When scale is surplus
Bibliographic Data
| ID | 10815290 |
|---|---|
| Authors | Sean Gryb (0000-0002-0439-3548, University of Groningen), David Sloan (0000-0002-8302-7879, Lancaster University) |
| Year | 2021 |
| Volume | 199 |
| Issue | 5-6 |
| Pages | 14769-14820 |
| Publication date | 2021-12-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Synthese (JOURNAL) |
| Journal identifiers | ISSN: 0039-7857 • E-ISSN: 1573-0964 |
| Publisher | Springer Science and Business Media LLC (PUBLISHER) |
| DOI | 10.1007/s11229-021-03443-7 |
| OpenAlex | W3139460578 |
| Language | EN |
| Citations received | 3 |
| References cited | 59 |
We study a long-recognised but under-appreciated symmetry called dynamical similarity and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton’s principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology
Dynamical systems theory · Gravitational singularity · Image (mathematics) · Physics · Principal (computer security) · Quantum mechanics · Relevance (law) · Similarity (geometry) · Statistical physics · Symmetry (geometry) · Theoretical physics · Artificial Intelligence · Black Holes and Theoretical Physics · Computer Science · Cosmology and Gravitation Theories · Mathematics · Protein Structure and Dynamics
The “Past Hypothesis”
The role of symmetry in the interpretation of physical theories
Change in Hamiltonian general relativity from the lack of a time-like Killing vector field
On Dirac's incomplete analysis of gauge transformations
Sophistry about symmetries
Understanding Gauge
Rethinking Newton’s Principia
Typicality and the Approach to Equilibrium in Boltzmannian Statistical Mechanics
Boltzmann's Time Bomb
Symmetry as an Epistemic Notion (Twice Over)
Empirical Consequences of Symmetries
Why Surplus Structure Is Not Superfluous
Newtonian Spacetime Structure in Light of the Equivalence Principle
The Empirical Status of Symmetries in Physics
Symmetry, Empirical Equivalence, and Identity
Sophistication about Symmetries
Are Gauge Symmetry Transformations Observable
Perfect Symmetries
A Puzzle about Laws, Symmetries and Measurability
| Citations per year | 1 |
|---|---|
| Citation span | 2023 - 2025 (3) |
| Highly cited | No |