It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalisation group. This paper has three aims: to clarify the structure of the explanation of universality; to discuss the physics of such renormalisation group explanations; and to examine the extent to which universality is thus explained.The derivation of critical exponents proceeds via a real-space or a fieldtheoretic approach to the renormalisation group. Building on Mainwood (2006), this paper argues that these approaches ought to be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. * alexander.a.franklin@kcl.ac.uk † I would like to thank
Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our understanding of a molecule in isolation, as well as of chemistry's relation to quantum physics. 1 Introduction 2 The Problems of Molecular Structure 2.1 Enantiomers and Hund's paradox 2.2 Isomers and the inability of resultant Hamiltonians to determine molecular structure 2.3 Symmetry breaking 3 The Measurement Problem 3.1 Enantiomers and Hund's paradox 3.2 Isomers and the inability of resultant Hamiltonians to determine molecular structure 3.3 Symmetry breaking 4 Interpretations of Quantum Mechanics: Implications for the Ontology of Chemistry 4.1 The Everett interpretation 4.2 De Broglie-Bohm theory 4.3 Spontaneous collapse theories 5 Conclusion * Authors listed in alphabetical order.
Effective Quantum Field Theories (EFTs) are effective insofar as they apply within a prescribed range of length-scales, but within that range they predict and describe with extremely high accuracy and precision. The effectiveness of EFTs is explained by identifying the features -the scaling behaviour of the parameters -which lead to effectiveness. The explanation relies on distinguishing autonomy with respect to changes in microstates (autonomy ms ), from autonomy with respect to changes in microlaws (autonomy ml ), and relating these, respectively, to renormalisability and naturalness. It is claimed that the effectiveness of EFTs is a consequence of each theory's autonomy ms rather than its autonomy ml .
The universality of critical phenomena is best explained by appeal to the Renormalisation Group (RG). Batterman and Morrison, among others, have claimed that this explanation is irreducible. I argue that the RG account is reducible, but that the higher-level explanation ought not to be eliminated. I demonstrate that the key assumption on which the explanation relies-the scale invariance of critical systems-can be explained in lower-level terms; however, we should not replace the RG explanation with a bottom-up account, rather we should acknowledge that the explanation appeals to dependencies which may be traced down to lower levels.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.