Editing Special relativity (section)

=== Thomas rotation ===
{{See also|Thomas rotation}}
{{multiple image
 | direction = vertical
 | width = 220
 | footer = Figure 4-5. Thomas–Wigner rotation
 | image1 = Thomas-Wigner Rotation 1.svg
 | image2 = Thomas-Wigner Rotation 2.svg
}}

The composition of two non-collinear Lorentz boosts (i.e., two non-collinear Lorentz transformations, neither of which involve rotation) results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation.

Thomas rotation results from the relativity of simultaneity. In Fig.&nbsp;4-5a, a rod of length <math>L</math> in its rest frame (i.e., having a [[proper length]] of {{tmath|1= L }}) rises vertically along the y-axis in the ground frame.

In Fig.&nbsp;4-5b, the same rod is observed from the frame of a rocket moving at speed <math>v</math> to the right. If we imagine two clocks situated at the left and right ends of the rod that are synchronized ''in the frame of the rod'', relativity of simultaneity causes the observer in the rocket frame to observe (not [[#Measurement_versus_visual_appearance|''see'']]) the clock at the right end of the rod as being advanced in time by {{tmath|1= Lv/c^2 }}, and the rod is correspondingly observed as tilted.<ref name="Taylor1992"/>{{rp|98–99}}

Unlike second-order relativistic effects such as length contraction or time dilation, this effect becomes quite significant even at fairly low velocities. For example, this can be seen in the [[Spin–orbit interaction|spin of moving particles]], where [[Thomas precession]] is a relativistic correction that applies to the [[Spin (physics)|spin]] of an elementary particle or the rotation of a macroscopic [[gyroscope]], relating the [[angular velocity]] of the spin of a particle following a [[curvilinear]] orbit to the angular velocity of the orbital motion.<ref name="Taylor1992"/>{{rp|169–174}}

Thomas rotation provides the resolution to the well-known "meter stick and hole paradox".<ref name="Shaw" group=p>{{cite journal |last1=Shaw |first1=R. |title=Length Contraction Paradox |journal=American Journal of Physics |date=1962 |volume=30 |issue=1 |page=72 |doi=10.1119/1.1941907 |bibcode=1962AmJPh..30...72S |s2cid=119855914 }}</ref><ref name="Taylor1992"/>{{rp|98–99}}