Editing Frame of reference (section)

== Observational frame of reference ==
{{further|Inertial frame of reference}}
[[File:Minkowski diagram - 3 systems.svg|thumb|right|256px|Three frames of reference in special relativity. The black frame is at rest. The primed frame moves at 40% of light speed, and the double primed frame at 80%. Note the scissors-like change as speed increases.]]

An '''observational frame of reference''', often referred to as a ''physical frame of reference'', a ''frame of reference'', or simply a ''frame'', is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized ''only by its state of motion''.<ref name=Kubar>See {{cite book |author1=Arvind Kumar |author2=Shrish Barve |page=115 |title=How and Why in Basic Mechanics |url=https://books.google.com/books?id=czlUPz38MOQC&q=%22characterized+only+by+its+state+of+motion%22+inauthor:Kumar&pg=PA115|isbn=81-7371-420-7 |year= 2003 |publisher =Orient Longman}}</ref> However, there is lack of unanimity on this point. In special relativity, the distinction is sometimes made between an ''observer'' and a ''frame''. According to this view, a ''frame'' is an ''observer'' plus a coordinate lattice constructed to be an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector. See Doran.<ref name=Doran>{{cite book |url=http://www.worldcat.org/search?q=9780521715959&qt=owc_search |title=Geometric Algebra for Physicists |author1=Chris Doran |author2=Anthony Lasenby |page= §5.2.2, p. 133 |isbn=978-0-521-71595-9 |year=2003 |publisher=Cambridge University Press}}.</ref> This restricted view is not used here, and is not universally adopted even in discussions of relativity.<ref name=Moller>For example, Møller states: "Instead of Cartesian coordinates we can obviously just as well employ general curvilinear coordinates for the fixation of points in physical space.…we shall now introduce general "curvilinear" coordinates ''x''<sup>i</sup> in four-space…." {{cite book |author=C. Møller |title=The Theory of Relativity |page=222 and p. 233 |year=1952 |publisher=Oxford University Press}}</ref><ref name=Lightman>{{cite book |title=Problem Book in Relativity and Gravitation |author1=A. P. Lightman |author2=W. H. Press |author3=R. H. Price |author4=S. A. Teukolsky |page=[https://archive.org/details/problembookinrel00ligh/page/15 15] |url=https://archive.org/details/problembookinrel00ligh|url-access=registration |quote=relativistic  general coordinates. |isbn=0-691-08162-X |publisher=Princeton University Press |year=1975}}</ref> In [[general relativity]] the use of general coordinate systems is common (see, for example, the [[Karl Schwarzschild|Schwarzschild]] solution for the gravitational field outside an isolated sphere<ref name= Faber>{{cite book |title=Differential Geometry and Relativity Theory: an introduction |author=Richard L Faber |url=https://books.google.com/books?id=ctM3_afLuVEC&q=relativistic++%22general+coordinates%22&pg=PA149
|page=211 |isbn=0-8247-1749-X |year=1983 |publisher=CRC Press}}</ref>).

There are two types of observational reference frame: [[Inertial frame of reference|inertial]] and [[non-inertial reference frame|non-inertial]]. An inertial frame of reference is defined as one in which all laws of physics take on their simplest form. In [[special relativity]] these frames are related by [[Lorentz transformation]]s, which are parametrized by [[rapidity]]. In Newtonian mechanics, a more restricted definition requires only that [[Newton's first law]] holds true; that is, a Newtonian inertial frame is one in which a [[free particle]] travels in a [[straight line]] at constant [[speed]], or is at rest. These frames are related by [[Galilean transformation]]s. These relativistic and Newtonian transformations are expressed in spaces of general dimension in terms of [[Representation theory|representations]] of the [[Representation theory of the Poincaré group|Poincaré group]] and of the [[Representation theory of the Galilean group|Galilean group]].

In contrast to the inertial frame, a non-inertial frame of reference is one in which [[fictitious force]]s must be invoked to explain observations. An example is an observational frame of reference centered at a point on the Earth's surface. This frame of reference orbits around the center of the Earth, which introduces the fictitious forces known as the [[Coriolis force]], [[centrifugal force]], and [[gravitational force]]. (All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall.)