# Proper length

In relativistic physics, proper length is an invariant quantity which is the rod distance between spacelike events in a frame of reference in which the events are simultaneous. (Unlike classical mechanics, simultaneity is relative in relativity. See relativity of simultaneity for more information.)

In special relativity, the proper length L between spacelike events is

,

where
Along an arbitrary spacelike path P in either special relativity or general relativity, the proper length is given in tensor syntax by the line integral

,

where
Proper length is analogous to proper time. The difference is that proper length is the invariant interval of a spacelike path while proper time is the invariant interval of a timelike path. For more information on the path integral above and examples of its use, see the proper time article.

## Notes

• Note 1: By mutiplying or dividing by c2, a metric can be made to produce an invariant interval in units of either space or time. For convenience, physicists often avoid this issue by using geometrized units, which are set up so that c=G=1.

theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity.

The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end. This may be distinguished from height, which is vertical extent, and width or breadth
In mathematics and theoretical physics, an invariant is that which remains unchanged under some transformation. Examples of invariants include the speed of light under a Lorentz transformation and time under a Galilean transformation.
This article is about the drawing and measuring instrument. Ruler can also refer to a statesman in charge or ceremonial head of state of a country or minor politically significant principality; for this meaning see Monarch or Lists of incumbents.

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A frame of reference is a particular perspective from which the universe is observed. Specifically, in physics, it refers to a provided set of axes from which an observer can measure the position and motion of all points in a system, as well as the orientation of objects in it.
Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies.
Simultaneity is the property of two events happening at the same time in at least one reference frame.

The noun Simult means a supernatural coincidence, two or more divinely inspired events that occur at or near the same period of time that are related to each other
The relativity of simultaneity is the concept that simultaneity is not absolute, but dependent on the observer. That is, according to the special theory of relativity formulated by Albert Einstein in 1905, it is impossible to say in an absolute
special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bodies". Some three centuries earlier, Galileo's principle of relativity had stated that all uniform motion was relative, and that there was no absolute and
time.

One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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• , a Canadian science-fiction channel
• The Society for Promotion of Alternative Computing and Employment
• DSPACE, a term in computational complexity theory

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Path, PATH or pathway may refer to:

In natural and built environments:

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spacetime is any mathematical model that combines space and time into a single construct called the space-time continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of the fourth dimension.
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