dorsal/arxiv
View SchemaNewtownian Relativity, Gravity, and Cosmology
| Authors | J. L. McCauley |
|---|---|
| Categories | |
| ArXiv ID | physics/0001027 |
| URL | https://arxiv.org/abs/physics/0001027 |
Abstract
Well-known to specialists but little-known to the wider audience is that Newtonian gravity can be understood as geodesic motion in space-time, where time is absolute and space is Euclidean. Newtonian cosmology formulated by Heckmann agrees implicitly with Cartan's formulation of Newtonian mechanics as geodesic motion in space-time, but does not unfold the underlying geometric picture. I present the transformation theory of Newtonian mechanics and gravity developed by Cartan and Heckmann, and show via coordinate transformations that Heckmann's Newtonian cosmological model has a center, so that the cosmological principle cannot hold globally. It is possible to confuse the relativity principle with a position of relativism. Mach's principle has much to do with the latter and nothing to do with the former. Both general relativity and nonlinear dynamics inform us that most coordinate systems ae defined locally by differential equations that are globally nonintegrable: global extensions of local coordinates usually do not exist. I explain how defining inertial frames locally by free fall short-circuits Mach's philosophic objectios to Newtonian dynamics.
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"abstract": "Well-known to specialists but little-known to the wider audience is that\nNewtonian gravity can be understood as geodesic motion in space-time, where\ntime is absolute and space is Euclidean. Newtonian cosmology formulated by\nHeckmann agrees implicitly with Cartan\u0027s formulation of Newtonian mechanics as\ngeodesic motion in space-time, but does not unfold the underlying geometric\npicture. I present the transformation theory of Newtonian mechanics and gravity\ndeveloped by Cartan and Heckmann, and show via coordinate transformations that\nHeckmann\u0027s Newtonian cosmological model has a center, so that the cosmological\nprinciple cannot hold globally.\n It is possible to confuse the relativity principle with a position of\nrelativism. Mach\u0027s principle has much to do with the latter and nothing to do\nwith the former. Both general relativity and nonlinear dynamics inform us that\nmost coordinate systems ae defined locally by differential equations that are\nglobally nonintegrable: global extensions of local coordinates usually do not\nexist. I explain how defining inertial frames locally by free fall\nshort-circuits Mach\u0027s philosophic objectios to Newtonian dynamics.",
"arxiv_id": "physics/0001027",
"authors": [
"J. L. McCauley"
],
"categories": [
"physics.class-ph",
"physics.pop-ph"
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"title": "Newtownian Relativity, Gravity, and Cosmology",
"url": "https://arxiv.org/abs/physics/0001027"
},
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