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, … - Willem de Sitter

A question which has long troubled astronomers and physicists is what becomes of the energy that is continually being poured out into space by the sun and the stars. To this question a complete answer is given by the new theory. It is used up, diluted, or degraded, by the expansion of the universe. ...the light travelling through the expanding universe and, so to say, trying to reach a particular star, or stellar system, which is continually receding with great velocity, is losing energy in trying to catch up with it. It is this degradation of the light, technically known as the redshift of the spectral lines, by which we become aware of the receding velocities of the extra-galactic nebulae. It can be shown that the decrease of the total amount of radiant energy in the universe by this degradation exceeds the increase by the radiation of the stars. It would not be correct, however, to conclude that the expansion is caused by the energy thus lost by the radiation...

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 g_αβ), the first order corresponding to about 10^-8. How the g_αβ 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 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.