Frame of reference: Difference between revisions

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{{Classical mechanics |Fundamentals}}

In [[physics]] and [[astronomy]], a '''frame of reference''' (or '''reference frame''') is an abstract [[coordinate system]], whose [[origin (mathematics)|origin]], [[orientation (geometry)|orientation]], and [[scale (geometry)|scale]] arehave been specified byin [[physical space]]. It is based on a set of '''reference points'''―, defined as [[point (geometry)|geometric points]] whose [[position (geometry)|position]] is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers).<ref name="Kovalevsky Mueller 1989 pp. 1–12">{{cite book | last1=Kovalevsky | first1=J. | last2=Mueller |author-link=Jean Kovalevsky |first2=Ivan I. |author-link2=Ivan I. Mueller |title=Reference Frames | chapter=Introduction | series=Astrophysics and Space Science Library | publisher=Springer Netherlands | publication-place=Dordrecht | year=1989 | volume=154 | issn=0067-0057 | doi=10.1007/978-94-009-0933-5_1 | pages=1–12| isbn=978-94-010-6909-0 }}</ref>

An important special case is that of an ''[[inertial reference frame]]s'', a stationary or uniformly moving frame.

For ''n'' dimensions, {{nowrap|''n'' + 1}} reference points are sufficient to fully define a reference frame. Using [[Cartesian coordinate system|rectangular Cartesian coordinates]], a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the ''n'' coordinate [[Cartesian coordinate system|axes]].{{Citation needed|date=December 2020}}

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== Definition ==

The neeedneed to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in ''Cartesian frame of reference''. Sometimes the state of motion is emphasized, as in ''[[Rotating reference frame|rotating frame of reference]]''. Sometimes the way it transforms to frames considered as related is emphasized as in ''[[Galilean frame of reference]]''. Sometimes frames are distinguished by the scale of their observations, as in ''macroscopic'' and ''microscopic frames of reference''.<ref name=macroscopic>The distinction between macroscopic and microscopic frames shows up, for example, in electromagnetism where [[Constitutive equation|constitutive relations]] of various time and length scales are used to determine the current and charge densities entering [[Maxwell's equations]]. See, for example, {{cite book |title=Electromagnetic and Optical Pulse Propagation 1: Spectral Representations in Temporally Dispersive Media |author=Kurt Edmund Oughstun |page=165 |url=https://books.google.com/books?id=behRnNRiueAC&q=macroscopic+frame++electromagnetism&pg=PA165|isbn=0-387-34599-X |year=2006 |publisher=Springer}}. These distinctions also appear in thermodynamics. See {{cite book |title=Classical Theory |author=Paul McEvoy |page=205 |url=https://books.google.com/books?id=dj0wFIxn-PoC&q=macroscopic+frame&pg=PA206 |isbn=1-930832-02-8 |year=2002 |publisher=MicroAnalytix}}.</ref>

In this article, the term ''observational frame of reference'' is used when emphasis is upon the ''state of motion'' rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a ''coordinate system'' may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs ''[[generalized coordinates]]'', ''[[normal modes]]'' or ''[[eigenvectors]]'', which are only indirectly related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below:

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In physics experiments, the frame of reference in which the laboratory measurement devices are at rest is usually referred to as the [[laboratory frame]] or simply "lab frame." An example would be the frame in which the detectors for a particle accelerator are at rest. The lab frame in some experiments is an inertial frame, but it is not required to be (for example the laboratory on the surface of the Earth in many physics experiments is not inertial). In particle physics experiments, it is often useful to transform energies and momenta of particles from the lab frame where they are measured, to the [[center of momentum frame]] "COM frame" in which calculations are sometimes simplified, since potentially all kinetic energy still present in the COM frame may be used for making new particles.

In this connection it may be noted that the clocks and rods often used to describe observers' measurement equipment in thought, in practice are replaced by a much more complicated and indirect [[metrology]] that is connected to the nature of the [[vacuum]], and uses [[atomic clocks]] that operate according to the [[standardStandard modelModel]] and that must be corrected for [[gravitational time dilation]].<ref name= Wolfson>{{cite book |author= Richard Wolfson |title=Simply Einstein |url=https://books.google.com/books?id=OUJWKdlFKeQC&q=%22gravitational+time+dilation+%22&pg=PA216|page=216 |isbn=0-393-05154-4 |publisher=W W Norton & Co. |year=2003}}</ref> (See [[second]], [[meter]] and [[kilogram]]).

In fact, Einstein felt that clocks and rods were merely expedient measuring devices and they should be replaced by more fundamental entities based upon, for example, atoms and molecules.<ref name=Rizzi>See {{cite book |title=Relativity in rotating frames |page=33 |url=https://books.google.com/books?id=_PGrlCLkkIgC&q=centrifugal+%22+%22+relativity+OR+relativistic&pg=PA226

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==Generalization==

The discussion is taken beyond simple space-time coordinate systems by [[Katherine Brading|Brading]] and Castellani.<ref name=Brading>{{cite book |title=Symmetries in Physics: Philosophical Reflections |author1=Katherine Brading|author1-link=Katherine Brading |author2=Elena Castellani |page=417 |url=https://books.google.com/books?id=SnmBN64cAdYC&q=%22idea+of+a+reference+frame%22&pg=PA417|isbn=0-521-82137-1 |year=2003 |publisher=Cambridge University Press}}</ref> Extension to coordinate systems using generalized coordinates underlies the [[Hamilton's principle|Hamiltonian]] and [[Lagrangian mechanics|Lagrangian]] formulations<ref name=Johns>{{cite book |title=Analytical Mechanics for Relativity and Quantum Mechanics |page=Chapter 16 |author=Oliver Davis Johns |url=https://books.google.com/books?id=PNuM9YDN8CIC&q=coordinate+observer&pg=PA318

|isbn=0-19-856726-X |year=2005 |publisher=Oxford University Press |no-pp=true }}</ref> of [[quantum field theory]], [[classical mechanics|classical relativistic mechanics]], and [[quantum gravity]].<ref name=Greenwood>{{cite book |title=Classical dynamics |author=Donald T Greenwood |page=313 |year=1997 |edition=Reprint of 1977 edition by Prentice-Hall |publisher=Courier Dover Publications |url=https://books.google.com/books?id=x7rj83I98yMC&q=%22relativistic+%22+Lagrangian+OR+Hamiltonian&pg=RA2-PA314

|isbn=0-486-69690-1 }}</ref><ref name=Trump>{{cite book |title=Classical Relativistic Many-Body Dynamics |author1=Matthew A. Trump |author2=W. C. Schieve |page= 99 |url=https://books.google.com/books?id=g2yfLOp0IzwC&q=relativity+%22generalized+coordinates%22&pg=PA99

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* [[Moving frame|Moving frame in mathematics]]

== See also ==

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* [[Analytical mechanics]]

* [[Applied mechanics]]

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* [[Principle of relativity]]

* [[Quantum reference frame]]

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{{Relativity}}

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== Notes ==

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== References ==

{{reflist}}

{{Relativity}}

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[[Category:Frames of reference|*]]