30 dec. 2016 Learning physics.Length/ Space contraction.

30 dec. 2016

Special relativity
Introduction to special relativity Principle of relativity Theory of relativity
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Length/ Space contraction.
is the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any non-zero velocity relative to the object.
This contraction (more formally called Lorentz contraction or Lorentz–FitzGerald contraction after Hendrik Lorentz and George Francis FitzGerald) is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction parallel to the direction in which the observed body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes. Only at greater speeds, or for electron motion, does it become significant. At a speed of 13,400,000 m/s (30 million mph, 0.0447c) contracted length is 99.9% of the length at rest; at a speed of 42,300,000 m/s (95 million mph, 0.141c), the length is still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as can be seen from the formula:

${\displaystyle L={\frac {L_{0}}{\gamma (v)}}=L_{0}{\sqrt {1-v^{2}/c^{2}}}}$

where

L₀ is the proper length (the length of the object in its rest frame),

L is the length observed by an observer in relative motion with respect to the object,

v is the relative velocity between the observer and the moving object,

c is the speed of light,

and the Lorentz factor, γ(v), is defined as

${\displaystyle \gamma (v)\equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}\ }$.

In this equation it is assumed that the object is parallel with its line of movement. For the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object. For more general conversions, see the Lorentz transformations. An observer at rest viewing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero.