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Proper length [1] or rest length [2] is the length of an object in the object's rest frame. The measurement of lengths is more complicated in the theory of relativity than in classical mechanics . In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously.
The formal definition of proper time involves describing the path through spacetime that represents a clock, observer, or test particle, and the metric structure of that spacetime. Proper time is the pseudo-Riemannian arc length of world lines in four-dimensional spacetime. From the mathematical point of view, coordinate time is assumed to be ...
On this usage, comoving and proper distances are numerically equal at the current age of the universe, but will differ in the past and in the future; if the comoving distance to a galaxy is denoted , the proper distance () at an arbitrary time is simply given by = where () is the scale factor (e.g. Davis & Lineweaver 2004). [2]
This is the formula for length contraction. As there existed a proper time for time dilation, there exists a proper length for length contraction, which in this case is ℓ. The proper length of an object is the length of the object in the frame in which the object is at rest.
The roles of time t and proper time have switched so that proper time takes the role of the coordinate for the 4th spatial dimension. A universal velocity c {\displaystyle c} for all objects moving through four-dimensional space appears from the regular time derivative c 2 = ( d x / d t ) 2 + ( d y / d t ) 2 + ( d z / d t ) 2 + ( c d τ / d t ...
In the following, the rest length [3] or proper length [4] of an object is its length measured in the object's rest frame. (This length corresponds to the proper distance between two events in the special case, when these events are measured simultaneously at the endpoints in the object's rest frame. [4])
What one nurse learned about humanity amidst the Ebola epidemic
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. [1] It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald ) and is usually only noticeable ...