Editing Special relativity (section)

== Overview ==
===Basis===
Unusual among modern topics in physics, the theory of special relativity needs only mathematics at high school level and yet it fundamentally alters our understanding, especially our understanding of the concept of [[time]].<ref name=Mermin-2009/>{{rp|ix}} Built on just two postulates or assumptions, many interesting consequences follow. 

The two postulates both concern observers moving at a constant speed relative to each other. The first postulate, the {{slink|#principle of relativity}}, says the laws of physics do not depend on objects being at absolute rest: an observer on a moving train sees natural phenomena on that train that look the same whether the train is moving or not.<ref name=Mermin-2009/>{{rp|5}} The second postulate, constant speed of light, says observers on a moving train or on in the train station see light travel at the same speed. A light signal from the station to the train has the same speed, no matter how fast a train goes.<ref name=Mermin-2009/>{{rp|25}}

In the theory of special relativity, the two postulates combine to change the definition of "relative speed". Rather than the simple concept of distance traveled divided by time spent, the new theory incorporates the speed of light as the maximum possible speed. In special relativity, covering ten times more distance on the ground in the same amount of time according to a moving watch does not result in a speed up as seen from the ground by a factor of ten.<ref name=Mermin-2009/>{{rp|28}}

===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" />