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On Hilbert's Sixth Problem (Synthese Library, 441) - da Costa, Newton C. A.,Dori
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- 物品狀況
- Book Title
- On Hilbert's Sixth Problem (Synthese Library, 441)
- ISBN
- 9783030838362
關於產品
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3030838366
ISBN-13
9783030838362
eBay Product ID (ePID)
27050408424
Product Key Features
Number of Pages
Xiii, 191 Pages
Publication Name
On Hilbert's Sixth Problem
Language
English
Subject
Philosophy & Social Aspects, General, Logic, Physics / General
Publication Year
2022
Type
Textbook
Subject Area
Mathematics, Science
Series
Synthese Library
Format
Hardcover
Dimensions
Item Weight
17 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Dewey Edition
23
Reviews
"This book is a compilation, 'an essay', of the bulk of their work from 1990 to the present. This 191 page essay includes some historical background and lots of snippets and parts of da Costa and Doria's work on the meta-mathematics of mathematical physics. It starts with a primer on graduate-level basic physics ... ending with a consideration of hypercomputation." (Deborah Konkowski, zbMATH 1494.00005, 2022)
Series Volume Number
441
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
531
Table Of Content
Foreword.- 1. Preliminary.- Part I. Physics: A Primer. 2. Classical mechanics.- 3. Variational calculus.- 4. Lagrangian formulation.- 5. Hamilton's equations.- 6. Hamilton-Jacobi theory.- 7. Where the action is.- 8. From classical to quantum.- 9. Field theory.- 10. Electromagnetism.- 11. Special relativity.- 12. General relativity.- 13. Gauge field theories.- Part II. Axiomatics. 14. Axiomatizations in ZFC.- Part III. Technicalities. 15. Hierarchies.- Part IV. More applications. 16. Arnol'd's 1974 problems.- 17. Forcing and gravitation.- 18. Economics and ecology.- Part V. Computer science. 19. Fast-growing functions.- Part VI. Hypercomputation. 20. Hypercomputation.- References.
Synopsis
This book explores the premise that a physical theory is an interpretation of the analytico-canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico-canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism.The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler-Lagrange equations. The theory of Suppes predicates as the main tool inthe axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences.This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set-theoretically generic spacetimes., This book explores the premise that a physical theory is an interpretation of the analytico-canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico-canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism. The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler-Lagrange equations. The theory of Suppes predicates as the main tool inthe axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences. This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set-theoretically generic spacetimes.
LC Classification Number
Q174-175.3
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