A Middle Way A Non-Fundamental Approach to Many-Body Physics

by Batterman, Robert W.

• ISBN13: 9780197568613
• ISBN10: 0197568610
• Format: Hardcover
• Copyright: 2021-07-28
• Publisher: Oxford University Press

Summary

Robert W. Batterman's monograph examines a ubiquitous methodology in physics and the science of materials that has virtually been ignored in the philosophical literature. This method focuses on mesoscale structures as a means for investigating complex many-body systems. It challenges foundational pictures of physics where the most important properties are taken to be found at lower, more fundamental scales.

This so-called "hydrodynamic approach" has its origins in Einstein's pioneering work on Brownian motion. This work can be understood to be one of the first instances of "upscaling" or homogenization whereby values for effective continuum scale parameters can be theoretically determined. Einstein also provided the first statement of what came to be called the "Fluctuation-Dissipation" theorem. This theorem justifies the use of equilibrium statistical mechanics to study the nonequilibrium behaviors of many-body systems.

Batterman focuses on the consequences of the Fluctuation-Dissipation theorem for a proper understanding of what can be considered natural parameters or natural kinds for studying behaviors of such systems. He challenges various claims that such natural, or joint carving, parameters are always to be found at the most fundamental level. Overall, Batterman argues for mesoscale first, middle-out approach to many questions concerning the relationships between fundamental theories and their phenomenological, continuum scale cousins.

Author Biography

Robert W. Batterman is Distinguished Professor of Philosophy at the University of Pittsburgh. Prior to his arrival in Pittsburgh, he was the Rotman Canada Research Chair in Philosophy of Science at the University of Western Ontario. He is a Fellow of the Royal Society of Canada. He is the author of
The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence (Oxford, 2002) and editor of The Oxford Handbook of Philosophy of Physics (2013). He works in the philosophy of physics and philosophy of applied mathematics, focusing primarily upon the area of condensed matter
broadly construed. His research interests include the foundations of statistical physics, materials science, dynamical systems and chaos, asymptotic reasoning, mathematical idealizations, explanation, reduction, and emergence.

Table of Contents

Contents
Preface
1. Introduction
1.1 Philosophy and Foundational Problems
1.2 Autonomy and Fundamentality
1.3 Two-ish Senses of Fundamental
1.4 Hydrodynamic Methods: A First Pass
1.5 Representative Volume Elements
1.6 Fluctuation and Dissipation
1.7 Preview of Upcoming Chapters
2. Autonomy
2.1 Pegs and Boards
2.2 How to Answer (AUT)
2.2.1 Multiple Realizability? Really?
2.2.2 Universality
2.2.3 Renormalization Group
2.3 Generalizations
2.3.1 Multi-scale Modeling of Materials
2.4 A Brief Thought Experiment
2.5 Conclusion
3. Hydrodynamics
3.1 Conserved Quantities and Transport
3.1.1 Spin Diffusion Equations
3.2 Correlation Functions
3.3 Linear Response
3.4 Conclusion
4. Brownian Motion
4.1 Introduction
4.2 The Hydrodynamic Equation
4.3 Effective Viscosity in Brownian Contexts
4.3.1 Summary: An Answer to (AUT)
4.4 Brownian Motion and the F-D Theorem
4.5 Conclusion
5. From Brownian Motion to Bending Beams
5.1 Introduction
5.2 Bulk Properties of Heterogeneous Systems
5.3 Conclusion
6. An Engineering Approach
6.1 Introduction
6.2 Schwinger's Engineering Approach
6.3 Order Parameters, Mesoscales, Correlations
6.4 Multiscale Modeling in Biology
6.4.1 Modeling Bone Fracture
6.5 Conclusion
7. The Right Variables and Natural Kinds
7.1 Introduction
7.2 Woodward on Variable Choice
7.3 The Right (Mesoscale) Variables
7.4 Another Minimal Model Example
7.4.1 The Model: Lattice Gas Automaton
7.5 Conclusion
8. Conclusions
8.1 Foundational Problems vs. Methodology
8.2 Autonomy and Heterogeneity
8.3 Brownian Motion and the F-D Theorem
8.4 A Middle-Out/Engineering Methodology
8.5 A Physical Argument for the Right Variables