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Derivation of Classical Mechanics in an Energetic Framework via Conservation and Relativity

Goyal, Philip (2020) Derivation of Classical Mechanics in an Energetic Framework via Conservation and Relativity. [Preprint]

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Abstract

The concepts of conservation and relativity lie at the heart of classical mechanics. In the hands of Descartes, Galileo, and Huygens, these concepts led to early results which were critical to its early development. However, over the following two centuries, their perceived importance to the struc- ture of mechanics underwent considerable change. In view of this complex historical development, to what extent do conservation and relativity determine the structure of mechanics? In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continu- ously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Goyal, Philip
Subjects: Specific Sciences > Physics > Classical Physics
General Issues > Laws of Nature
General Issues > Science Education
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr Philip Goyal
Date Deposited: 19 Apr 2020 01:52
Last Modified: 19 Apr 2020 01:52
Item ID: 17090
Subjects: Specific Sciences > Physics > Classical Physics
General Issues > Laws of Nature
General Issues > Science Education
General Issues > Structure of Theories
Specific Sciences > Physics > Symmetries/Invariances
Date: 18 April 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17090

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