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observer

In the context of relativity, “observer” can mean two different things.

Often, observer is synonymous with reference frame or (spacetime-)coordinate system: An observer in this sense is someone who assigns coordinates to everything that happens around him. In particular, all events are assigned space coordinate values and a time coordinate value. In the context of special relativity, it is often the case that when one talks about an observer, what is really meant is 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.

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space

In a strict sense: Space as we know it from everyday life: the totality of all locations in which objects can sit, with three dimensions. In a more general sense used by mathematicians, all kinds of sets of points are spaces - a line for instance, which has but a single dimension, or a two-dimensional surface, but also higher-dimensional spaces. Also, in such more general spaces, geometry can be different from the standard Euclidean geometry taught in high schools - such spaces can be curved.

reference frame

Already in special relativity, motion is relative, and whenever there is talk about a moving clock, one must give the additional information: Moving relative to whom or what? Such a "whom or what", in other words: An object together with a recipe to determine locations relative to that object and to measure time, is called a reference frame.

In special relativity, there exists a special and very important class of reference frame, so-called inertial reference frames, in short: inertial frames.

point

Elementary "building block" of geometrical entities such as surfaces or more general spaces. For instance, a surface is the set of all its points, of all possible locations on the surface, and all geometrical objects in that surface are defined by the points that belong to them - for instance, a line on the surface is the set of (infinitely many) points.

observer

In the context of relativity, "observer" can mean two different things. Often, observer is synonymous with reference frame or (spacetime-)coordinate system: An observer in this sense is someone who assigns coordinates to everything that happens around him. In particular, all events are assigned space coordinate values and a time coordinate value. In the context of special relativity, it is often the case that when one talks about an observer, what is really meant is 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.

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observer

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