“The models of Einstein and de Sitter are static solutions”

— Gerald James Whitrow

The Structure of the Universe: An Introduction to Cosmology (1949)
Context: The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity.
It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.<!--p.82

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Gerald James Whitrow 39

British mathematician 1912–2000

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“We… come to the conclusion… that the actual universe is neither the static nor the empty one. It differs so much from both of these that neither can be used as an appropriate grand scale model. We must thus look for other solutions of the general field-equations. On account of the expansion our solution must necessarily be a non-static one, and it must have a finite density. There is only one possible static solution possessing a finite density, viz. our old friend A, but of non-static solutions with finite density there exists a great variety.”

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Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“In 1922, Friedmann… broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.”

Gerald James Whitrow (1912–2000) British mathematician

The Structure of the Universe: An Introduction to Cosmology (1949)
Context: The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity.
It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.<!--p.82

“It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. …The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake.”

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“In February 1917, it was found that a static solution with a positive curvature—the solution A—was not possible without the λ. In fact the curvature is proportional to λ (in solution A, λ is equal to the curvature; in B… it is three times the curvature). Thus, at the time when we had only the two static solutions A and B, and thought that these were the only possible ones, here was a plausible physical interpretation of the meaning of λ: it was the curvature of the world, and the square root of its reciprocal, the radius of curvature, could be conceived as providing a natural unit of length.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“The equilibrium… in order to become static—should be steady, permanent, lasting. …This type of equilibrium… is… independent of any scale. A reduced model will show the same effects as the proper structure. Experiments on models are simple and… instrumental for understanding such structural problems.”

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Steve Keen (1953) Australian economist

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“Make small commitments and keep them. Be a light, not a judge. Be a model, not a critic. Be part of the solution, not part of the problem.”

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