There is significant interest in the Philosophy of Science community to understand the role that "effective theories" have in the work of forefront science. The ideas of effective theories have been implicit in science for a long time, but have only been articulated well in the last few decades. Since Wilson's renormalization group revolution in the early 1970's, the science community has come to more fully understand its power, and by the mid-1990's it had gained its apotheosis. It is still one of the most powerful concepts in science, which has direct impact in how one thinks about and formulates theories of nature. It is this power that this Brief sets out to emphasize through historical analysis and current examples.
Author(s): James D. Wells
Series: Springer Briefs in Physics
Edition: 1
Publisher: Springer
Year: 2012
Language: English
Pages: 84
Tags: Physics; Planetary Orbits; Harmonic Oscillator; Elementary Particle Masses
Effective Theoriesin Physics
Preface
Acknowledgments
Contents
Acronyms
1 The Utility of Effective Theories
1.1 Definition of Effective Theories and Their Purpose
1.2 Galileo's Law of Falling Bodies as an Effective Theory
References
2 Harmonic Oscillator as an Effective Theory
2.1 Basics of the Harmonic Oscillator
2.2 Ubiquity of the Harmonic Oscillator
2.3 First Theory
2.4 Second Theory
2.5 Fancy Explanations
2.6 Third Theory
2.7 Deep Theory Conjecture
2.8 Ultimate Test?
3 Effective Theories of Classical Gravity
3.1 Introduction
3.2 Orbits in Newton's Theory
3.2.1 Orbital Solution
3.2.2 The Hamiltonian and Veff Description
3.3 Perihelion Precessions from Perturbations
3.3.1 1/r2 Correction to the Central Potential
3.3.2 1/r3 Correction to the Central Potential
3.4 Philosophical Challenges to Newton's Theory
3.5 Effective Theories
3.5.1 Application to Newton's Gravitation
3.5.2 Inevitable Perihelion Precession
3.6 Mercury's Anomalous Perihelion Precession
3.6.1 Analyzing Bob's 1/r2 Correction Theory
3.6.2 Analyzing Alice's 1/r3 Correction Theory
3.6.3 Gerber's ``Utterly Worthless'' Theory
3.7 Perturbation from General Relativity
3.8 Conclusions
References
4 Effective Theories and Elementary Particle Masses
4.1 Introduction
4.2 The Problem of Mass in Chiral Gauge Theories
4.3 Standard Model Electroweak Theory
4.4 The Special Case of Neutrino Masses
4.5 Natural Effective Theories, the Higgs Boson, and the Hierarchy Problem
References
5 Effective Theories and Theory Choice
5.1 Introduction
5.2 The Standard Model's Triumphs and Woes
5.3 Theory Choice Among Practitioners
5.4 The Standard Model Versus the Effective Standard Model
5.5 Richter's IBE Criteria
5.6 Thagard's IBE Criteria
5.7 Non-negotiable Attributes of a Best Explanation
5.8 Effective Field Theories and Consistency
5.9 Relation to Thagard's Analogy Criterion
5.10 Summary: The Preeminence of Consistency
5.11 Implications for the LHC and Beyond
References
