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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… - Willem de Sitter
" "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 g<sub>44</sub> and not for the other g<sub>αβ</sub>), the first order corresponding to about 10<sup>-8</sup>. How the g<sub>αβ</sub> 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.
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About Willem de Sitter
Willem de Sitter (6 May 1872 – 20 November 1934) was a Dutch mathematician, physicist, astronomer and cosmologist who applied the general theory of relativity to the early investigation of the structure of the universe.
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W. de Sitter
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Additional quotes by Willem de Sitter
The "universe" is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure. What we observe are the stars and nebulae constituting "our neighbourhood." All that goes beyond that, in time or in space, or both, is pure extrapolation.The conclusions derived about the expanding universe depend on the assumed homogeneity and isotropy, i.e. on the hypothesis that the observed finite material density and expansion of our neighbourhood are not local phenomena, but properties of the "universe." It is not inconceivable that this hypothesis may at some future stage of the development of science have to be given up, or modified, or at least differently interpreted.
There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ.
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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