User:A. di M./Sandbox2

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Fundamental role in physics[edit]

See also: Introduction to special relativity and 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,[1] motivated by Maxwell's theory of electromagnetism and the results of the Michelson–Morley experiment, and has since been confirmed by various experiments.[2][Note 1][3] 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.[4][5]

The plot starts at zero and curves sharply upward toward the right
Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity as v approaches c.

Special relativity has many implications, which often are counter-intuitive, but have been verified in many experiments.[6] These include the equivalence of mass and energy (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 γ = 1/√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".

Event A precedes B in the red frame, is simultaneous with B in the green frame, and follows B in the blue frame.

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.[7] 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.[8]

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.[9]

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.[10][11] Although no conclusive evidence for such theories has been found, they remain the subject of ongoing research.[12][13][14]

  1. ^ Einstein, A (30 June 1905). "Zur Elektrodynamik bewegter Körper" (PDF). Annalen der Physik (in German). 17: 890–921. Retrieved 2009-11-27. English translation: Perrett, W and Jeffery, GB (tr.). "On the Electrodynamics of Moving Bodies". Fourmilab. Retrieved 2009-11-27. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)CS1 maint: multiple names: authors list (link)
  2. ^ Hsu, J-P; Zhang, YZ (2001). Lorentz and Poincaré Invariance. Advanced Series on Theoretical Physical Science. Vol. 8. World Scientific. pp. 543ff. ISBN 9810247214.
  3. ^ Zhang, YZ (1997). Special Relativity and Its Experimental Foundations. Advanced Series on Theoretical Physical Science. Vol. 4. World Scientific. pp. 172–173. ISBN 9810227493.
  4. ^ d'Inverno, R (1992). Introducing Einstein's Relativity. Oxford University Press. pp. 19–20. ISBN 0198596863.
  5. ^ Sriranjan, B (2004). "Postulates of the special theory of relativity and their consequences". The Special Theory to Relativity. PHI Learning. pp. 20 ff. ISBN 812031963X.
  6. ^ Roberts, T (2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. University of California, Riverside. Retrieved 2009-11-27. {{cite web}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  7. ^ Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. pp. 52–59. ISBN 9810227493.
  8. ^ Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. p. 332. ISBN 9810227493.
  9. ^ Cite error: The named reference Gibbs1997 was invoked but never defined (see the help page).
  10. ^ Ellis, GFR; Uzan, J-P (2005). "'c' is the speed of light, isn't it?". American Journal of Physics. 73 (3): 240–247. arXiv:gr-qc/0305099. doi:10.1119/1.1819929. S2CID 119530637. 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.
  11. ^ An overview can be found in the dissertation of Mota, DF (2006). "Variations of the fine structure constant in space and time". arXiv:astro-ph/0401631. {{cite arXiv}}: |class= ignored (help)
  12. ^ Uzan, J-P (2003). "The fundamental constants and their variation: observational status and theoretical motivations". Reviews of Modern Physics. 74: 403. arXiv:hep-ph/0205340. doi:10.1103/RevModPhys.75.403. S2CID 118684485.
  13. ^ Farrell, DJ; Dunning-Davies, J (2007). "The constancy, or otherwise, of the speed of light". In Ross, LV (ed.). New Research on Astrophysics, Neutron Stars and Galaxy Clusters. Nova Publishers. pp. 71ff. ISBN 978-1600211102.
  14. ^ Amelino-Camelia, G (2013). "Quantum-Spacetime Phenomenology". Living Reviews in Relativity. 16 (1): 5. arXiv:0806.0339. doi:10.12942/lrr-2013-5. PMC 5255913. PMID 28179844.


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