Proper length

Information about 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.

See also

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)
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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.
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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
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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.
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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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Distance is a numerical description of how far apart objects are at any given moment in time. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").
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In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated.
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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.
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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.
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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
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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
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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
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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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prevew not available
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In mathematics, orthogonal, as a simple adjective, not part of a longer phrase, is a generalization of perpendicular. It means at right angles, from the Greek ὀρθός orthos
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The term SPACE (capitalized) can refer to:
  • , 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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speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
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A path or pathway is a line representing the course or route of actual, potential or abstract movement (change of location over time).

Path, PATH or pathway may refer to:

In natural and built environments:

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General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16.[1] It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational
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The term tensor has slightly different meanings in mathematics and physics. In the mathematical fields of multilinear algebra and differential geometry, a tensor is a multilinear function.
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In mathematics, a line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. Various different line integrals are in use. In the case of a closed curve it is also called a contour integral.
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metric tensor (or simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime.
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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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coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. "Scalars" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other commutative ring.
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coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. "Scalars" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other commutative ring.
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This article or section may be confusing or unclear for some readers.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since December 2006.
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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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In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events.
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In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated.
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In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events.
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