Dictionary Definition
inertial adj : of or relating to inertia
User Contributed Dictionary
English
Pronunciation

 Rhymes: ɜː(r)ʃəl
Translations
 French: inertiel
Extensive Definition
\mathbf^ = \mathbf  \mathbf_  \mathbf t
t^ = t  t_
where \mathbf_ and t_ represent shifts in the
origin of space and time, and \mathbf is the relative velocity of
the two inertial reference frames. Under Galilean
transformations, the time between two events (t_  t_) is the
same for all inertial
reference frames and the distance between two
simultaneous events (or, equivalently, the length of any object,
\left \mathbf_  \mathbf_ \right) is also the same.
Einstein's theory of special relativity
Einstein's
theory of
special relativity, like Newtonian mechanics, assumes the
equivalence of all inertial reference frames, but makes an
additional assumption, foreign to Newtonian mechanics, namely, that
in free
space light always is propagated with the speed of
light c0, a defined value independent
of its direction of propagation and its frequency, and also
independent of the state of motion of the emitting body. This
second assumption has been verified experimentally and leads to
counterintuitive deductions including:
 time dilation (moving clocks tick more slowly)
 length contraction (moving objects are shortened in the direction of motion)
 relativity of simultaneity (simultaneous events in one reference frame are not simultaneous in almost all frames moving relative to the first).
These deductions are logical consequences of the
stated assumptions, and are general properties of spacetime, not
properties pertaining to the structure of individual objects like
atoms or stars, nor to the mechanisms of clocks.
These effects are expressed mathematically by the
Lorentz
transformation
 x^ = \gamma \left(x  v t \right)
 y^ = y
 z^ = z
 t^ = \gamma \left(t  \frac\right)
where shifts in origin have been ignored, the
relative velocity is assumed to be in the xdirection and the
Lorentz
factor γ is defined by:
\gamma \ \stackrel\ \frac \ \ge 1.
The Lorentz transformation is equivalent to the
Galilean
transformation in the limit c0 → ∞ (a hypothetical
case) or v → 0 (low speeds).
Under Lorentz
transformations, the time and distance between events may
differ among inertial reference frames; however, the Lorentz
scalar distance s2 between two events is the same in all
inertial reference frames
s^ = \left( x_  x_ \right)^ + \left( y_  y_
\right)^ + \left( z_  z_ \right)^  c_0^ \left(t_ 
t_\right)^
From this perspective, the speed of
light is only accidentally a property of light, and is rather a property of
spacetime, a conversion
factor between conventional time units (such as seconds) and length units (such
as meters).
Einstein’s general theory of relativity
Einstein’s general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Euclidean geometry with a curved nonEuclidean metric. In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.However, the general theory reduces to the
special theory over sufficiently small regions of spacetime, where
curvature effects become less important and the earlier inertial
frame arguments can come back into play. Consequently, modern
special relativity is now sometimes described as only a “local
theory”. (However, this refers to the theory’s application rather
than to its derivation.)
External links
 Stanford Encyclopedia of Philosophy entry
 Animation clip showing scenes as viewed from both an inertial frame and a rotating frame of reference, visualizing the Coriolis and centrifugal forces.
References
Further Reading
 Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics, 2nd ed. (Freeman, NY, 1992)
 Albert Einstein, Relativity, the special and the general theories, 15th ed. (1954)
 Henri Poincaré, (1900) "La theorie de Lorentz et la Principe de Reaction", Archives Neerlandaises, V, 253–78.
 Albert Einstein, On the Electrodynamics of Moving Bodies, included in The Principle of Relativity, page 38. Dover 1923
inertial in Arabic: إطار مرجعي عطالي
inertial in Bengali: জড় প্রসঙ্গ কাঠামো
inertial in Belarusian: Інерцыяльная сістэма
адліку
inertial in Bosnian: Inercijski referentni
okvir
inertial in Catalan: Sistema inercial
inertial in Czech: Inerciální vztažná
soustava
inertial in Danish: Inertialsystem
inertial in German: Inertialsystem
inertial in Modern Greek (1453): Αδρανειακό
σύστημα αναφοράς
inertial in Spanish: Sistema de referencia
inercial
inertial in Basque: Erreferentziasistema
inertzial
inertial in Persian: دستگاه مرجع لخت
inertial in French: Référentiel galiléen
inertial in Galician: Sistema inercial
inertial in Korean: 관성 좌표계
inertial in Croatian: Inercijski referentni
okvir
inertial in Indonesian: Kerangka acuan
inersial
inertial in Italian: Sistema di riferimento
inerziale
inertial in Mongolian: Инерциал тооллын
систем
inertial in Dutch: Inertiaalstelsel
inertial in Japanese: 慣性系
inertial in Norwegian: Treghetssystem
inertial in Polish: Układ inercjalny
inertial in Portuguese: Referencial
inercial
inertial in Romanian: Sistem de referinţă
inerţial
inertial in Russian: Инерциальная система
отсчёта
inertial in Slovak: Inerciálna vzťažná
sústava
inertial in Slovenian: Inercialni opazovalni
sistem
inertial in Finnish:
Inertiaalikoordinaatisto
inertial in Swedish: Inertialsystem
inertial in Ukrainian: Інерційна система
відліку
inertial in Chinese: 惯性参考系