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Absolute simultaneity refers to the concurrence of events in time at different locations in space in a manner agreed upon in all frames of reference. The theory of relativity does not have a concept of absolute time because there is a relativity of simultaneity .
The metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the Einstein field equations). Using the weak-field approximation , the metric tensor can also be thought of as representing the 'gravitational potential'.
A point in spacetime is called an event, and requires four numbers to be specified: the three-dimensional location in space, plus the position in time (Fig. 1). An event is represented by a set of coordinates x, y, z and t. [4]
By definition, all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. [8] The norm of a vector v in a normed vector space can be considered to be the magnitude of v.
Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at the speed of light is depicted as following a 45° angle to the diagram's axes.
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O , and its direction represents the angular orientation with respect to given reference axes.
The radar-time definition of extended-simultaneity further facilitates visualization of the way that acceleration curves spacetime for travelers in the absence of any gravitating objects. This is illustrated in the figure at right, which shows radar time/position isocontours for events in flat spacetime as experienced by a traveler (red ...