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Willem de Sitter war ein niederländischer Astronom.

✵ 6. Mai 1872 – 20. November 1934
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Willem de Sitter: Zitate auf Englisch

“The manner in which time and space are bound up with each other in the four-dimensional continuum is variable. It is difficult to express this variability of the cross-connections between space and time in simple language, and different interpretations of it are possible, corresponding to different mathematical transformations of the fundamental line-element, e. g. a different choice of the variable which we interpret as "time." Perhaps the best way we can express it is by saying that the solution of the field-equations of the theory of relativity shows that there is in the universe a tendency to change its scale, which at the present time results in an expansion, but may perhaps at other times become, or have been, a shrinking. This is true of the grand scale model of the universe.”

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Willem de Sitter

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

“Both the law of inertia and the law of gravitation contain a numerical factor or a constant belonging to matter, which is called mass. We have thus two definitions of mass; one by the law of inertia: mass is the ratio between force and acceleration. We may call the mass thus defined the inertial or passive mass, as it is a measure of the resistance offered by matter to a force acting on it. The second is defined by the law of gravitation, and might be called the gravitational or active mass, being a measure of the force exerted by one material body on another. The fact that these two constants or coefficients are the same is, in Newton's system, to be considered as a most remarkable accidental coincidence and was decidedly felt as such by Newton himself. He made experiments to determine the equality of the two masses by swinging a pendulum, of which the bob was hollow and could be filled up with different materials. The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i. e., the inertial and the gravitational mass are the same. These experiments have been repeated in the nineteenth century by Bessel, and in our own times by Eötvös and Zeeman, and the identity of the inertial and the gravitational mass is one of the best ascertained empirical facts in physics-perhaps the best. It follows that the so-called fictitious forces introduced by a motion of the body of reference, such as a rotation, are indistinguishable from real forces…. In Einstein's general theory of relativity there is also no formal theoretical difference, as there was in Newton's system…. the equality of inertial and gravitational mass is no longer an accidental coincidence, but a necessity.”

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Willem de Sitter

p, 125
"The Astronomical Aspect of the Theory of Relativity" (1933)

“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.”

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Willem de Sitter

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

“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.”

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

“It was early 1932, when Einstein and I both were at the California Institute of Technology in Pasedena, and we just decided to look for a simple relativistic model that agreed reasonably well with the known observational data, namely, the Hubble recession rate and the mean density of matter in the universe. So we took the space curvature to be zero and also the cosmological constant and the pressure term to be zero, and then it follows straightforwardly that the density is proportional to the square of the Hubble constant. It gives a value for the density that is high, but not impossibly high. That's about all there was to it. It was not an important paper, although Einstein apparently thought that it was. He was pleased to have a simple model with no cosmological constant. That's it.”

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As quoted by Helge Kragh, Masters of the Universe: Conversations with Cosmologists of the Past (2014)

“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.”

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Willem de Sitter

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

“Gradually… during the second half of the nineteenth century, the uncomfortable feeling of dislike of the action at a distance, which had been so strong in Huygens and other contemporaries of Newton, but had subsided during the eighteenth century, began to emerge again, and gained strength rapidly.
This was favoured by the purely mathematical transformation (which can be compared in a sense with that from the Ptolemaic to the Copernican system), replacing Newton's finite equations by the differential equations, the potential becoming the primary concept, instead of the force, which is only the gradient of the potential. These ideas, of course, arose first in the theory of electricity and magnetism or perhaps one should say in the brain of Faraday.”

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Willem de Sitter

Kosmos (1932)

“In astronomy two characteristics are common to all data on which the solution of the great problems depends. The first is the extreme minuteness of the quantities to be measured. …New epochs were inaugurated in the beginning of the seventeenth century by the invention of the telescope, and in the last third of the nineteenth by the discovery of photography and spectroscopy…. The other characteristic is that astronomy always requires a very large number of data. …These two characteristics of the data that the astronomer requires to build his science on make two things more necessary in astronomy than in any other science: patience and organised coöperation. …The astronomer—each working at his own task…—is always conscious of belonging to a community, whose members, separated in space and time, nevertheless feel joined by a very real tie, almost of kinship. …whatever his special work may be it is always a link in a chain, which derives its value from the fact that there is another link to the left and one to the right of it. It is the chain that is important, not the separate links.”

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Kosmos (1932)

“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?”

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Willem de Sitter

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

“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.”

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Willem de Sitter

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

“To help us to understand three-dimensional spaces, two-dimensional analogies may be very useful… A two-dimensional space of zero curvature is a plane, say a sheet of paper. The two-dimensional space of positive curvature is a convex surface, such as the shell of an egg. It is bent away from the plane towards the same side in all directions. The curvature of the egg, however, is not constant: it is strongest at the small end. The surface of constant positive curvature is the sphere… The two-dimensional space of negative curvature is a surface that is convex in some directions and concave in others, such as the surface of a saddle or the middle part of an hour glass. Of these two-dimensional surfaces we can form a mental picture because we can view them from outside… But… a being… unable to leave the surface… could only decide of which kind his surface was by studying the properties of geometrical figures drawn on it. …On the sheet of paper the sum of the three angles of a triangle is equal to two right angles, on the egg, or the sphere, it is larger, on the saddle it is smaller. …The spaces of zero and negative curvature are infinite, that of positive curvature is finite. …the inhabitant of the two-dimensional surface could determine its curvature if he were able to study very large triangles or very long straight lines. If the curvature were so minute that the sum of the angles of the largest triangle that he could measure would… differ… by an amount too small to be appreciable… then he would be unable to determine the curvature, unless he had some means of communicating with somebody living in the third dimension…. our case with reference to three-dimensional space is exactly similar. …we must study very large triangles and rays of light coming from very great distances. Thus the decision must necessarily depend on astronomical observations.”

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Willem de Sitter

Kosmos (1932)

“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?”

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Willem de Sitter

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

“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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Willem de Sitter

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

“Both the law of inertia and the law of gravitation contain a numerical factor or a constant belonging to matter, which is called mass.”

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Willem de Sitter

We have thus two definitions of mass; one by the law of inertia: mass is the ratio between force and acceleration. We may call the mass thus defined the inertial or passive mass, as it is a measure of the resistance offered by matter to a force acting on it. The second is defined by the law of gravitation, and might be called the gravitational or active mass, being a measure of the force exerted by one material body on another. The fact that these two constants or coefficients are the same is, in Newton's system, to be considered as a most remarkable accidental coincidence and was decidedly felt as such by Newton himself. He made experiments to determine the equality of the two masses by swinging a pendulum, of which the bob was hollow and could be filled up with different materials. The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i.e., the inertial and the gravitational mass are the same. These experiments have been repeated in the nineteenth century by Bessel, and in our own times by Eötvös and Zeeman, and the identity of the inertial and the gravitational mass is one of the best ascertained empirical facts in physics-perhaps the best. It follows that the so-called fictitious forces introduced by a motion of the body of reference, such as a rotation, are indistinguishable from real forces. ...In Einstein's general theory of relativity there is also no formal theoretical difference, as there was in Newton's system. ...the equality of inertial and gravitational mass is no longer an accidental coincidence, but a necessity.
"The Astronomical Aspect of the Theory of Relativity" (1933)

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