Willem de Sitter Quotes

Willem de Sitter was a Dutch mathematician, physicist, and astronomer.

✵ 6. May 1872 – 20. November 1934
Willem de Sitter photo
Willem de Sitter: 44   quotes 0   likes

Famous Willem de Sitter Quotes

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

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

Willem de Sitter Quotes about space

Willem de Sitter Quotes about time

“We know by actual observation only a comparatively small part of the whole universe. I will call this "our neighborhood." Even within the confines of this province our knowledge decreases very rapidly as we get away from our own particular position in space and time. It is only within the solar system that our empirical knowledge extends to the second order of small quantities (and that only for g44 and not for the other gαβ), the first order corresponding to about 10-8. How the gαβ outside our neighborhood are, we do not know, and how they are at infinity of space or time we shall never know. Infinity is not a physical but a mathematical concept, introduced to make our equations more symmetrical and elegant. From the physical point of view everything that is outside our neighborhood is pure extrapolation, and we are entirely free to make this extrapolation as we please to suit our philosophical or aesthetical predilections—or prejudices. It is true that some of these prejudices are so deeply rooted that we can hardly avoid believing them to be above any possible suspicion of doubt, but this belief is not founded on any physical basis. One of these convictions, on which extrapolation is naturally based, is that the particular part of the universe where we happen to be, is in no way exceptional or privileged; in other words, that the universe, when considered on a large enough scale, is isotropic and homogeneous.”

"The Astronomical Aspect of the Theory of Relativity" (1933)

Willem de Sitter Quotes

“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.”

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

“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?”

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.”

Kosmos (1932)

“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.
"The Astronomical Aspect of the Theory of Relativity" (1933)

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