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Inertial Frame of Reference
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An '''inertial frame''' is a
coordinate system defined by the non-accelerated motion of objects with a common direction and speed (as opposed to a
non-inertial reference frame).
Introduction
In
physics, an object has '''inertial motion''' if no external forces are being applied to it, famously stated as
Newton's first law of motion. When such an object’s state of motion is extrapolated over a region of space to take in all other possible objects in the region with the same state of motion, and these are used to define a common
coordinate system, this system is referred to as a '''frame'''.
Use of inertial frames
Inertial frames of reference are relevant to
Newtonian relativity and
Albert Einstein Einstein's
special relativity special theory of relativity.
* Under '''
Newtonian physics Newtonian mechanics''', all inertial states of motion are considered to be equivalent: if two inertial observers, '''"A"''' and '''"B"''' have a relative velocity, then the laws of physics should be the same regardless of whether we take '''"A"''' as our “stationary� reference and say that '''"B"''' is moving, or if we take '''"B"''' as our fixed reference and say that '''"A"''' is moving. Included in these rules of physics is the explicit assumption that time progresses at the same rate for all observers, meaning that clocks calibrated in one inertial coordinate system will not become uncalibrated due to one of them being moved into another inertial frame of reference.
* '''Under special relativity''', this equivalence of different inertial states of motion still applies. However, the assumption of constant progression of
proper time in all frames of reference is replaced by the assumption that the
speed of light is constant, and that this is equally true for every inertial observer. This required the use of a set of protocols, originally discussed by
Henri Poincaré (1900) in relation to
Hendrik Lorentz's local time and used, apparently independently, by Einstein (
Einstein synchronisation,
relativity of simultaneity). This protocol allows observers to define apparent distances and times according to the assumption of fixed light speed in their own frame, and then build an extended coordinate system for labeling the times and distances of distant events. Observers using different reference frames will derive different nominal distance and time separations between the same two events. The formulas for converting, or "
Lorentz transformation transforming" values between different frames of reference allow each observer to calculate how the physics taking place appears for another observer. As seen from different points of view the nominal distance and time separation between two events differs, but the combined
spacetime interval is unchanged: it is "frame-independent", or "
invariant (physics) invariant".
Transformations
The way that nominal distances and times are converted from one coordinate system to another is referred to as a
Transformation (mathematics) transformation.
In classical mechanics the
kinetic energy of a system depends on the inertial frame of reference. It is lowest with respect to the
center of mass, i.e., in a frame of reference in which the center of mass is stationary. In another frame of reference the additional kinetic energy is that corresponding to the total mass and the speed of the center of mass.
Einstein argued that if we only assume that light propagates at ''c'' in a single
preferred frame (i.e., if we assume an absolute fixed aether,
classical theory and special relativity classical theory), transformation of space and time coordinates is performed using
Galilean transformations, whereas with special relativity we obtain
Lorentz transformations, which only coincide with the earlier results for relative velocities that are reasonably small in comparison with the speed of light.
Einstein’s general theory of relativity
Einstein’s
general relativity general theory modifies the distinction between nominally "inertial" and "noninertial" effects, by replacing special relativity's "flat",
Euclidean geometry with a curved
non-Euclidean geometry non-Euclidean metric. In general relativity, the principle of inertia is replaced with the principle of
geodesic (general relativity) 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 given 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 SR 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
References
* 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)
* Poincaré, H. (1900) "La theorie de Lorentz et la Principe de Reaction", ''Archives Neerlandaises'', '''V''', 253-78.
Category:Astrodynamics
Category:Classical mechanics
Category:Relativity
Category:Frames of reference
{{relativity-stub}}
ar:إطار مرجعي عطالي
ca:Sistema inercial
cs:Inerciálnà vztažná soustava
da:Inertialsystem
de:Inertialsystem
es:Sistema inercial
fr:Référentiel galiléen
gl:Sistema inercial
ko:관성계
hr:Inercijski referentni okvir
it:Sistema di riferimento inerziale
nl:Inertiaalstelsel
pl:Układ inercjalny
pt:Referencial inercial
ru:ИнерциальнаÑ? Ñ?иÑ?тема отÑ?чёта
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zh:惯性�考系
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