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In special relativity, Poincaré transformations are a class of affine transformations which can be characterized as the transformations between alternative Cartesian coordinate charts on Minkowski spacetime corresponding to alternative states of inertial motion (and different choices of an origin).
The length of any object in a moving frame will appear foreshortened in the direction of motion, or contracted. The amount of contraction can be calculated from the Lorentz transformation. The length is maximum in the frame in which the object is at rest.
Length contraction is the decrease in the measured length of an object from its proper length when measured in a reference frame that is moving with respect to the object: L = L0 1 − v2 c2− −−−−−√ (5.5.2) where L0 is the length of the object in its rest frame, and L is the length in the frame moving with velocity v.
Time Dilation, Length Contraction and Simultaneity: An animated introduction to Galilean relativity, electromagnetism and their incompatibility; an explanation of how Einstein's relativity resolves this problem, and some consequences of relativity for our ideas of time, space and mechanics.
Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth. Length contraction \(L\) is the shortening of the measured length of an object moving relative to the observer’s frame: \[L = L_0 \sqrt{1 - \dfrac{v^2}{c^2}} = \dfrac{L_0}{\gamma}.\]
One of the peculiar aspects of Einstein's theory of special relativity is that the length of objects moving at relativistic speeds undergoes a contraction along the dimension of motion. An observer at rest (relative to the moving object) would observe the moving object to be shorter in length.
This course will introduce you to the concepts behind special relativity including, but not limited to, length contraction, time dilation, the Lorentz transformation, relativistic kinematics, Doppler shifts, and even so-called “paradoxes.”