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In the context of relativity, "observer" can mean two different things.
Often, observer is synonymous with reference frame or (space-time-)coordinate system: An observer in this sense is someone who assigns coordinate to everything that happens around him. In particular, all events are assigned space coordinate values and a time cordinate value. In the context of special relativity, it is often the case that when there is talk of an observer, what is meant is really an inertial observer, corresponding to a special type of reference frame.
On other occasions, the term is used in a more narrow sense - in those cases, an observer is someone sitting at a certain point in space and using the light signals reaching that location to construct an image of his surroundings. In the context of optical effects in relativity, for instance gravitational lensing, observer is usually meant in this way.
- 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.
In the context of relativity, more concretely: cosmology, oxygen is interesting as an indicator of chemical evolution: Oxygen nuclei are not produced during Big Bang Nucleosynthesis, but they are produced by nuclear fusion reactions in the interior of stars. The presence of oxygen in an astronomical object is an indicator that stellar fusion has taken place, and that the abundances of the different elements thus do not reflect the element abundances in the early universe.