![]() These authors claim that NCG is characterized not by any single symmetry group, but by numerous nested symmetries. On the other hand, a version of NCG as a purported Yang–Mills-type theory has been proposed in the physics literature, primarily by Duval and Künzle (1984). S218) observes that NCG cannot be derived from an action principle hence, it cannot be formulated as a constrained Hamiltonian system, and to the extent that gauge talk is talk about constrained Hamiltonian systems, gauge talk cannot characterize NCG. But how this gauge structure relates to the standard formulation is a bit cryptic, as is how it relates to other notions of gauge symmetry. Most authors agree that NCG has a gauge structure represented explicitly by a freedom in choosing how to distinguish inertial trajectories from gravitationally accelerated trajectories. Second, while the symmetries of the standard formulation of Newtonian gravity are relatively straight-forward, those for NCG are, at best, open to debate. In particular, it will be seen that “non-geometricized” Newtonian gravity can also be formulated in background spacetimes with less structure than Neo-Newtonian spacetime, and that one version of NCG is the legitimate empirically indistinguishable partner to these theories. But this will involve distinguishing between different versions of NCG, as well as different versions of the standard formulation. I will claim that this is not the case-that NCG and the standard formulation, appropriately construed, are legitimate non-trivial examples of empirically indistinguishable theories. In particular, perhaps NCG, so-constrained, is simply the standard formulation in disguise. However, if the standard formulation is only recoverable from NCG under the imposition of certain constraints, and if these constraints effectively reduce the ontology of NCG to the ontology of the standard formulation, then perhaps they are not significantly different after all. In particular, an anti-realist may question whether a realist interpretation of Newtonian gravity is possible, given that there are non-trivial empirically indistinguishable versions of it. This claim is significant in the debate over scientific realism. Some authors have claimed that NCG and the standard formulation of Newtonian gravity make identical empirical claims, but subscribe to different ontologies hence they count as a non-trivial example of empirically indistinguishable theories. At least two versions of NCG have appeared in the latter, and these versions affect the status of NCG as an alleged example of empirical indistinguishability. While it has been given considerable attention in the philosophical literature (see, e.g., Earman & Friedman, 1973 Friedman, 1983 Earman, 1989 Malament 1986, Malament 1995 Norton, 1995), I think it deserves a second look, for a number of reasons.įirst, the philosophical literature does not reflect the current state of affairs in the physics literature. This geometricized version of the theory was first described by Cartan and is usually referred to as Newton–Cartan gravity (NCG, hereafter). Newtonian gravity can also be given a curved spacetime formulation by geometricizing the gravitational field and incorporating it into the curvature tensor in a manner similar to general relativity. The latter is normally taken to be flat Neo-Newtonian spacetime, the spacetime characterized by automorphisms belonging to the Galilei group (the symmetry group for Newtonian dynamics). This relationship is not possible based on lifespan dates.The standard way of formulating Newton's theory of gravity is as the theory of a gravitational field in a background spacetime. You have chosen this person to be their own family member. Year should not be greater than current year Continuing with this request will add an alert to the cemetery page and any new volunteers will have the opportunity to fulfill your request. Sorry! There are no volunteers for this cemetery. GREAT NEWS! There is 1 volunteer for this cemetery. This photo was not uploaded because you have already uploaded 15 photos to this memorial This photo was not uploaded because this memorial already has 30 photos This photo was not uploaded because you have already uploaded 5 photos to this memorial This photo was not uploaded because this memorial already has 20 photos You may not upload any more photos to this memorial
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