Editing Principle of relativity (section)

==Special principle of relativity==
{{see also|Inertial frame of reference}}

According to the first postulate of the special theory of relativity:<ref name=Einstein>{{cite book
|title=The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity |author=Einstein, A., Lorentz, H. A., Minkowski, H., and Weyl, H.
|page=111
|url=https://books.google.com/books?id=yECokhzsJYIC&pg=PA111|publisher=Dover Publications
|place=Mineola, NY
|year=1952
|orig-year=1923
|editor=Arnold Sommerfeld
|editor-link=Arnold Sommerfeld
|isbn=0-486-60081-5}}</ref>

{{Quotation|''Special principle of relativity'': If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the ''same'' laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.|Albert Einstein: ''The Foundation of the General Theory of Relativity'', Part A, §1}}
This postulate defines an '''inertial frame of reference'''.

The '''special principle of relativity''' states that physical laws should be the same in every [[inertial frame of reference]], but that they may vary across non-inertial ones. This principle is used in both [[Newtonian mechanics]] and the theory of [[special relativity]]. Its influence in the latter is so strong that [[Max Planck]] named the theory after the principle.<ref>{{cite book |title=Einstein's Pathway to the Special Theory of Relativity |first1=Galina |last1=Weistein |publisher=Cambridge Scholars Publishing |year=2015 |isbn=978-1-4438-7889-0 |page=272 |url=https://books.google.com/books?id=FWIHCgAAQBAJ}} [https://books.google.com/books?id=FWIHCgAAQBAJ&pg=PA272 Extract of page 272]</ref>

The principle requires physical laws to be the same for any body moving at constant velocity as they are for a body at rest. A consequence is that an observer in an inertial reference frame cannot determine an absolute speed or direction of travel in space,  and may only speak of speed or direction relative to some other object.

The principle does not extend to [[non-inertial reference frame]]s because those frames do not, in general experience, seem to abide by the same laws of physics. In [[classical physics]], [[fictitious forces]] are used to describe acceleration in non-inertial reference frames.

===In Newtonian mechanics===
{{main|Galilean invariance}}
The special principle of relativity was first explicitly enunciated by [[Galileo Galilei]] in 1632 in his ''[[Dialogue Concerning the Two Chief World Systems]]'', using the metaphor of [[Galileo's ship]].

Newtonian mechanics added to the special principle several other concepts, including laws of motion, gravitation, and an assertion of an [[absolute time]]. When formulated in the context of these laws, the special principle of relativity states that the laws of mechanics are ''invariant'' under a [[Galilean transformation]].

===In special relativity===
{{main|Special relativity}}

[[Joseph Larmor]] and [[Hendrik Lorentz]] discovered that [[Maxwell's equations]], used in the theory of [[electromagnetism]], were invariant only by a certain change of time and length units. This left some confusion among physicists, many of whom thought that a [[luminiferous aether]] was incompatible with the relativity principle, in the way it was defined by [[Henri Poincaré]]:

{{Quotation|The principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not and could not have any means of discerning whether or not we are carried along in such a motion.|Henri Poincaré, 1904<ref>{{Cite book|author=Poincaré, Henri|year=1904–1906|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=Congress of arts and science, universal exposition, St. Louis, 1904|volume=1|pages=604–622|publisher=Houghton, Mifflin and Company|place=Boston and New York}}</ref>}}

In their 1905 papers on [[Annus Mirabilis Papers#Papers|electrodynamics]], Henri Poincaré and [[Albert Einstein]] explained that with the [[Lorentz transformations]] the relativity principle holds perfectly. Einstein elevated the (special) principle of relativity to a [[postulate]] of the theory and derived the Lorentz transformations from this principle combined with the principle of the independence of the speed of light (in vacuum) from the motion of the source. These two principles were reconciled with each other by a re-examination of the fundamental meanings of space and time intervals.

The strength of special relativity lies in its use of simple, basic principles, including the [[covariance and contravariance of vectors|invariance]] of the laws of physics under a shift of [[inertial reference frame]]s and the invariance of the speed of light in vacuum. (See also: [[Lorentz covariance]].)

It is possible to derive the form of the Lorentz transformations from the principle of relativity alone. Using only the isotropy of space and the symmetry implied by the principle of special relativity, one can show that the space-time transformations between inertial frames are either Galilean or Lorentzian. Whether the transformation is actually Galilean or Lorentzian must be determined with physical experiments. It is not possible to conclude that the speed of light ''c'' is invariant by mathematical logic alone. In the Lorentzian case, one can then obtain relativistic interval conservation and the constancy of the speed of light.<ref name=Friedman>Yaakov Friedman, ''Physical Applications of Homogeneous Balls'', Progress in Mathematical Physics '''40''' Birkhäuser, Boston, 2004, pages 1-21.</ref>