Editing Squeeze mapping (section)

===Relativistic spacetime===
[[File:Orthogonality and rotation.svg|thumb|350px|Euclidean [[orthogonality]] is preserved by rotation in the left diagram; [[hyperbolic orthogonality]] with respect to hyperbola (B) is preserved by squeeze mapping in the right diagram]]
Spacetime geometry is conventionally developed as follows: Select (0,0) for a "here and now" in a spacetime. Light radiant left and right through this central event tracks two lines in the spacetime, lines that can be used to give coordinates to events away from (0,0). Trajectories of lesser velocity track closer to the original timeline (0,''t''). Any such velocity can be viewed as a zero velocity under a squeeze mapping called a [[Lorentz boost]]. This insight follows from a study of [[split-complex number]] multiplications and the [[split-complex number#The diagonal basis|diagonal basis]] which corresponds to the pair of light lines.
Formally, a squeeze preserves the hyperbolic metric expressed in the form ''xy''; in a different coordinate system. This application in the [[theory of relativity]] was noted in 1912 by Wilson and Lewis,<ref>[[Edwin Bidwell Wilson]] & [[Gilbert N. Lewis]] (1912) "The space-time manifold of relativity. The non-Euclidean geometry of mechanics and electromagnetics", Proceedings of the [[American Academy of Arts and Sciences]] 48:387&ndash;507, footnote p.&nbsp;401</ref> by Werner Greub,<ref>W. H. Greub (1967) ''Linear Algebra'', Springer-Verlag. See pages 272 to 274</ref> and by [[Louis Kauffman]].<ref>[[Louis Kauffman]] (1985) "Transformations in Special Relativity", [[International Journal of Theoretical Physics]] 24:223&ndash;36</ref> Furthermore, the squeeze mapping form of Lorentz transformations was used by [[Gustav Herglotz]] (1909/10)<ref>{{Citation|author=Herglotz, Gustav|year=1910|orig-year=1909|title=Über den vom Standpunkt des Relativitätsprinzips aus als starr zu bezeichnenden Körper|trans-title=Wikisource translation: [[s:Translation:On bodies that are to be designated as "rigid"|On bodies that are to be designated as "rigid" from the standpoint of the relativity principle]]|journal=Annalen der Physik|volume=336|issue=2 |pages=408|doi=10.1002/andp.19103360208|bibcode = 1910AnP...336..393H |url=https://zenodo.org/record/1424161}}</ref> while discussing [[Born rigidity]], and was popularized by [[Wolfgang Rindler]] in his textbook on relativity, who used it in his demonstration of their characteristic property.<ref>[[Wolfgang Rindler]], ''Essential Relativity'', equation 29.5 on page 45 of the 1969 edition, or equation 2.17 on page 37 of the 1977 edition, or equation 2.16 on page 52 of the 2001 edition</ref>

The term ''squeeze transformation'' was used in this context in an article connecting the [[Lorentz group]] with [[Jones calculus]] in optics.<ref>Daesoo Han, Young Suh Kim & Marilyn E. Noz (1997) "Jones-matrix formalism as a representation of the Lorentz group", [[Journal of the Optical Society of America]] A14(9):2290–8</ref>