What Is It Like To Be A Conservation Law? Between Laws and Principles
Benedetta Spigola
Organização:  Dept. of Philosophy, University of Bergen
Dept. of Philosophy, University of Bergen
19 / 10 / 2023

For physicists, a conservation law is a physical law associated with a regularity stating that a certain measurable property of an isolated physical system is conserved, i.e., it does not change as the system evolves over time. Philosophically, conservation laws are thought to have an ambiguous nature. For Feynman, conservation laws prove to have a special status because they behave as ‘great general principles’ to which ‘all the various physical laws obey’ (Feynman 1967: 59). Similarly, Wigner argued that conservation laws differ from the ordinary physical laws because their validity ‘transcends’ (cf. Wigner 1972: 13)that of any special theory, e.g., gravitational, electromagnetic, and soon. More recently, the philosophical debate around the controversial and ambiguous nature of conservation laws has focused on the status of necessity that is normally attached to them. In general, the debate splits into two main accounts depending on whether the necessity status is considered as either a matter of degree or of species. In the first view(see in particular Lange 2009), there is only one criterion whereby we know whether a proposition is necessary or not. Nevertheless, propositions of physics are not necessary to the same degree–a certain proposition p can be more necessary than another proposition r. Whether p has greater necessity than r is established by the fact that p is more resilient to counterfactual suppositions than r. In contrast, the second view argues that there are species of necessity. Fine(2002), for instance, holds that a proposition is naturally necessary if it depends on what happens in the (actual) world, while a proposition is metaphysically necessary if it depends on the identity of things. In this view, conservation laws are ‘more fundamental’ than ordinary physical laws because of their metaphysical necessity(see also Wolff 2013).
In this paper, I aim to shed light on the controversial and ambiguous nature of conservation laws by referring to an unduly neglected perspective on the question of what general structure physical theories should have. Despite substantial differences, this structuralist approach has been defended by Poincaré(1902), Duhem(1906), and Cassirer(1937).In this view, every physical proposition has specific structural properties that determine its status and function in a physical theory. For these philosophers, a proposition of physics can be either a statement of measurement, a law, or a principle. The aim of this paper is to show that it is possible to clarify the nature of conservation laws by reflecting on whether they have structural properties of laws or structural properties of principles. In my view, this approach is promising because, far from focusing merely on the necessity status of a single proposition, it reflects on the function and behaviour that a proposition has in a certain theory.

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