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Olbers’ paradox

In an infinitely extended universe that does not change over time and is evenly filled with stars, the “night sky” would look as bright as the surface of the sun. The reason: The farther away a star, the weaker the light we receive from it. But: The greater the distance, the greater the number of stars that have exactly that distance from us. In an eternal and infinite universe, the two effects cancel exactly.

The big bang models based on Einstein’s general theory of relativity, with a changing universe evolving out of a hot initial state, make no such counter-factual prediction.

Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

surface

Geometric space with two dimensions. Examples include the plane or the surface of a sphere.

sun

The central (and most massive) body of our solar system; the star closest to us; a ball of gas with a radius of ca. 700000 km (for comparison the radius of the earth: 12756 km) and a mass of 1.989·10³⁰ kilograms [see exponential notation]. In the interior of the sun, nuclear fusion processes run their course; they are responsible for the sun's impressive brightness.

star

A cosmic gas ball that is massive enough for pressure and temperatur in its core to reach values where self-sustained nuclear fusion reactions set in. The energy set free in these reactions makes stars into very bright sources of light and other forms of electromagnetic radiation. Once the nuclear fuel is exhausted, the star becomes a white dwarf, a neutron star or a black hole.

stars (star)

light

Light in the strict sense of the word is electromagnetic radiation the human eye can detect, with wave-lengths between 400 and 700 nano metres. In relativity theory and in astronomy, the word is often used in a more general sense, encompassing all kinds of electromagnetic radiation. For instance, astronomers might talk about "infrared light" or "gamma light"; in this context, light in the stricter sense is referred to as "visible light". Within classical physics, the properties of light are governed by Maxwell's equations; in quantum physics, it turns out that light is a stream of energy packets called light quanta or photons. In the context of relativistic physics, light is of great interest, and for a number of reasons. First of all, the speed of light plays a central role in both special and general relativity. Also, there are a number of interesting effects in general relativity which are associated with the propagation of light, namely deflection, the Shapiro effect and the gravitational redshift.

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Olbers’ paradox

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