Book contents
- Frontmatter
- Contents
- Chapter 1 Introduction
- Chapter 2 The pre-history of classical dynamics
- Chapter 3 The astronomical revolution
- Chapter 4 Precursors to Newtonian dynamics
- Chapter 5 The Newtonian synthesis
- Chapter 6 Philosophical aspects of the Newtonian synthesis
- Chapter 7 The history of statics
- Chapter 8 The development of dynamics after Newton
- Chapter 9 The “Newtonian” approach after Newton
- Chapter 10 From virtual work to Lagrange's equation
- Chapter 11 Extremal principles
- Chapter 12 Some philosophical reflections on explanation and theory
- Chapter 13 Conservation principles
- Chapter 14 Hamilton's equations
- Chapter 15 Canonical transformations, optical analogies and algebraic structures
- Chapter 16 The search for new foundations
- Chapter 17 New directions in the applications of dynamics
- Chapter 18 Spacetime formulations of Newtonian dynamics
- Chapter 19 Formalization: mass and force
- Chapter 20 Relationist dynamics
- Chapter 21 Modes of explanation
- Chapter 22 Retrospective and conclusions
- References
- Index
Chapter 20 - Relationist dynamics
Published online by Cambridge University Press: 05 December 2012
- Frontmatter
- Contents
- Chapter 1 Introduction
- Chapter 2 The pre-history of classical dynamics
- Chapter 3 The astronomical revolution
- Chapter 4 Precursors to Newtonian dynamics
- Chapter 5 The Newtonian synthesis
- Chapter 6 Philosophical aspects of the Newtonian synthesis
- Chapter 7 The history of statics
- Chapter 8 The development of dynamics after Newton
- Chapter 9 The “Newtonian” approach after Newton
- Chapter 10 From virtual work to Lagrange's equation
- Chapter 11 Extremal principles
- Chapter 12 Some philosophical reflections on explanation and theory
- Chapter 13 Conservation principles
- Chapter 14 Hamilton's equations
- Chapter 15 Canonical transformations, optical analogies and algebraic structures
- Chapter 16 The search for new foundations
- Chapter 17 New directions in the applications of dynamics
- Chapter 18 Spacetime formulations of Newtonian dynamics
- Chapter 19 Formalization: mass and force
- Chapter 20 Relationist dynamics
- Chapter 21 Modes of explanation
- Chapter 22 Retrospective and conclusions
- References
- Index
Summary
Machian dynamics
We have seen how Newton attacked spatio-temporal relationism not through a typical philosophical argument that might be argued by a substantivalist, but by claiming that “absolute” space and time were necessary for dynamics. Inertially moving systems are radically distinguished from those which, under the influence of external forces, are not moving inertially. But, to make sense of motion in a constant direction and at a constant speed, we need an absolute frame relative to which constant direction is constant and relative to which our changing positions are to be measured, and we need an absolute lapse of time (up to a linear transformation) relative to which constant speed is constant. The discovery that absolute place and velocity play no role and can be eliminated even in the framework of Newtonian dynamics in favor of Galilean or neo-Newtonian spacetime with its class of inertial frames should give the relationist no comfort.
In Chapter 16 we briefly sketched the version of relationism proposed by Mach. The core of this program sought a “cosmic” solution to the problem of the reference frame relative to which accelerations were absolute, with the source of the inertial forces sought in acceleration-dependent relations of test systems to the distant “fixed stars.” We noted that Mach's proposal remained shrouded in vagueness and that subsequent proposals in his vein were generally deemed unsatisfactory. In the twentieth century a new kind of Machianism has been proposed by J. Barbour and B. Bertotti. It is to their theory that we must now turn our attention.
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- Information
- Philosophy and the Foundations of Dynamics , pp. 235 - 244Publisher: Cambridge University PressPrint publication year: 2012