Bentley's paradox (named after

Richard Bentley Richard Bentley FRS (; 27 January 1662 – 14 July 1742) was an English classical scholar, critic, and theologian. Considered the "founder of historical philology", Bentley is widely credited with establishing the English school of Hellen ...

) is a cosmological paradox pointing to a problem occurring when

Newton's theory of gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...

is applied to cosmology. Namely, if all the stars are drawn to each other by gravitation, they should collapse into a single point.

History

In 1687,

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...

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 equilibritum 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." Both Newton and Bentley thought that the stars did not move and did not consider stars in motion. A finite number of mutually attracting stars in motion can indeed avoid collapse. Today it is known that an infinite universe uniformly filled with gravitating matter cannot be analyzed using Newtonian mechanics, as the resulting force at each point in each direction would indeed be infinite. The

general theory of relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...

can deal with this problem. 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 Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potential ...

", the opposite phenomenon of the "

Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...

".{{cite book , last = Clegg , first = Brian , author-link = Brian Clegg (writer) , date = 4 August 2009 , title = Before the Big Bang: The Prehistory of Our Universe , url = https://archive.org/details/beforebigbangpre0000cleg , url-access = registration , publisher =

St. Martin's Press St. Martin's Press is a book publisher headquartered in Manhattan, New York City, in the Equitable Building. St. Martin's Press is considered one of the largest English-language publishers, bringing to the public some 700 titles a year under si ...

, pages
32–35
, chapter = What and How Big? , isbn = 9780312385477 , postscript = none

References and notes

Physical cosmology Gravity Paradoxes