User:A. di M./Sandbox2
Fundamental role in physics
{{See also|Introduction to special relativity|Special relativity}}
The speed at which light propagates in vacuum is independent of both the source of the light and the inertial frame of reference of the observer. This was postulated by Albert Einstein in 1905,{{cite journal
| last = Einstein
| first = A
| authorlink = Albert Einstein
|date=30 June 1905
| title = Zur Elektrodynamik bewegter Körper
| journal = Annalen der Physik
| volume = 17
| pages = 890–921
| url = http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf
| language = German
| accessdate = 2009-11-27
}} English translation: {{cite web
| url =http://www.fourmilab.ch/etexts/einstein/specrel/www/
| title =On the Electrodynamics of Moving Bodies
| author =Perrett, W and Jeffery, GB (tr.)
| coauthors =Walker, J (ed.)
| publisher =Fourmilab
| accessdate =2009-11-27
}} motivated by Maxwell's theory of electromagnetism and the results of the Michelson–Morley experiment, and has since been confirmed by various experiments.
{{cite book
|last1=Hsu |first1=J-P |last2=Zhang |first2=YZ
|year=2001
|title=Lorentz and Poincaré Invariance
|url=https://books.google.com/books?id=jryk42J8oQIC&pg=RA1-PA541
|publisher=World Scientific
|series=Advanced Series on Theoretical Physical Science
|volume=8 |pages=543ff
|isbn=9810247214
}}Strictly speaking, it is only possible to experimentally verify that the two-way speed of light (for example from a source to a mirror and back again) is frame-independent, since it is impossible to measure the one-way speed of light (for example from a source to a distant detector) without some convention as to how clocks at the source and detector should be synchronized. However, by adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two way speed of light by definition.
{{cite book
|last=Zhang |first=YZ
|year=1997
|title=Special Relativity and Its Experimental Foundations
|url=http://www.worldscibooks.com/physics/3180.html
|publisher=World Scientific
|series=Advanced Series on Theoretical Physical Science
|volume=4 |pages=172–173
|isbn=9810227493
}} The theory of special relativity explores the consequences of the existence of such an invariant speed c and the assumption that the laws of physics are the same in all inertial frames of reference.
{{cite book
|last=d'Inverno |first=R
|year=1992
|title=Introducing Einstein's Relativity
|pages=19–20
|publisher=Oxford University Press
|isbn=0198596863
{{cite book
|last=Sriranjan |first=B
|year=2004
|chapter=Postulates of the special theory of relativity and their consequences
|chapter-url=https://books.google.com/books?id=FsRfMvyudlAC&pg=PA20
|title=The Special Theory to Relativity
|publisher=PHI Learning
|isbn=812031963X
|pages=20 ff
}}
Special relativity has many implications, which often are counter-intuitive, but have been verified in many experiments.{{cite web
| url =http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
| title =What is the experimental basis of Special Relativity?
| first =T
| last =Roberts
| coauthors =Schleif, S; Dlugosz, JM (ed.)
| year =2007
| work =Usenet Physics FAQ
| publisher =University of California, Riverside
| accessdate =2009-11-27
}}
These include the equivalence of mass and energy {{nowrap|(E {{=}} mc2)}}, length contraction (moving objects are shorter), and time dilation (moving clocks run slower). The factor by which the energy and lifetime of an object with a speed v increase and its length decreases is the Lorentz factor {{nowrap|γ {{=}} 1/{{radic|1 − v2/c2}}}}; it is nearly equal to 1 for speeds much less than c, so the differences between special relativity and Galilean relativity are usually negligible in everyday life; but it diverges to infinity as v approaches c, so a massive particle can have arbitrarily large energies without exceeding the speed of light. On the other hand, γ is always finite for speeds strictly less than c, so massless particles with non-zero energy (infinite γ) can only travel at c. This includes photons of light, which justifies calling c the "speed of light".
File:Relativity of Simultaneity.svg
Another counter-intuitive consequence of special relativity is the relativity of simultaneity; if the spatial distance between two events A and B is greater than the time interval between them multiplied by c, then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous, with the consequence that such events cannot have a causal relation.
The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (with c relating units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter c.
{{cite book
|last=Hartle |first=JB
|year=2003
|title=Gravity: An Introduction to Einstein's General Relativity
|pages=52–59
|publisher=Addison-Wesley
|isbn=9810227493
}} Lorentz invariance has become an almost universal assumption for modern physical theories, such as quantum electrodynamics (QED), quantum chromodynamics (QCD), the Standard Model of particle physics, and general relativity. As such, the parameter c has become ubiquitous in modern physics, appearing in many contexts which may seem at first unrelated to light. For example, general relativity predicts that c is also the speed of gravity and of gravitational waves.
{{cite book
|last=Hartle |first=JB
|year=2003
|title=Gravity: An Introduction to Einstein's General Relativity
|pages=332
|publisher=Addison-Wesley
|isbn=9810227493
}}
In non-inertial frames (gravitationally curved space or accelerated frames), the local speed of light is constant and equal to c, but the speed of light along a trajectory of finite length can differ from c, depending on how distances and times are defined.
It is generally assumed in physics that fundamental constants such as c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time. However, various theories have suggested that the speed of light has changed over time.
{{cite journal
|last1=Ellis |first1=GFR |last2=Uzan |first2=J-P
|year=2005
|title='c' is the speed of light, isn't it?
|journal=American Journal of Physics
|volume=73 |issue=3 |pages=240–247
|doi=10.1119/1.1819929
|arxiv=gr-qc/0305099
|s2cid=119530637 |quote=The possibility that the fundamental constants may vary during the evolution of the universe offers an exceptional window onto higher dimensional theories and is probably linked with the nature of the dark energy that makes the universe accelerate today.
}}An overview can be found in the dissertation of {{cite arXiv
|last=Mota |first=DF
|year=2006
|title=Variations of the fine structure constant in space and time
|class=astro-ph
|eprint=astro-ph/0401631
}} Although no conclusive evidence for such theories has been found, they remain the subject of ongoing research.
{{cite journal
|last=Uzan |first=J-P
|year=2003
|title=The fundamental constants and their variation: observational status and theoretical motivations
|journal=Reviews of Modern Physics
|volume=74 |page=403
|doi=10.1103/RevModPhys.75.403
|arxiv=hep-ph/0205340
|s2cid=118684485
{{cite book
|last1=Farrell |first1=DJ |last2=Dunning-Davies |first2=J
|year=2007
|chapter=The constancy, or otherwise, of the speed of light
|chapter-url=https://books.google.com/books?id=CZzOKIcQqxMC&pg=PA71
|editor=Ross, LV
|title=New Research on Astrophysics, Neutron Stars and Galaxy Clusters
|pages=71ff
|publisher=Nova Publishers
|isbn=978-1600211102
{{cite journal
|last=Amelino-Camelia |first=G
|year=2013
|title=Quantum-Spacetime Phenomenology
|journal=Living Reviews in Relativity
|volume=16
|issue=1
|page=5
|doi=10.12942/lrr-2013-5
|doi-access=free
|pmid=28179844
|pmc=5255913
|arxiv=0806.0339
}}
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