Bentley's paradox (named after Richard Bentley) is a cosmological paradox pointing to a problem occurring when Newton's theory of gravitation is applied to cosmology. Namely, if all the stars are drawn to each other by gravitation, they should collapse into a single point.
In 1687, Isaac Newton published the Principia which contained his universal law of gravitational attraction. Five years later, Richard Bentley, a young churchman and scholar who was preparing a lecture about Newton's theories and the rejection of atheism, wrote a letter to Newton: in a finite universe, if all stars attract each other, would they not collapse into a point? And in an infinite universe with infinitely many stars, would not every star be pulled apart by infinite forces acting in all directions? In his reply, Newton agreed with the first point and favored an infinite universe with infinitely many stars, so that each star would be drawn in all directions equally, the forces would cancel and no collapse would occur. Newton acknowledged the problem that the stars would have to be precisely placed to maintain such an unstable equilibrium without collapse, and later claimed that God prevented the collapse by making "constant minute corrections"; "a continual miracle is needed to prevent the Sun and the fixt stars from rushing together through gravity."[1][2]
Both Newton and Bentley thought that the stars did not move and did not consider stars in motion.[2] A finite number of mutually attracting stars in motion can indeed avoid collapse.[3]
Today it is known that an infinite universe uniformly filled with gravitating matter, if it originated in a static configuration, would indeed collapse. This conclusion originally arose from the general theory of relativity,[3] but it is also predicted by Newtonian gravity with the use of mathematical tools that were not available to Newton.[4][5]
Though Newton's explanation was rather unsatisfactory from a cosmological aspect, Bentley's paradox could prove to be the reason behind the "Big Crunch", the opposite phenomenon of the "Big Bang".[6]
The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. The notion of an expanding universe was first scientifically originated by physicist Alexander Friedmann in 1922 with the mathematical derivation of the Friedmann equations. The earliest empirical observation of the notion of an expanding universe is known as Hubble's Law, published in work by physicist Edwin Hubble in 1929, which discerned that galaxies are moving away from Earth at a rate that accelerates proportionally with distance. Independent of Friedmann's work, and independent of Hubble's observations, physicist Georges Lemaître proposed that the universe emerged from a "primeval atom" in 1931, introducing the modern notion of the Big Bang.
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever present matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations.
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