Willem de Sitter

“[Einstein's cosmological constant] is a name without any meaning. ...We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality.”

“Our own galaxy system is only one of a great many, and observations made from any of the others would show exactly the same thing: all systems are receding, not from any particular centre, but from each other: the whole system of galaxies is expanding.”

“The inconsistency of first explaining matter by atoms and then explaining atoms by matter was only slowly realised, and it is only comparatively recently that we have come to see that there is nothing paradoxical in the fact that an atom or an electron, which are not matter, may have properties different from those of matter, and must be allowed to do things that a material particle could not do.”

“How does it come about that we have been able to find satisfactory hypotheses to explain electricity and magnetism, light and heat, in short all other physical phenomena, but have been unsuccessful in the case of gravitation?”

“In Einstein's general theory of relativity the identity of these two coefficients, the gravitational and the inertial mass, is no longer a miracle, but a necessity, because gravitation and inertia are identical.”

“All systems are receding, not from any particular centre, but from each other: the whole system of galactic systems is expanding.”

“These... are the two observational facts about our neighbourhood, which have to be accounted for by the theory: there is a finite density of matter, and there is expansion, i.e. the mutual distances are increasing, and therefore the density is decreasing.”

“Since we only consider the universe on a very large scale, and make abstraction of all details and local irregularities, our universe must be homogeneous and isotropic. It follows... that the three-dimensional space of it must be what mathematicians call a space of constant curvature.”

“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.”

“Purely mathematical symbols have no meaning by themselves; it is the privilege of pure mathematicians, to quote Bertrand Russell, not to know what they are talking about. ...It is the physicist, and not the mathematician, who must know what he is talking about.”

“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.”

“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?”

“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.”

“We had become so accustomed to think of λ as an essentially positive quantity, and of a finite world with positive curvature, that the idea of investigating the possibility of solutions with negative or zero values of λ and of the curvature simply did not arise. But when this oversight was corrected, it appeared at once that in the non-static case both λ and the curvature need not be positive, but can be negative or zero quite as well.”

“Observations give us two data, viz. the rate of expansion and the average density, and there are three unknowns: the value of λ, the sign of the curvature, and the scale of the figure, i.e. the units of R and of the time. The problem is indeterminate.”

“If the curvature is small (as we know it must be, because it is imperceptible by ordinary geometric methods in our neighbourhood), then λ must be small, and if the curvature is very small, then λ must be very small. On the other hand, if λ is very small, or zero, then the curvature must be very small, and may even be zero.”

“If we put in the details, the singularities of the field, viz. the galactic systems and the stars, we find that there is... a tendency, called gravitation, to decrease the mutual distances of these "singularities." At short distances, within the confines of a galactic system, this second tendency is by far the strongest, and the galactic systems retain their size independent of the expansion or contraction of the universe...”

“It is possible to relegate the epoch of the starting of the expansion to minus infinity, e.g. by using instead of the ordinary time the logarithm of the time elapsed since the beginning. But this is only a mathematical trick. We call zero minus infinity, but that only means that we allow the universe an infinite time to get well started on its course of expansion, but it does not make the time during which anything really happens any longer.”