Dictionary

coordinates

A rule for assigning to each point of a general space or spacetime a set of numbers for purposes of identification.

Many readers will know two examples from school: In the case of the line of real numbers, every point on the line corresponds to a real number which can be seen as its coordinate. What’s important is that these coordinates reflect neighbourly relations: The number 1 lies between the number 0 and the number 2, and so does the point corresponding to it lie between the two points corresponding to 0 and 2. The second example is the usual X-Y-coordinate system (sometimes called Cartesian coordinates), by which every point in a plane can be characterized by two numbers: the first its X coordinate value, the second its Y coordinate value.

The examples reflect an important property of coordinates: To uniquely identify a point in space, one needs as many coordinate values as the space has dimensions.

Of the four coordinates defining an event in spacetime, three serve to fix its location in three-dimensional space, while the fourth gives the point in time for the event.

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.

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.

second

In the International System of units: the basic unit of time. Defined as a certain multiple of the oscillation period of electromagnetic radiation set free in a certain transition within the electron shell of atoms of the type Cesium-133.

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.

plane

A surface within which the axioms of Euclidean geometry (synonym: plane geometry) hold - the rules of geometry as they are taught in high school, with well-known formulae such as Pythagoras's theorem and "the perimeter of a circle is 2 times pi times its radius" hold.

line

Geometric object with a single dimension. A line can either be an independent one-dimensional space (in the abstract mathematical space where a space does not need to have three dimensions), or it can be embedded into a more general space, like a line drawn onto a piece of paper (i.e. a surface).

event

In the context of special or general relativity: Anything that is defined by a single point in time and a single point in space, i.e. something that happens at a definite time at a definite location. Synonym: spacetime point.

coordinates

A rule for assigning to each point of a general space or spacetime a set of numbers for purposes of identification. Many readers will know two examples from school: In the case of the line of real numbers, every point on the line corresponds to a real number which can be seen as its coordinate. What's important is that these coordinates reflect neighbourly relations: The number 1 lies between the number 0 and the number 2, and so does the point corresponding to it lie between the two points corresponding to 0 and 2. The second example is the usual X-Y-coordinate system (sometimes called Cartesian coordinates), by which every point in a plane can be characterized by two numbers: the first its X coordinate value, the second its Y coordinate value. The examples reflect an important property of coordinates: To uniquely identify a point in space, one needs as many coordinate values as the space has dimensions. Of the four coordinates defining an event in spacetime, three serve to fix its location in three-dimensional space, while the fourth gives the point in time for the event.

coordinate system (coordinates)

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coordinates

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