“Matter is actually distributed very unevenly… conglomerated into stars and galactic systems. The average density is the density that we should get if all… could be evaporated into atoms of hydrogen, or protons, and… distributed evenly over the whole of space. …three or four protons in every cubic foot. …a million million times less than that of the most perfect vacuum that we can produce… The universe thus consists mostly of emptiness… consider a universe without any matter at all, an empty universe, as a good approximation. But we may also take as our first approximation a universe containing… three or four protons per cubic foot. The local deviations from the average, caused by the conglomeration of matter into stars and stellar systems, are then disregarded in the grand scale model, and are only taken into account when we come to study details.”

Kosmos (1932)

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Willem de Sitter44

Dutch cosmologist 1872–1934

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“In the beginning of 1917, two solutions of the field equations for a homogeneous isotropic universe had been found, which I… call the solutions "A" and "B."… at that time only static solutions were looked for. It was thought that the universe must be a stable structure… In one of these solutions (B) the average density was zero, it was empty; the other one (A) had a finite density…. In B, to get the real universe, we should have to put in a few galactic systems, in A we should have to condense the evenly distributed matter into galactic systems. The universe A… has an average density, but no expansion. It is therefore called the static universe. B, on the other hand… expands, and it could only parade in the garb of a static universe because there is nothing in it to show the expansion. B is therefore called the empty universe. Thus we had two approximations : the static universe with matter and without expansion, and the empty one without matter and with expansion. The actual universe… has both matter and expansion… In 1917… the actual value of the density was still entirely unknown, and the expansion had not yet been discovered.”

Willem de Sitter (1872–1934) Dutch cosmologist

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

“It is easy to compute the density of a static universe of a radius of two thousand million lightyears, and it comes out only very little larger than the observed density. The actual universe is thus very far from empty, it is, on the contrary, nearly full.”

Willem de Sitter (1872–1934) Dutch cosmologist

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

“Is the density anywhere near that corresponding to the static universe, or is it so small that we can consider the empty universe as a good approximation?”

Willem de Sitter (1872–1934) Dutch cosmologist

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

“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.”

Frank Wilczek (1951) physicist

Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

“Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.

As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

pp. 56–57 https://books.google.co.uk/books?id=KHyV4-2EyrUC&pg=PA56 <br class="br">The Expanding Universe (1933)

“In both the solutions A and B the curvature is positive, in both three-dimensional space is finite: the universe has a definite size, we can speak of its radius, and, in the case A, of its total mass. In the case A… the density is proportional to the curvature… Thus, if we wish to have a finite density in a static universe, we must have a finite positive curvature.”

Willem de Sitter (1872–1934) Dutch cosmologist

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

“Ultimately the galaxy, indeed the sum of the universe in its entirety, was mostly nothing; average it all out and it made a pretty good vacuum. But within the foci of matter there were the systems, the stars and planets and habitats—what a cornucopia of life was there!”

Iain Banks Culture series

Source: Culture series, Matter (2008), Chapter 10 “A Certain Lack” (p. 167)

“Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium on symmetry and believed that the sphere was the most perfect of all shapes. Hence the universe must be spherical. …An important feature of the spherical shape… was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind. …A vacuum was impossible. It could no more exist than an infinite physical quantity. …Circular motion was the most perfect and natural movement of all.”

John D. Barrow (1952–2020) British scientist

The Book of Universes: Exploring the Limits of the Cosmos (2011)

“Looked at from the perspective of twentieth-century earth, we see three great stages in the dynamic process of the universe. To this whole process, as it spreads out over perhaps ten billion years of time and ten billion light years of space, we give the name evolution, and we see three great patterns within it. The first is physical evolution. This presumably started with the development of the most elementary particles (whatever they may be); then of neutrons, protons, electrons, and radiations; then of elements from hydrogen to uranium and beyond formed by combining protons and electrons; then of chemical compounds; then finally of increasingly complex molecules from amino acids, and proteins to the great watershed of DNA, the beginnings of life.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1970s, Ecodynamics: A New Theory Of Societal Evolution, 1978, p. 28

“In the "static" universe expansion is impossible, the "empty" universe does expand. Therefore we may be tempted to consider the empty universe as the most likely approximation; and we can proceed to compute the radius of curvature of the universe, supposing it to be of the empty type, from the observed rate of expansion.”

Willem de Sitter (1872–1934) Dutch cosmologist

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

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