What you are talking about is a classic paradox known as Olbers Paradox. Historically, it had, understandably, generated a fascinating and entertaining discussion. Evidently, the night sky is dark. in 1826, Heinrich Olbers (1758--1840) articulated the paradox that come to be attached to his name, although he was not the first to talk about it: if the universe is eternal, static and infinite, then the night sky should be as bright as the surface of the sun. If the stars were distributed uniformly in this universe, then, no matter which direction one looks, one's sight has to encounter a star. The fact that now we know that stars are grouped into galaxies does not really solve the problem. It merely compels us to rephrase it: if galaxies are uniformly distributed in the universe, then no matter which way one looks, one's sight has to encounter a galaxy. As we go farther out, the stars will become less luminous. However, their number will increase with distance, which will compensate for their decreased luminosity. In any event, one should expect that to see "a lot of light" at night, which is not consistent with what actually one sees. Why?
From a logical point of view, the argument above is very sound. That is if the premises are correct, then the conclusion must be correct. But are the premises factually correct? No, they are not. The Theory of General Relativity indicates otherwise. On one hand, contrary to what was assumed above, the universe is not static. It is expending. Because the universe is expanding, the light waves coming to us from far away regions are stretched out and the energy they carry is reduced. On the other hand, the time it takes to receive the light wave is lengthened over the time is took to emit it. Remember that luminosity = energy/time. As a result the apparent brightness will be reduced by the expansion to a degree that makes the night sky appear as it does at night.
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