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In [[classical physics]] and [[special relativity]], an '''inertial frame of reference''' (also called an '''inertial space''' or a '''Galilean reference frame''') is a [[frame of reference]] in which objects exhibit [[inertia]]: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration. | In [[classical physics]] and [[special relativity]], an '''inertial frame of reference''' (also called an '''inertial space''' or a '''Galilean reference frame''') is a [[frame of reference]] in which objects exhibit [[inertia]]: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration. | ||
All frames of reference with zero acceleration are in a state of constant [[rectilinear motion]] (straight-line motion) with respect to one another. In such a frame, an object with zero [[net force]] acting on it, is perceived to move with a constant [[velocity]], or, equivalently, [[Newton's laws of motion#Newton's first law|Newton's first law of motion]] holds. Such frames are known as inertial. Some physicists, like [[Isaac Newton]], originally thought that one of these frames was absolute — the one approximated by the [[fixed stars]]. However, this is not required for the definition, and it is now known that those stars are in fact moving, relative to one another. | All frames of reference with zero acceleration are in a state of constant [[rectilinear motion]] (straight-line motion) with respect to one another. In such a frame, an object with zero [[net force]] acting on it, is perceived to move with a constant [[velocity]], or, equivalently, [[Newton's laws of motion#Newton's first law|Newton's first law of motion]] holds.<ref>{{Cite web |date=2017-11-11 |title=2.3: Inertial Frames of reference |url=https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/02%3A_Review_of_Newtonian_Mechanics/2.03%3A_Inertial_Frames_of_reference |access-date=2026-01-03 |website=Physics LibreTexts |language=en}}</ref> Such frames are known as inertial. Some physicists, like [[Isaac Newton]], originally thought that one of these frames was absolute — the one approximated by the [[fixed stars]]. However, this is not required for the definition, and it is now known that those stars are in fact moving, relative to one another. | ||
According to the [[Principle of relativity#Special principle of relativity|principle of special relativity]], all [[physical laws]] look the same in all inertial reference frames, and no inertial frame is privileged over another. [[Measurement|Measurements]] of objects in one inertial frame can be converted to measurements in another by a simple transformation — the [[Galilean transformation]] in [[Newtonian physics]] or the [[Lorentz transformation]] (combined with a translation) in [[special relativity]]; these approximately match when the relative speed of the frames is low, but differ as it approaches the [[speed of light]]. | According to the [[Principle of relativity#Special principle of relativity|principle of special relativity]], all [[physical laws]] look the same in all inertial reference frames, and no inertial frame is privileged over another. [[Measurement|Measurements]] of objects in one inertial frame can be converted to measurements in another by a simple transformation — the [[Galilean transformation]] in [[Newtonian physics]] or the [[Lorentz transformation]] (combined with a translation) in [[special relativity]]; these approximately match when the relative speed of the frames is low, but differ as it approaches the [[speed of light]]. | ||
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This principle differs from the [[#principle|special principle]] in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares the special principle of the invariance of the form of the description among mutually translating reference frames.<ref name=note1>However, in the Newtonian system the Galilean transformation connects these frames and in the special theory of relativity the [[Lorentz transformation]] connects them. The two transformations agree for speeds of translation much less than the [[speed of light]].</ref> The role of fictitious forces in classifying reference frames is pursued further below. | This principle differs from the [[#principle|special principle]] in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares the special principle of the invariance of the form of the description among mutually translating reference frames.<ref name=note1>However, in the Newtonian system the Galilean transformation connects these frames and in the special theory of relativity the [[Lorentz transformation]] connects them. The two transformations agree for speeds of translation much less than the [[speed of light]].</ref> The role of fictitious forces in classifying reference frames is pursued further below. | ||
== Examples == | == Examples == | ||
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== Non-inertial frames == | == Non-inertial frames == | ||
{{main | {{main|Non-inertial frame}} | ||
{{further|Fictitious force}} | |||
Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below. | Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below. | ||
===Inertial frames and rotation=== | ===Inertial frames and rotation=== | ||
{{main|Rotating frame of reference}} | |||
In an inertial frame, [[Newton's first law]], the ''law of inertia'', is satisfied: Any free motion has a constant magnitude and direction.<ref name=LandauMechanics>{{cite book|last1=Landau|first1=L. D.|last2=Lifshitz|first2=E. M.|title=Mechanics|url=https://archive.org/download/landau-and-lifshitz-physics-textbooks-series/Vol%201%20-%20Landau%2C%20Lifshitz%20-%20Mechanics%20%283rd%20ed%2C%201976%29.pdf#page=31|date=1960|publisher=Pergamon Press|pages=4–6}}</ref> [[Newton's second law]] for a [[Point particle|particle]] takes the form: | In an inertial frame, [[Newton's first law]], the ''law of inertia'', is satisfied: Any free motion has a constant magnitude and direction.<ref name=LandauMechanics>{{cite book|last1=Landau|first1=L. D.|last2=Lifshitz|first2=E. M.|title=Mechanics|url=https://archive.org/download/landau-and-lifshitz-physics-textbooks-series/Vol%201%20-%20Landau%2C%20Lifshitz%20-%20Mechanics%20%283rd%20ed%2C%201976%29.pdf#page=31|date=1960|publisher=Pergamon Press|pages=4–6}}</ref> [[Newton's second law]] for a [[Point particle|particle]] takes the form: | ||
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with '''F''' the net force (a [[Euclidean vector|vector]]), ''m'' the mass of a particle and '''a''' the [[acceleration]] of the particle (also a vector) which would be measured by an observer at rest in the frame. The force '''F''' is the [[vector sum]] of all "real" forces on the particle, such as [[contact force]]s, electromagnetic, gravitational, and nuclear forces. | with '''F''' the net force (a [[Euclidean vector|vector]]), ''m'' the mass of a particle and '''a''' the [[acceleration]] of the particle (also a vector) which would be measured by an observer at rest in the frame. The force '''F''' is the [[vector sum]] of all "real" forces on the particle, such as [[contact force]]s, electromagnetic, gravitational, and nuclear forces. | ||
In contrast, Newton's second law in a [[rotating frame of reference]] (a '''non-inertial frame of reference'''), rotating at angular rate ''Ω'' about an axis, takes the form: | In contrast, Newton's second law in a [[rotating frame of reference]] (a kind of '''non-inertial frame of reference'''), rotating at angular rate ''Ω'' about an axis, takes the form: | ||
:<math>\mathbf{F}' = m \mathbf{a} \ ,</math> | :<math>\mathbf{F}' = m \mathbf{a} \ ,</math> | ||
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As now known, the fixed stars are not fixed. Those that reside in the [[Milky Way]] turn with the galaxy, exhibiting [[proper motion]]s. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to [[expansion of the universe]], and partly due to [[peculiar velocity|peculiar velocities]].<ref name=Balbi>{{Cite book|title=The Music of the Big Bang |author=Amedeo Balbi |isbn=978-3-540-78726-6 |publisher=Springer |date=2008 |page= 59 |url=https://books.google.com/books?id=vEJM7s909CYC&q=CMB+%22rotation+of+the+universe%22&pg=PA58 }}</ref> For instance, the [[Andromeda Galaxy]] is on [[Andromeda–Milky Way collision|collision course with the Milky Way]] at a speed of 117 km/s.<ref>{{Cite journal |title=Constraints on the proper motion of the Andromeda Galaxy based on the survival of its satellite M33 |pages=894–898 |author1=Abraham Loeb |author2=Mark J. Reid |author3=Andreas Brunthaler |author4=Heino Falcke |journal=The Astrophysical Journal |volume=633 |date=2005 |url=http://www.mpifr-bonn.mpg.de/staff/abrunthaler/pub/loeb.pdf |doi=10.1086/491644 |bibcode=2005ApJ...633..894L |arxiv=astro-ph/0506609 |issue=2 |s2cid=17099715 |access-date=15 December 2008 |archive-date=11 August 2017 |archive-url=https://web.archive.org/web/20170811143825/http://www3.mpifr-bonn.mpg.de/staff/abrunthaler/pub/loeb.pdf |url-status=live }}</ref> The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based on the simplicity of the laws of physics in the frame. | As now known, the fixed stars are not fixed. Those that reside in the [[Milky Way]] turn with the galaxy, exhibiting [[proper motion]]s. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to [[expansion of the universe]], and partly due to [[peculiar velocity|peculiar velocities]].<ref name=Balbi>{{Cite book|title=The Music of the Big Bang |author=Amedeo Balbi |isbn=978-3-540-78726-6 |publisher=Springer |date=2008 |page= 59 |url=https://books.google.com/books?id=vEJM7s909CYC&q=CMB+%22rotation+of+the+universe%22&pg=PA58 }}</ref> For instance, the [[Andromeda Galaxy]] is on [[Andromeda–Milky Way collision|collision course with the Milky Way]] at a speed of 117 km/s.<ref>{{Cite journal |title=Constraints on the proper motion of the Andromeda Galaxy based on the survival of its satellite M33 |pages=894–898 |author1=Abraham Loeb |author2=Mark J. Reid |author3=Andreas Brunthaler |author4=Heino Falcke |journal=The Astrophysical Journal |volume=633 |date=2005 |url=http://www.mpifr-bonn.mpg.de/staff/abrunthaler/pub/loeb.pdf |doi=10.1086/491644 |bibcode=2005ApJ...633..894L |arxiv=astro-ph/0506609 |issue=2 |s2cid=17099715 |access-date=15 December 2008 |archive-date=11 August 2017 |archive-url=https://web.archive.org/web/20170811143825/http://www3.mpifr-bonn.mpg.de/staff/abrunthaler/pub/loeb.pdf |url-status=live }}</ref> The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based on the simplicity of the laws of physics in the frame. | ||
The laws of nature take a simpler form in inertial frames of reference because in these frames one did not have to introduce inertial forces when writing down Newton's law of motion.<ref name=Stachel>{{Cite book|pages= 235–236 |url=https://books.google.com/books?id=OAsQ_hFjhrAC&q=%22laws+of+nature+took+a+simpler+form%22&pg=PA235 |title=Einstein from "B" to "Z" |author=John J. Stachel |isbn=0-8176-4143-2 |publisher=Springer |date=2002}}</ref> | The laws of nature take a simpler form in inertial frames of reference because in these frames one did not have to introduce inertial forces when writing down Newton's law of motion.<ref name=Stachel>{{Cite book|pages= 235–236 |url=https://books.google.com/books?id=OAsQ_hFjhrAC&q=%22laws+of+nature+took+a+simpler+form%22&pg=PA235 |title=Einstein from "B" to "Z" |author=John J. Stachel |author-link=John Stachel |isbn=0-8176-4143-2 |publisher=Springer |date=2002}}</ref> | ||
In practice, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun about the galactic center.<ref name=Graneau>{{Cite book|title=In the Grip of the Distant Universe |author1=Peter Graneau |author2=Neal Graneau |page= 147 |url=https://books.google.com/books?id=xpIJZxDkWAUC&q=universe+%22fixed+stars%22+date:2004-2010&pg=PA144 |isbn=981-256-754-2 |publisher=World Scientific |date=2006}}</ref> | In practice, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun about the galactic center.<ref name=Graneau>{{Cite book|title=In the Grip of the Distant Universe |author1=Peter Graneau |author2=Neal Graneau |page= 147 |url=https://books.google.com/books?id=xpIJZxDkWAUC&q=universe+%22fixed+stars%22+date:2004-2010&pg=PA144 |isbn=981-256-754-2 |publisher=World Scientific |date=2006}}</ref> | ||
To illustrate further, consider the question: "Does the Universe rotate?" An answer might explain the shape of the [[Milky Way]] galaxy using the laws of physics,<ref name=Genz>{{Cite book |title=Nothingness |author=Henning Genz |page=275 |url=https://books.google.com/books?id=Cn_Q9wbDOM0C&q=%22rotation+of+the+universe%22&pg=PA274 |isbn=0-7382-0610-5 |date=2001 |publisher=Da Capo Press }}{{Dead link|date=January 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> although other observations might be more definitive; that is, provide larger [[Observational error|discrepancies]] or less [[measurement uncertainty]], like the anisotropy of the [[microwave background radiation]] or [[Big Bang nucleosynthesis]].<ref name=Thompson>{{Cite book|title=Advances in Astronomy |chapter-url= https://books.google.com/books?id=3TrsMTmbr-sC&q=CMB+%22rotation+of+the+universe%22&pg=PA32 |author=J Garcio-Bellido|editor=J. M. T. Thompson |publisher=Imperial College Press |date=2005 |page= 32, §9 |chapter=The Paradigm of Inflation |isbn=1-86094-577-5}}</ref><ref name=Szydlowski>{{Cite journal|title=Dark energy and global rotation of the Universe |author1=Wlodzimierz Godlowski |author2=Marek Szydlowski |arxiv=astro-ph/0303248 |date=2003 |doi=10.1023/A:1027301723533 |journal=General Relativity and Gravitation |volume=35 |pages=2171–2187|issue=12|bibcode = 2003GReGr..35.2171G |s2cid=118988129 }}</ref> The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If its apparent rate of rotation is attributed entirely to rotation in an inertial frame, a different "flatness" is predicted than if it is supposed that part of this rotation is actually due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example, [[dark matter]] is invoked to explain the [[galactic rotation curve]]. So far, observations show any rotation of the universe is very slow, no faster than once every {{val|6|e=13}} years (10<sup>−13</sup> rad/yr),<ref name=Birch>{{cite journal |url=http://www.nature.com/nature/journal/v298/n5873/abs/298451a0.html |first=P. |last=Birch |title=Is the Universe rotating? |journal=[[Nature (journal)|Nature]] |volume=298 |pages=451–454 |date=29 July 1982 |issue=5873 |doi=10.1038/298451a0 |bibcode=1982Natur.298..451B |s2cid=4343095 |access-date=14 December 2008 |archive-date=5 March 2016 |archive-url=https://web.archive.org/web/20160305064307/http://www.nature.com/nature/journal/v298/n5873/abs/298451a0.html |url-status=live |url-access=subscription }}</ref> and debate persists over whether there is ''any'' rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter along the geodesics in general relativity.<ref>{{citation|title= | To illustrate further, consider the question: "Does the Universe rotate?" An answer might explain the shape of the [[Milky Way]] galaxy using the laws of physics,<ref name=Genz>{{Cite book |title=Nothingness |author=Henning Genz |page=275 |url=https://books.google.com/books?id=Cn_Q9wbDOM0C&q=%22rotation+of+the+universe%22&pg=PA274 |isbn=0-7382-0610-5 |date=2001 |publisher=Da Capo Press }}{{Dead link|date=January 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> although other observations might be more definitive; that is, provide larger [[Observational error|discrepancies]] or less [[measurement uncertainty]], like the anisotropy of the [[microwave background radiation]] or [[Big Bang nucleosynthesis]].<ref name=Thompson>{{Cite book|title=Advances in Astronomy |chapter-url= https://books.google.com/books?id=3TrsMTmbr-sC&q=CMB+%22rotation+of+the+universe%22&pg=PA32 |author=J Garcio-Bellido|editor=J. M. T. Thompson |publisher=Imperial College Press |date=2005 |page= 32, §9 |chapter=The Paradigm of Inflation |isbn=1-86094-577-5}}</ref><ref name=Szydlowski>{{Cite journal|title=Dark energy and global rotation of the Universe |author1=Wlodzimierz Godlowski |author2=Marek Szydlowski |arxiv=astro-ph/0303248 |date=2003 |doi=10.1023/A:1027301723533 |journal=General Relativity and Gravitation |volume=35 |pages=2171–2187|issue=12|bibcode = 2003GReGr..35.2171G |s2cid=118988129 }}</ref> The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If its apparent rate of rotation is attributed entirely to rotation in an inertial frame, a different "flatness" is predicted than if it is supposed that part of this rotation is actually due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example, [[dark matter]] is invoked to explain the [[galactic rotation curve]]. So far, observations show any rotation of the universe is very slow, no faster than once every {{val|6|e=13}} years (10<sup>−13</sup> rad/yr),<ref name=Birch>{{cite journal |url=http://www.nature.com/nature/journal/v298/n5873/abs/298451a0.html |first=P. |last=Birch |title=Is the Universe rotating? |journal=[[Nature (journal)|Nature]] |volume=298 |pages=451–454 |date=29 July 1982 |issue=5873 |doi=10.1038/298451a0 |bibcode=1982Natur.298..451B |s2cid=4343095 |access-date=14 December 2008 |archive-date=5 March 2016 |archive-url=https://web.archive.org/web/20160305064307/http://www.nature.com/nature/journal/v298/n5873/abs/298451a0.html |url-status=live |url-access=subscription }}</ref> and debate persists over whether there is ''any'' rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter along the geodesics in general relativity.<ref>{{citation|title=Dark Energy and Global Rotation of the Universe|first1=James G.|last1=Gilson|journal=General Relativity and Gravitation |date=1 September 2004|volume=35 |issue=12 |pages=2171–2187 |doi=10.1023/A:1027301723533 |arxiv=physics/0409010|bibcode = 2004physics...9010G }}</ref> | ||
When [[quantum mechanics|quantum]] effects are important, there are additional conceptual complications that arise in [[quantum reference frame]]s. | When [[quantum mechanics|quantum]] effects are important, there are additional conceptual complications that arise in [[quantum reference frame]]s. | ||
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A [[gyrocompass]], employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference.<ref>{{Cite book |last=Bowditch |first=Nathaniel |title=The American Practical Navigator |date=25 September 2002 |publisher=[[National Geospatial-Intelligence Agency]] |isbn=9780939837540}}</ref> The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour.<ref name=l>{{cite magazine|title=The gyroscope pilots ships & planes |magazine=Life|date=15 March 1943 |pages=80–83|url=https://books.google.com/books?id=YlEEAAAAMBAJ&pg=PA82}}</ref>{{unreferenced section|date=July 2013}} | A [[gyrocompass]], employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference.<ref>{{Cite book |last=Bowditch |first=Nathaniel |title=The American Practical Navigator |date=25 September 2002 |publisher=[[National Geospatial-Intelligence Agency]] |isbn=9780939837540}}</ref> The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour.<ref name=l>{{cite magazine|title=The gyroscope pilots ships & planes |magazine=Life|date=15 March 1943 |pages=80–83|url=https://books.google.com/books?id=YlEEAAAAMBAJ&pg=PA82}}</ref>{{unreferenced section|date=July 2013}} | ||
==Relativity== | |||
===Special relativity=== | |||
{{Main|Special relativity}} | |||
[[Albert Einstein|Einstein's]] [[special relativity|theory of special relativity]], like Newtonian mechanics, postulates the equivalence of all inertial reference frames. However, because special relativity postulates that the [[speed of light]] in [[free space]] is [[Invariant (physics)|invariant]], the transformation between inertial frames is the [[Lorentz transformation]], not the [[Galilean transformation]] which is used in Newtonian mechanics. | |||
The invariance of the speed of light leads to counter-intuitive phenomena, such as [[time dilation]], [[length contraction]], and the [[relativity of simultaneity]]. The predictions of special relativity have been extensively verified experimentally.<ref>{{cite book |last1=Skinner |first1=Ray |url=https://books.google.com/books?id=pnlpAwAAQBAJ |title=Relativity for Scientists and Engineers |publisher=Courier Corporation |year=2014 |isbn=978-0-486-79367-2 |edition=reprinted |page=27}} [https://books.google.com/books?id=pnlpAwAAQBAJ&pg=PA27 Extract of page 27]</ref> The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero.<ref name="Landau">{{Cite book |author1=LD Landau |title=The Classical Theory of Fields |author2=LM Lifshitz |date=1975 |publisher=Pergamon Press |isbn=978-0-7506-2768-9 |edition=4th Revised English |pages=273–274}}</ref> | |||
===General relativity=== | |||
{{Main|General relativity|Introduction to general relativity}} | |||
{{See also|Equivalence principle|Eötvös experiment}} | |||
General relativity is based upon the principle of equivalence:<ref name=Morin>{{Cite book|title=Introduction to Classical Mechanics |author=David Morin |page=[https://archive.org/details/introductiontocl00mori/page/649 649] |url=https://archive.org/details/introductiontocl00mori |url-access=registration |quote=acceleration azimuthal Morin. |isbn=978-0-521-87622-3 |publisher=Cambridge University Press |date=2008}}</ref><ref name=Giancoli>{{Cite book|title=Physics for Scientists and Engineers with Modern Physics |author=Douglas C. Giancoli |url=https://books.google.com/books?id=xz-UEdtRmzkC&q=%22principle+of+equivalence%22&pg=PA155 | |||
|page=155 |date=2007 |publisher=Pearson Prentice Hall |isbn=978-0-13-149508-1 }}</ref> | |||
{{blockquote|<i>There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating.</i>|Douglas C. Giancoli, ''Physics for Scientists and Engineers with Modern Physics'', p. 155.}} | |||
This idea was introduced in Einstein's 1907 article "Principle of Relativity and Gravitation" and later developed in 1911.<ref name=General_theory>A. Einstein, "[http://www.relativitycalculator.com/pdfs/On_the_influence_of_Gravitation_on_the_Propagation_of_Light_English2.pdf On the influence of gravitation on the propagation of light] {{Webarchive|url=https://web.archive.org/web/20201224033225/http://www.relativitycalculator.com/pdfs/On_the_influence_of_Gravitation_on_the_Propagation_of_Light_English2.pdf |date=24 December 2020 }}", ''Annalen der Physik'', vol. 35, (1911) : 898–908</ref> Support for this principle is found in the [[Eötvös experiment]], which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 10<sup>11</sup>.<ref name=NRC>{{Cite book|title=Physics Through the Nineteen Nineties: Overview |page=15 |url=https://books.google.com/books?id=Hk1wj61PlocC&q=equivalence+gravitation&pg=PA15 | |||
|isbn=0-309-03579-1 |date=1986 |author=National Research Council (US) |publisher=National Academies Press }}</ref> For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin.<ref name=Franklin>{{Cite book|title=No Easy Answers: Science and the Pursuit of Knowledge |author=Allan Franklin |page=66 |url=https://books.google.com/books?id=_RN-v31rXuIC&q=%22Eotvos+experiment%22&pg=PA66 | |||
|isbn=978-0-8229-5968-7 |date=2007 |publisher=University of Pittsburgh Press }}</ref> | |||
Einstein's [[general relativity|general theory]] modifies the distinction between nominally "inertial" and "non-inertial" effects by replacing special relativity's "flat" [[Minkowski space]] with a metric that produces non-zero curvature. 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 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.<ref>{{cite book |title=Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process |first1=Herbert S. |last1=Green |publisher=Springer |date=2000 |isbn=354066517X |page=154 |url=https://books.google.com/books?id=CUJiQjSVCu8C}} [https://books.google.com/books?id=CUJiQjSVCu8C&pg=PA154 Extract of page 154]</ref><ref>{{cite book |title=Theory of Special Relativity |first1=Nikhilendu |last1=Bandyopadhyay |publisher=Academic Publishers |date=2000 |isbn=8186358528 |page=116 |url=https://books.google.com/books?id=qMOyfi_i0j8C}} [https://books.google.com/books?id=qMOyfi_i0j8C&pg=PA116 Extract of page 116]</ref> Consequently, modern special relativity is now sometimes described as only a "local theory".<ref>{{cite book |title=Cosmological Inflation and Large-Scale Structure |first1=Andrew R. |last1=Liddle |first2=David H. |last2=Lyth |publisher=Cambridge University Press |date=2000 |isbn=0-521-57598-2 |page=329 |url=https://books.google.com/books?id=XmWauPZSovMC}} [https://books.google.com/books?id=XmWauPZSovMC&pg=PA329 Extract of page 329]</ref> "Local" can encompass, for example, the entire [[Milky Way galaxy]]: The astronomer [[Karl Schwarzschild]] observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the [[Solar System]]. Schwarzschild pointed out that that was invariably seen: the direction of the [[angular momentum]] of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is approximately Galilean or Minkowskian.<ref>[http://www.mpiwg-berlin.mpg.de/Preprints/P271.PDF In the Shadow of the Relativity Revolution] {{Webarchive|url=https://web.archive.org/web/20170520084821/http://www.mpiwg-berlin.mpg.de/Preprints/P271.PDF |date=20 May 2017 }} Section 3: The Work of Karl Schwarzschild (2.2 MB PDF-file)</ref> | |||
==See also== | ==See also== | ||