SUPPORT THE WORK

GetWiki

inertial frame of reference

ARTICLE SUBJECTS
news  →
unix  →
wiki  →
ARTICLE TYPES
feed  →
help  →
wiki  →
ARTICLE ORIGINS
inertial frame of reference
[ temporary import ]
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{Other uses|Framing (disambiguation){{!}}Framing}}{{Use dmy dates|date=August 2019}}{{Classical mechanics|cTopic=Core topics}}{{tone|date=January 2018}}An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant speed in a straight line.{{citation| url=http://physics.unm.edu/Courses/Fields/Phys262/lecture26.pdf| accessdate=27 May 2018| author=Douglas Fields|date=2015| title=Galilean Relativity |work=Physics 262-01 Spring 2018, University of New Mexico}} An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.BOOK, Landau, L. D., Lifshitz, E. M., Mechanics, 1960, Pergamon Press, 4â€“6, Conceptually, the physics of a system in an inertial frame have no causes external to the system.{{citation|title=Einstein's Space-Time: An Introduction to Special and General Relativity|first1=Rafael|last1=Ferraro|publisher=Springer Science & Business Media|date=2007|isbn=9780387699462|pp=209â€“210|bibcode=2007esti.book.....F}} An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.BOOK, Puebe, Jean-Laurent, Fluid Mechanics, 62,weblink 2009, 978-1-84821-065-3, All inertial frames are in a state of constant, (wiktionary:rectilinear|rectilinear) motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, in any region small enough for the curvature of spacetime and tidal forcesBOOK, Einstein's Physics: Atoms, Quanta, and Relativity â€“ Derived, Explained, and Appraised, illustrated, Ta-Pei, Cheng, OUP Oxford, 2013, 978-0-19-966991-2, 219,weblink Extract of page 219 to be negligible, one can find a set of inertial frames that approximately describe that region.BOOK, Relativity: The Special and General Theory, Albert Einstein, 71,weblink 0-486-41714-X, Courier Dover Publications, 2001, 3rd, Reprint of edition of 1920 translated by RQ Lawson, BOOK, Special Relativity, Domenico Giulini, 19,weblink 0-19-856746-4, 2005, Oxford University Press, In a non-inertial reference frame in classical physics and special relativity, the physics of a system vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces.BOOK, Discovering the Natural Laws: The Experimental Basis of Physics, Milton A. Rothman, 23,weblink
publisher=Courier Dover Publications PUBLISHER=MCGRAW-HILL URL=HTTPS://BOOKS.GOOGLE.COM/BOOKS?NUM=10&BTNG=GOOGLE+SEARCHAUTHOR1=SIDNEY BOROWITZ geodesic (general relativity)>geodesic motion.{{citationfirst1=James G.date=1 September 2004bibcode = 2004physics...9010G }} In classical physics, for example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating, which means the frame of reference of an observer on Earth is not inertial. The physics must account for the Coriolis effectâ€”in this case thought of as a forceâ€”to predict the horizontal motion. Another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force.

Introduction

The motion of a body can only be described relative to something elseâ€”other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body that has no external forces acting on it is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, a coordinate system could describe the simple flight of a free body in space as a complicated zig-zag in its coordinate system. Indeed, an intuitive summary of inertial frames can be given: in an inertial reference frame, the laws of mechanics take their simplest form.In an inertial frame, Newton's first law, the law of inertia, is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form:
mathbf{F} = m mathbf{a} ,
with F the net force (a 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 electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Î© about an axis, takes the form:
mathbf{F}' = m mathbf{a} ,
which looks the same as in an inertial frame, but now the force Fâ€² is the resultant of not only F, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics):
mathbf{F}' = mathbf{F} - 2m mathbf{Omega} times mathbf{v}_{B} - m mathbf{Omega} times (mathbf{Omega} times mathbf{x}_B ) - m frac{d mathbf{Omega}}{dt} times mathbf{x}_B ,

Background

A set of frames where the laws of physics are simple

According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation: {{anchor|principle}}BOOK, The Principle of Relativity: a collection of original memoirs on the special and general theory of relativity, Einstein, A., Lorentz, H. A., Minkowski, H., & Weyl, H., 111,weblink
publisher=Courier Dover Publications weblink 0-915144-71-9, Hackett Publishing, 1979, and also BlagojeviÄ‡.BOOK, Gravitation and Gauge Symmetries, Milutin BlagojeviÄ‡, 4,weblink 0-7503-0767-6, CRC Press, 2002, In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame.BOOK, Relativity: The Special and General Theory, Albert Einstein, 17, 1920, H. Holt and Company,weblink BOOK, Six not-so-easy pieces: Einstein's relativity, symmetry, and space-time, Richard Phillips Feynman, 73, 0-201-32842-9, 1998, Basic Books,weblink According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the PoincarÃ© group of symmetry transformations, of which the Lorentz transformations are a subgroup.BOOK, Compendium of Theoretical Physics, Armin Wachter, Henning Hoeber, 98,weblink 0-387-25799-3, BirkhÃ¤user, 2006, In Newtonian mechanics, which can be viewed as a limiting case of special relativity in which the speed of light is infinite, inertial frames of reference are related by the Galilean group of symmetries.

Absolute space

Newton posited an absolute space considered well approximated by a frame of reference stationary relative to the fixed stars. An inertial frame was then one in uniform translation relative to absolute space. However, some scientists (called "relativists" by Mach), even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced.Indeed, the expression inertial frame of reference () was coined by Ludwig Lange in 1885, to replace Newton's definitions of "absolute space and time" by a more operational definition.JOURNAL, Lange, Ludwig, 1885, Ãœber die wissenschaftliche Fassung des Galileischen Beharrungsgesetzes, Philosophische Studien
EDITION=REPRINT OF 1989 ABSOLUTE OR RELATIVE MOTION? URL=HTTPS://BOOKS.GOOGLE.COM/?ID=WQIDKYKLEXCC&PG=PA645&DQ=LUDWIG+LANGE+%22OPERATIONAL+DEFINITION%22PUBLISHER=OXFORD UNIVERSITY PRESS Lange proposed the following definition:L. Lange (1885) as quoted by Max von Laue in his book (1921) Die RelativitÃ¤tstheorie, p. 34, and translated by 169 AUTHOR=HARALD IRO ISBN=981-238-213-5 PUBLISHER=WORLD SCIENTIFIC, A discussion of Lange's proposal can be found in Mach.BOOK, The Science of Mechanics, 38, Ernst Mach,weblink The Open Court Publishing Co., 1915, The inadequacy of the notion of "absolute space" in Newtonian mechanics is spelled out by BlagojeviÄ‡:BOOK, Gravitation and Gauge Symmetries, Milutin BlagojeviÄ‡, 5,weblink 0-7503-0767-6, CRC Press, 2002, The utility of operational definitions was carried much further in the special theory of relativity.BOOK, Special relativity, NMJ Woodhouse, 58,weblink 1-85233-426-6, Springer, London, 2003, Some historical background including Lange's definition is provided by DiSalle, who says in summary:BOOK, Robert DiSalle, Space and Time: Inertial Frames, The Stanford Encyclopedia of Philosophy, Edward N. Zalta,weblink Summer 2002,

Newton's inertial frame of reference

250px|thumbnail|Figure 1: Two frames of reference moving with relative velocity stackrel{vec v}{}. Frame S' has an arbitrary but fixed rotation with respect to frame S. They are both inertial frames provided a body not subject to forces appears to move in a straight line. If that motion is seen in one frame, it will also appear that way in the other.Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame, is one in which Newton's first law of motion is valid.BOOK, C MÃ¸ller, The Theory of Relativity, Oxford University Press, Oxford UK, 0-19-560539-X, 1976, 1, 220221617, Second, However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton's first law.Newton viewed the first law as valid in any reference frame that is in uniform motion relative to the fixed stars;The question of "moving uniformly relative to what?" was answered by Newton as "relative to absolute space". As a practical matter, "absolute space" was considered to be the fixed stars. For a discussion of the role of fixed stars, see BOOK, Nothingness: The Science of Empty Space, Henning Genz, 150, 0-7382-0610-5, Da Capo Press, 2001,weblink
, that is, neither rotating nor accelerating relative to the stars.BOOK, Physics, Volume 1, Chapter 3, 0-471-32057-9,weblink
date=2001 author1=Robert Resnick author3=Kenneth S. Krane absolute space" is abandoned, and an inertial frame in the field of classical mechanics is defined as:HTTPS://BOOKS.GOOGLE.COM/?ID=R5P29CN6S6QC&PG=PA70&DQ=FIXED+STARS+%22INERTIAL+FRAME%22 PAGE=70 PUBLISHER=TATA MCGRAW-HILLISBN=0-07-096617-6 PAGE=6 PUBLISHER=SPRINGER ISBN=1-85233-426-6, London/Berlin, Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformlyâ€”that is, in a straight line and at constant speed. Newtonian inertial frames transform among each other according to the Galilean group of symmetries.If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then we have to be able to determine when zero net force is applied. The problem was summarized by Einstein:BOOK, The Meaning of Relativity, A Einstein, 58, 1950,weblink Princeton University Press, There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that a body is far enough away from all sources to ensure that no force is present.BOOK, Introductory Special Relativity, William Geraint Vaughan Rosser, 3,weblinkdate=1991, CRC Press, A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is that we might miss something, or account inappropriately for their influence, perhaps, again, due to Mach's principle and an incomplete understanding of the universe. A third approach is to look at the way the forces transform when we shift reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames, and have complicated rules of transformation in general cases. On the basis of universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces.Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion:BOOK, Six not-so-easy pieces: Einstein's relativity, symmetry, and space-time, Richard Phillips Feynman, 50, 0-201-32842-9, 1998, Basic Books,weblink See the Principia on line at Andrew Motte Translation This principle differs from the special principle in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares with the special principle the invariance of the form of the description among mutually translating reference frames.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. The role of fictitious forces in classifying reference frames is pursued further below.

Separating non-inertial from inertial reference frames

Theory

{{See also|Non-inertial frame|Rotating spheres|Bucket argument}}thumb|180px|Figure 2: Two spheres tied with a string and rotating at an angular rate Ï‰. Because of the rotation, the string tying the spheres together is under tension.thumb|Figure 3: Exploded view of rotating spheres in an inertial frame of reference showing the centripetal forces on the spheres provided by the tension in the tying string.Inertial and non-inertial reference frames can be distinguished by the absence or presence of fictitious forces, as explained shortly. The presence of fictitious forces indicates the physical laws are not the simplest laws available so, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame:BOOK, Mathematical Methods of Classical Mechanics, 129, V. I. Arnol'd, 978-0-387-96890-2, 1989,weblink Springer, Bodies in non-inertial reference frames are subject to so-called fictitious forces (pseudo-forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames.How then, are "fictitious" forces to be separated from "real" forces? It is hard to apply the Newtonian definition of an inertial frame without this separation. For example, consider a stationary object in an inertial frame. Being at rest, no net force is applied. But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force (which is made up of the Coriolis force and the centrifugal force). How can we decide that the rotating frame is a non-inertial frame? There are two approaches to this resolution: one approach is to look for the origin of the fictitious forces (the Coriolis force and the centrifugal force). We will find there are no sources for these forces, no associated force carriers, no originating bodies.For example, there is no body providing a gravitational or electrical attraction. A second approach is to look at a variety of frames of reference. For any inertial frame, the Coriolis force and the centrifugal force disappear, so application of the principle of special relativity would identify these frames where the forces disappear as sharing the same and the simplest physical laws, and hence rule that the rotating frame is not an inertial frame.Newton examined this problem himself using rotating spheres, as shown in Figure 2 and Figure 3. He pointed out that if the spheres are not rotating, the tension in the tying string is measured as zero in every frame of reference.That is, the universality of the laws of physics requires the same tension to be seen by everybody. For example, it cannot happen that the string breaks under extreme tension in one frame of reference and remains intact in another frame of reference, just because we choose to look at the string from a different frame. If the spheres only appear to rotate (that is, we are watching stationary spheres from a rotating frame), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed. If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion. Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value. That is, the inertial frame is the one where the fictitious forces vanish.So much for fictitious forces due to rotation. However, for linear acceleration, Newton expressed the idea of undetectability of straight-line accelerations held in common:This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, we can define inertial frames collectively as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.For these ideas to apply, everything observed in the frame has to be subject to a base-line, common acceleration shared by the frame itself. That situation would apply, for example, to the elevator example, where all objects are subject to the same gravitational acceleration, and the elevator itself accelerates at the same rate.

Applications

Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it.BOOK, Chatfield, Averil B., Fundamentals of High Accuracy Inertial Navigation, Volume 174, 1997, AIAA, 9781600864278, {{rp|59}} Three orthogonal gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position. Thus, inertial navigation is a form of dead reckoning that requires no external input, and therefore cannot be jammed by any external or internal signal source.BOOK, Kennie, edited by T.J.M., Engineering Surveying Technology, 1993, Taylor & Francis, Hoboken, 9780203860748, 95, Pbk., Petrie, G., 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. 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.JOURNAL, The gyroscope pilots ships & planes, Life, 15 March 1943, 80â€“83,weblink

Newtonian mechanics

{{Unreferenced section|small=y|date=May 2018}} Classical theories that use the Galilean transformation postulate the equivalence of all inertial reference frames. Some theories may even postulate the existence of a privileged frame which provides absolute space and absolute time. The Galilean transformation transforms coordinates from one inertial reference frame, mathbf{s}, to another, mathbf{s}^{prime}, by simple addition or subtraction of coordinates:
mathbf{r}^{prime} = mathbf{r} - mathbf{r}_{0} - mathbf{v} t
t^{prime} = t - t_{0}where r0 and t0 represent shifts in the origin of space and time, and v is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time t2 âˆ’ t1 between two events is the same for all reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, |r2 âˆ’ r1|) is also the same.

Special relativity

Einstein's 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, 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 and length contraction, and the relativity of simultaneity, which have been extensively verified experimentally.BOOK, Relativity for Scientists and Engineers, reprinted, Ray, Skinner, Courier Corporation, 2014, 978-0-486-79367-2, 27,weblink Extract of page 27 The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero.BOOK, The Classical Theory of Fields, LD Landau, LM Lifshitz, 4th Revised English, 273â€“274, 1975, 978-0-7506-2768-9, Pergamon Press,

General relativity

{{See also|Equivalence principle|EÃ¶tvÃ¶s experiment}}General relativity is based upon the principle of equivalence:BOOK, Introduction to Classical Mechanics, David Morin, 649,weblink 978-0-521-87622-3, Cambridge University Press, 2008, BOOK, Physics for Scientists and Engineers with Modern Physics, Douglas C. Giancoli,weblink

{{Col-begin}}{{Col-1-of-2}} {{Col-2-of-2}} {{col-end}}

References

{{Reflist}}

• 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)
• Albert Einstein, On the Electrodynamics of Moving Bodies, included in The Principle of Relativity, page 38. Dover 1923

Rotation of the Universe
• BOOK, Mach's Principle: From Newton's Bucket to Quantum Gravity, 445, Julian B. Barbour, Herbert Pfister, 0-8176-3823-7, 1998,weblink BirkhÃ¤user,
• BOOK, Time Machines, PJ Nahin, 369; Footnote 12,weblink 1999, 0-387-98571-9, Springer,
• B Ciobanu, I Radinchi Modeling the electric and magnetic fields in a rotating universe Rom. Journ. Phys., Vol. 53, Nos. 1â€“2, P. 405â€“415, Bucharest, 2008
• Yuri N. Obukhov, Thoralf Chrobok, Mike Scherfner Shear-free rotating inflation Phys. Rev. D 66, 043518 (2002) [5 pages]
• Yuri N. Obukhov On physical foundations and observational effects of cosmic rotation (2000)
• Li-Xin Li Effect of the Global Rotation of the Universe on the Formation of Galaxies General Relativity and Gravitation, 30 (1998) {{doi|10.1023/A:1018867011142}}
• P Birch Is the Universe rotating? Nature 298, 451 â€“ 454 (29 July 1982)
• Kurt GÃ¶del An example of a new type of cosmological solutions of Einsteinâ€™s field equations of gravitation Rev. Mod. Phys., Vol. 21, p. 447, 1949.

- content above as imported from Wikipedia
- "inertial frame of reference" does not exist on GetWiki (yet)
- time: 1:03am EDT - Mon, Sep 23 2019
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 09 JUL 2019
Eastern Philosophy
History of Philosophy
GETWIKI 09 MAY 2016
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
GETWIKI 20 AUG 2014
GETWIKI 19 AUG 2014
CONNECT