Editing Special relativity (section)

== History ==
{{Main|History of special relativity}}

The principle of relativity, forming one of the two postulates of special relativity, was described by [[Galileo Galilei]] in 1632 using a thought experiment involving observing natural phenomena on a moving ship.<ref>{{cite book| title=[[Dialogue Concerning the Two Chief World Systems]]| last=Galilei| first=Galileo| date= 1632| pages=216–217}}</ref> His conclusions were summarized as [[Galilean relativity]] and used as the basis of [[Newtonian mechanics]].<ref name=Mermin-2009/>{{rp|1}} This principle can be expressed as a [[coordinate transformation]], between two coordinate systems. [[Isaac Newton]] noted that many transformations, such as those involving rotation or acceleration, will not preserve the observation of physical phenomena.  Newton considered only those transformations involving motion with respect to an immovable absolute space, now called transformations between inertial frames.<ref name=Weinberg-1972>{{cite book |last=Weinberg |first=Steven |url=https://archive.org/details/gravitationcosmo00stev_0 |title=Gravitation and cosmology |date=1972 |publisher=John Wiley & Sons |isbn=9780471925675 |author-link=Steven Weinberg |url-access=registration}}.</ref>{{rp|17}}

In 1864 [[James Clerk Maxwell]] presented a theory of [[Electromagnetism|electromagnetism]] which did not obey Galilean relativity. The theory specifically predicted a constant speed of light in vacuum, no matter the motion (velocity, acceleration, etc.) of the light emitter or receiver or its frequency, wavelength, direction, polarization, or phase. This, as yet untested theory, was thought at the time to be only valid in inertial frames fixed in an [[luminiferous aether|aether]] Numerous experiments followed, attempting to measure the speed of light as Earth moved through the proposed fixed aether, culminating in the 1887 [[Michelson-Morley experiment]] which only confirmed the constant speed of light.<ref name=Weinberg-1972/>{{rp|18}}

Several fixes to the aether theory where proposed, with those of [[George Francis Fitzgerald]], [[Hendrik Antoon Lorentz]], and [[Jules Henri Poincare]] all pointing in the direction of a result similar to the theory of special relativity. The final important step was taken by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies".<ref name="electro" group="p">[[Albert Einstein]] (1905) "[https://web.archive.org/web/20050220050316/http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf ''Zur Elektrodynamik bewegter Körper'']", ''Annalen der Physik'' 17: 891; English translation [http://www.fourmilab.ch/etexts/einstein/specrel/www/ On the Electrodynamics of Moving Bodies] by [[George Barker Jeffery]] and Wilfrid Perrett (1923); Another English translation [[s:On the Electrodynamics of Moving Bodies|On the Electrodynamics of Moving Bodies]] by [[Megh Nad Saha]] (1920).</ref> Einstein applied the [[Lorentz transformations]] known to be compatible with [[Maxwell's equations]] for electrodynamics to the classical laws of mechanics. This changed Newton's mechanics situations involving all motions, especially velocities close to that of light<ref name=Weinberg-1972/>{{rp|18}} (known as ''{{vanchor|relativistic velocities|relativistic velocity}}''). 

Another way to describe the advance made by the special theory is to say Einstein extended the Galilean principle so that it accounted for the constant speed of light,<ref name="Taylor1992"/> a phenomenon that had been observed in the Michelson–Morley experiment. He also postulated that it holds for all the [[laws of physics]], including both the laws of mechanics and of [[electrodynamics]].<ref name="Rindler0">{{cite book |title=Essential Relativity: Special, General, and Cosmological |first1= Wolfgang |edition=illustrated |last1=Rindler |page= §1,11 p. 7 |url=https://books.google.com/books?id=0J_dwCmQThgC&pg=PT148 |isbn=978-3-540-07970-5 |publisher=Springer Science & Business Media|date=1977 }}</ref>
The theory became essentially complete in 1907, with [[Hermann Minkowski]]'s papers on spacetime.<ref name="Lanczos-1970" />

Special relativity has proven to be the most accurate model of motion at any speed when gravitational and quantum effects are negligible.<ref>{{cite book |last=Goldstein |first=Herbert |title=Classical Mechanics |title-link=Classical Mechanics (Goldstein book) |publisher=Addison-Wesley Publishing Company |year=1980 |isbn=0-201-02918-9 |edition=2nd |chapter=Chapter 7: Special Relativity in Classical Mechanics |author-link=Herbert Goldstein }}</ref><ref name="Lanczos-1970">{{Cite book|last=Lanczos |first=Cornelius |title=The Variational Principles of Mechanics |publisher=Dover Publications |year=1970 |isbn=978-0-486-65067-8 |edition=4th |chapter=Chapter IX: Relativistic Mechanics |author-link=Cornelius Lanczos }}</ref> Even so, the Newtonian model remains accurate at low velocities relative to the speed of light, for example, everyday motion on Earth.

When updating his 1911 book on relativity, to include general relativity in 1920, [[Robert Daniel Carmichael]] called the earlier work the "restricted theory" as a "special case" of the new general theory; he also used the phrase "special theory of relativity".<ref>{{Cite book |last=Carmichael |first=R.D. |title=The Theory of Relativity |date=1920 |publisher=John Wiley & Sons, Incorporated. |location=United Kingdom}}</ref> In comparing to the general theory in 1923 Einstein specifically called his earlier work "the special theory of relativity", saying he meant a restriction to frames uniform motion.<ref>{{Cite book |last=Einstein |first=Albert |title=The principle of relativity: a collection of orig. memoirs on the special and general theory of relativity |date=1970 |publisher=Dover |isbn=978-0-486-60081-9 |editor-last=Lorentz |editor-first=Hendrik A. |edition=Nachdr. d. Ausg. 1923 |location=New York |chapter=The Foundation of the General Theory of Relativity |editor-last2=Einstein |editor-first2=Albert}}</ref>{{rp|111}}
Just as [[Galilean invariance|Galilean relativity]] is accepted as an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak [[gravitational field]]s, that is, at a sufficiently small scale (e.g., when [[tidal force]]s are negligible) and in conditions of [[free fall]]. But general relativity incorporates [[non-Euclidean geometry]] to represent gravitational effects as the geometric curvature of spacetime. Special relativity is restricted to the flat spacetime known as [[Minkowski space]]. As long as the universe can be modeled as a [[pseudo-Riemannian manifold]], a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this [[curved spacetime]].