On Hilbert's Sixth Problem

This book explores the premise that a physical theory is an interpretation of the analytico–canonical formalism, emphasizing that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. It uses the main criterion physicists use for a theory, the Lagrangian functional, to formulate a physical theory. The theory of Suppes is the main tool in the axiomatization and examples from the usual theories in physics.

Format: Paperback / softback
Length: 191 pages
Publication date: 27 January 2023
Publisher: Springer Nature Switzerland AG

This book delves into the concept that a physical theory can be seen as an interpretation of the analytico-canonical formalism. Throughout the text, the investigation emphasizes that classical mechanics, particularly in its Lagrangian formulation, serves as the formal backbone of theoretical physics. The authors begin by presenting the analytico-canonical formalism for classical mechanics, its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, culminating in the Higgs mechanism.

The analysis employs the primary criterion used by physicists to evaluate a theory: formulating a Lagrangian for it. A physical theory represents a specific instance of the Lagrangian functional. Therefore, a unified physical theory already exists. All that is required is to specify the corresponding Lagrangian (or Lagrangian density); the associated Euler-Lagrange equations form the dynamical equations. The theory of Suppes serves as the primary tool in the axiomatization and provides examples from the usual theories in physics.

For applications, a vast array of results from logic lead to intriguing and sometimes unexpected consequences.

This volume examines the context in which our physics takes place and the mathematical universe necessary for describing our concrete physical events. It also explores whether we employ the constructive universe or if we require set-theoretically generic spacetimes.

Weight: 326g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030838393
Edition number: 1st ed. 2022