Beyond Newtonian Gravitational Attraction: Superfluid Quantized Vortices and the Resolution of Bentley's Paradox

Abstract

For centuries, Isaac Newton's theory of universal gravitation reigned supreme, offering an elegant explanation for the celestial ballet [1]. However, nestled within its seemingly perfect framework lay a persistent thorn – the Bentley Paradox. Posed by the renowned mathematician Richard Bentley in 1728, it exposed a fundamental flaw: if every particle attracts every other, wouldn't the universe inevitably collapse in on itself under the combined pull? Newton grappled with the paradox but ultimately left it unresolved. The present article offers a resolution to both Bentley’s old paradox and also Zwicky paradox which now is known as Dark Matter hypothesis, from the viewpoint of superfluid vortices, and in the last section we provide hint toward close correspondence between low temperature physics and cosmology phenomena, one of which is already known in literature as Kibble-Zurek mechanism.