rethinking the Concept of Laws of Nature: Natural Order in the Light of Contemporary Science
Publisher: Springer
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Psychology > Evolutionary Psychology
General Issues > Causation
Specific Sciences > Neuroscience > Cognitive Neuroscience
Specific Sciences > Physics > Fields and Particles
General Issues > Laws of Nature
Specific Sciences > Neuroscience
Specific Sciences > Physics
Specific Sciences > Psychology
Specific Sciences > Physics > Relativity Theory
General Issues > Science and Religion
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Specific Sciences > Physics > Symmetries/Invariances
Date: 2022
URI: http://philsci-archive.pitt.edu/id/eprint/20294

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