More problems for Newtonian cosmology

TL;DR

This paper highlights a fundamental indeterminism in potential-based Newtonian gravity when boundary conditions are not specified, challenging its applicability as a complete cosmological theory.

Contribution

It reveals an overlooked indeterminism in Newtonian cosmology and critiques Saunders' alternative formulation for failing to match general relativity in certain universes.

Findings

Indeterminism arises without boundary conditions at infinity.

Saunders' formulation does not reproduce GR limits in anisotropic universes.

Newtonian gravity cannot be fully formulated as a cosmological theory.

Abstract

I point out a radical indeterminism in potential-based formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity (as is necessary, and indeed celebrated, in cosmological applications). This indeterminism, which is well known in theoretical cosmology but has received little attention in foundational discussions, can be removed only by specifying boundary conditions at all instants of time, which undermines the theory's claim to be fully cosmological, i.e., to apply to the Universe as a whole. A recent alternative formulation of Newtonian gravity due to Saunders (Philosophy of Science 80 (2013) pp.22-48) provides a conceptually satisfactory cosmology but fails to reproduce the Newtonian limit of general relativity in homogenous but anisotropic universes. I conclude that Newtonian gravity lacks a fully satisfactory cosmological formulation.