Summary: Studies in History and Philosophy of
Modern Physics 35 (2004) 345376
Theories of Newtonian gravity and empirical
Department of Humanities and Social Sciences, Polytechnic University, Brooklyn, NY 11201, USA
Received 28 September 2003; accepted 28 October 2003
In this essay, I examine the curved spacetime formulation of Newtonian gravity known as
NewtonCartan gravity and compare it with flat spacetime formulations. Two versions of
NewtonCartan gravity can be identified in the physics literature--a ``weak'' version and a
``strong'' version. The strong version has a constrained Hamiltonian formulation and con-
sequently a well-defined gauge structure, whereas the weak version does not (with some
qualifications). Moreover, the strong version is best compared with the structure of what Earman
(World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This
suggests that there are also two versions of Newtonian gravity in flat spacetime--a ``weak''
version in Maxwellian spacetime, and a ``strong'' version in Neo-Newtonian spacetime. I
conclude by indicating how these alternative formulations of Newtonian gravity impact the
notion of empirical indistinguishability and the debate over scientific realism.
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