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http://dx.doi.org/10.14477/jhm.2019.32.1.017

How the Geometries of Newton's Flat and Einstein's Curved Space-Time Explain the Laws of Motion  

Yang, Kyoung-Eun (Korea National Univ. of Edu.)
Publication Information
Journal for History of Mathematics / v.32, no.1, 2019 , pp. 17-25 More about this Journal
Abstract
This essay elucidates the way the geometries of space-time theories explain material bodies' motions. A conventional attempt to interpret the way that space-time geometry explains is to consider the geometrical structure of space-time as involving a causally efficient entity that directs material bodies to follow their trajectories corresponding to the laws of motion. Newtonian substantival space is interpreted as an entity that acts but is not acted on by the motions of material bodies. And Einstein's curved space-time is interpreted as an entity that causes the motions of bodies. This essay argues against this line of thought and provides an alternative understanding of the way space-time geometry explain the laws of motion. The workings of the way that Newton's flat and Einstein's curved space-time explains the law of motion is such that space-time geometry encodes the principle of inertia which specifies straight lines of moving bodies.
Keywords
Space-Time Geometry; Newton's Flat Space-Time; Einstein's Curved Space-Time; Laws of Motion; The Law of Inertia; The Principle of Equivalence;
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