A Middle Way
A Non-Fundamental Approach to Many-Body Physics
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Product details:
- Publisher OUP USA
- Date of Publication 29 September 2021
- ISBN 9780197568613
- Binding Hardback
- No. of pages190 pages
- Size 165x241x18 mm
- Weight 426 g
- Language English 125
Categories
Short description:
Robert W. Batterman's monograph in the philosophy of physics focuses on how the Fluctuation-Dissipation theorem reveals important consequences for exploring and understanding the behavior of large, many-body systems. He develops a powerful methodology that privileges mesoscale levels between theories describing everyday behaviors of fluids and bending beams and those theories that describe the more fundamental, atomic nature of materials. The "hydrodynamic approach," which has its origins in Einstein's work on Brownian motion, aims to describe and account for continuum behaviors by largely ignoring details at the "fundamental" level. Einstein's work led to a fundamental theorem of statistical mechanics called the "Fluctuation-Dissipation" theorem. He argues against reductionist attempts to derive directly upper level theories from fundamental theories. Instead, he presents an approach to inter-theory relations that starts in the middle, bridging up to theories describing large scale behavior and down to those describing fundamental features.
MoreLong description:
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.
unique and Impressive
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
