For the cosmological notion of proper distance, see Comoving distance.
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. But in the theory of relativity, the notion of simultaneity is dependent on the observer.
A different term, proper distance, provides an invariant measure whose value is the same for all observers.
Proper distance is analogous to proper time. The difference is that the proper distance is defined between two spacelike-separated events (or along a spacelike path), while the proper time is defined between two timelike-separated events (or along a timelike path).
^Moses Fayngold (2009). Special Relativity and How it Works. John Wiley & Sons. ISBN 978-3527406074.{{cite book}}: CS1 maint: location missing publisher (link)
^Franklin, Jerrold (2010). "Lorentz contraction, Bell's spaceships, and rigid body motion in special relativity". European Journal of Physics. 31 (2): 291–298. arXiv:0906.1919. Bibcode:2010EJPh...31..291F. doi:10.1088/0143-0807/31/2/006. S2CID 18059490.
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interpreting the length. The metre is considered to be a unit of properlength, whereas the AU is usually used as a unit of observed length in a given frame...
is the proper length of the atmosphere and L its contracted length. As the atmosphere is at rest in S, we have γ=1 and its properLength L0 is measured...
correspond to the proper time of accelerated clocks present at both events. Under all possible proper times between two events, the proper time of the unaccelerated...
s 2 , {\textstyle {\sqrt {-\Delta s^{2}}},} is called the proper distance, or properlength. For values of v {\displaystyle v} greater than and less than...
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relativity, arc length of timelike curves (world lines) is the proper time elapsed along the world line, and arc length of a spacelike curve the proper distance...
the bubble is an inertial reference frame and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion...
worldline, also called the proper time between these events. Length U upon the x-axis represents the rest length or properlength of a rod resting in S. The...
a total of 451 proper names of stars. Of the roughly 10,000 stars visible to the naked eye, only a few hundred have been given proper names in the history...
mundane activities", such as the order in which to cut fingernails or the properlength of a beard. In the pre-Islamic period, sunnah was used to mean "manner...
horizon, in practice this cannot be done. The proper distance to the horizon is finite, so the length of rope needed would be finite as well, but if...
which go through the two events that have either a longer or a shorter properlength than the geodesic, even in Minkowski space. In Minkowski space, the...
barrel, from the tip of the nib and lengthen it until it was of the properlength. They made care not to lengthen it extensively, because the pen was...
\phi )} the Schwarzschild metric (or equivalently, the line element for proper time) has the form d s 2 = c 2 d τ 2 = ( 1 − r s r ) c 2 d t 2 − ( 1 − r...
other record hosting venues like Stadio Olimpico in Rome, Italy. The properlength of the first lane of a competitive running track is 400 m (1,312.3 ft)...
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In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object...