Editing Special relativity (section)

===Consequences===
Special relativity has a wide range of consequences that have been experimentally verified.<ref>{{cite web |url=http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html |title=What is the experimental basis of Special Relativity? |access-date=2008-09-17 |author1=Tom Roberts |author2=Siegmar Schleif |name-list-style=amp |date=October 2007 |work=Usenet Physics FAQ}}</ref><ref>Will, C. M. (2005). Special relativity: a centenary perspective. In Einstein, 1905–2005: Poincaré Seminar 2005 (pp. 33-58). Basel: Birkhäuser Basel.</ref> The conceptual effects include:
* the {{slink|#relativity of simultaneity}}, events that appear simultaneous to one observer may not be simultaneous to an observer in motion,<ref name=Mermin-2009/>{{rp|49}}
* {{slink|#time dilation}}, time measured between two events by observers in motions differ,
* {{slink|#length contraction}}, distances between two events by observers in motions differ,
* the {{slink|#Lorentz transformation of velocities}}, velocities no longer simply add, 
Combined with other laws of physics, the two postulates of special relativity predict the equivalence of [[mass]] and [[energy]], as expressed in the [[mass–energy equivalence]] formula {{tmath|1= E = mc^2 }}, where <math>c</math> is the [[speed of light]] in vacuum.<ref name="relativity">{{cite book |author=Albert Einstein |title=Relativity: The Special and the General Theory |page= 48 |url=https://books.google.com/books?id=idb7wJiB6SsC&pg=PA50 |isbn=978-0-415-25384-0 |publisher=Routledge |date=2001 |edition=Reprint of 1920 translation by Robert W. Lawson}}</ref><ref name="Feynman">[https://feynmanlectures.caltech.edu/I_15.html#Ch15-S9 The Feynman Lectures on Physics Vol. I Ch. 15-9: Equivalence of mass and energy]</ref>
Special relativity replaced the conventional notion of an absolute, universal time with the notion of a time that is local to each observer.<ref>{{Cite book |last=Hawking |first=Stephen W. |title=The illustrated a brief history of time |date=1996 |publisher=Bantam Books |isbn=978-0-553-10374-8 |edition=Updated and expanded |location=New York}}</ref>{{rp|33}} Information about distant objects can arrive no faster than the speed of light so visual observations always report events that have happened in the past. This effect makes visual descriptions of the effects of special relativity especially prone to mistakes.<ref>{{Cite journal |last=Hughes |first=Theo |last2=Kersting |first2=Magdalena |date=2021-03-01 |title=The invisibility of time dilation |url=https://iopscience.iop.org/article/10.1088/1361-6552/abce02 |journal=Physics Education |volume=56 |issue=2 |pages=025011 |doi=10.1088/1361-6552/abce02 |issn=0031-9120|doi-access=free }}</ref> 

Special relativity also has profound technical consequences.
A defining feature of special relativity is the replacement of [[Euclidean geometry]] with [[Lorentzian geometry]].<ref name="Taylor1992"/>{{rp|8}} Distances in Euclidean geometry are calculated with the [[Pythagorean theorem]] and only involved spatial coordinates. In Lorentzian geometry, 'distances' become 'intervals' and include a time coordinate with a minus sign. Unlike spatial distances, the interval between two events has the same value for all observers independent of their relative velocity.  When comparing two sets of coordinates in relative motion is [[Lorentz transformation]] replace [[Galilean transformation]]s of Newtonian mechanics.<ref name="Taylor1992"/>{{rp|98}} 
Other effects include the relativistic corrects to the [[Doppler effect]] and the [[Thomas precession]].<ref name="Griffiths-2013" /><ref name="Jackson-1999" /> 
It also explains how electricity and magnetism are related.<ref name="Griffiths-2013" /><ref name="Jackson-1999" />