Editing Point particle

{{Short description|Idealised model of a particle in physics}}
[[File:Collage of point particles.png|thumb|300x300px|Examples of point particles: {{em|(counterclockwise from top left)}} point mass for [[Newton's law of universal gravitation]], point particles to measure distance between two charged particles, [[Pendulum|simple pendulum]] (point mass attached to the end of a massless string), [[ideal gas]] particles devoid of interactions (no collisions, gravitational force, or [[Coulomb's law|Coulomb's force]] between particles)]]
{{Use American English|date = February 2019}}

A '''point particle''', '''ideal particle'''<ref>{{cite book | first1 = H. C. | last1 = Ohanian | first2 = J. T. | last2 = Markert | year = 2007 | title = Physics for Engineers and Scientists | volume = 1 | edition = 3rd | publisher = [[W. W. Norton & Company|Norton]] | isbn = 978-0-393-93003-0 | page = 3 }}</ref> or '''point-like particle''' (often spelled '''pointlike particle''') is an [[idealization (science philosophy)|idealization]] of [[particle]]s heavily used in [[physics]]. Its defining feature is that it lacks spatial [[extension (metaphysics)|extension]]; being dimensionless, it does not take up [[space]].<ref>{{cite book | first1 = F. E. | last1 = Udwadia | first2 = R. E. | last2 = Kalaba | year = 2007 | title = Analytical Dynamics: A New Approach | publisher = [[Cambridge University Press]] | isbn = 978-0-521-04833-0 | page = 1 }}</ref> A point particle is an appropriate representation of any object whenever its size, shape, and structure are irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. Point masses and point charges, discussed below, are two common cases.  When a point particle has an additive property, such as mass or charge, it is often represented mathematically by a [[Dirac delta function]]. In classical mechanics there is usually no concept of rotation of point particles about their "center".

In [[quantum mechanics]], the concept of a point particle is complicated by the [[Uncertainty principle|Heisenberg uncertainty principle]], because even an [[elementary particle]], with no internal structure, occupies a nonzero volume. For example, the [[atomic orbital|atomic orbit]] of an [[electron]] in the [[hydrogen atom]] occupies a volume of ~{{val|e=-30|u=m3}}. There is nevertheless a distinction between elementary particles such as [[electron]]s or [[quark]]s, which have no known internal structure, and [[composite particle]]s such as [[proton]]s and neutrons, whose internal structures are made up of quarks.
Elementary particles are sometimes called "point particles" in reference to their lack of internal structure, but this is in a different sense than that discussed herein.

==Point mass==
'''Point mass''' ('''pointlike mass''') is the concept, for example in [[classical physics]], of a physical object (typically [[matter]]) that has nonzero mass, and yet explicitly and specifically is (or is being thought of or modeled as) [[infinitesimal]] (infinitely small) in its volume or [[length|linear dimension]]s.
In the theory of [[gravity]], extended objects can behave as point-like even in their immediate vicinity.  For example, spherical objects interacting in [[3-dimensional space]] whose interactions are described by the [[Law of universal gravitation|Newtonian gravitation]] behave, as long as they do not touch each other, in such a way as if all their matter were concentrated in their [[center of mass|centers of mass]].<ref>{{cite book | title = Analytical Mechanics | first1 = Grant R | last1 = Fowles | first2 = George L | last2 = Cassiday | at = §6.2 Gravitational Force between a Uniform Sphere and a Particle | year = }}</ref> In fact, this is true for all fields described by an [[inverse square law]].<ref>{{cite book | first = I. | last = Newton | year = 1999 | translator-first1 = I. B. | translator-last1 = Cohen | translator-first2 = A. | translator-last2 = Whitman | title = The Principia: Mathematical Principles of Natural Philosophy | publisher = [[University of California Press]] | isbn = 0-520-08817-4 | at = p. 956 (Proposition 75, Theorem 35) }}</ref><ref name=NewtonMotteMachin1>I. Newton, A. Motte, J. Machin (1729), p. 270–271.{{cite book | first = I. | last = Newton | year = 1729 | translator-first1 = A. | translator-last1 = Motte | translator-first2 = J. | translator-last2 = Machin | title = The Mathematical Principles of Natural Philosophy | url = https://archive.org/details/bub_gb_Tm0FAAAAQAAJ | pages = [https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n354 270]–271 | publisher = [[Benjamin Motte]] }}</ref>

==Point charge==
[[File:Scalar potential of a point charge.jpg|left|thumb|Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right.]]
Similar to point masses, in [[electromagnetism]] physicists discuss a '''{{vanchor|point charge|POINT_CHARGE}}''', a point particle with a nonzero [[electric charge]].<ref>{{cite book | first = R. | last = Snieder | year = 2001 | title = A Guided Tour of Mathematical Methods for the Physical Sciences | publisher = [[Cambridge University Press]] | isbn = 0-521-78751-3 | pages = 196–198 }}</ref> The fundamental [[equation]] of [[electrostatics]] is [[Coulomb's law]], which describes the electric force between two point charges. Another result, [[Earnshaw's theorem]], states that a collection of point charges cannot be maintained in a static [[mechanical equilibrium|equilibrium]] configuration solely by the electrostatic interaction of the charges. The [[electric field]] associated with a classical point charge increases to infinity as the distance from the point charge decreases towards zero, which suggests that the model is no longer accurate in this limit.

==In quantum mechanics==
[[Image:Quark_structure_proton.svg|thumb|200px|right|A proton is a combination of two [[up quark]]s and one [[down quark]], held together by [[gluon]]s.]]
In [[quantum mechanics]], there is a distinction between an [[elementary particle]] (also called "point particle") and a [[composite particle]]. An elementary particle, such as an [[electron]], [[quark]], or [[photon]], is a particle with no known internal structure. Whereas a composite particle, such as a [[proton]] or [[neutron]], has an internal structure.
However, neither elementary nor composite particles are spatially localized, because of the [[Uncertainty principle|Heisenberg uncertainty principle]]. The particle [[wavepacket]] always occupies a nonzero volume. For example, see [[atomic orbital]]: The electron is an elementary particle, but its quantum states form three-dimensional patterns.

Nevertheless, there is good reason that an elementary particle is often called a point particle. Even if an elementary particle has a delocalized wavepacket, the wavepacket can be represented as a [[quantum superposition]] of [[quantum state]]s wherein the particle is exactly localized. Moreover, the ''interactions'' of the particle can be represented as a superposition of interactions of individual states which are localized.  This is not true for a composite particle, which can never be represented as a superposition of exactly-localized quantum states. It is in this sense that physicists can discuss the intrinsic "size" of a particle: The size of its internal structure, not the size of its wavepacket. The "size" of an elementary particle, in this sense, is exactly zero.

For example, for the electron, experimental evidence shows that the size of an electron is less than {{val|e=-18|u=m}}.<ref>{{cite web | url=https://cerncourier.com/a/precision-pins-down-the-electrons-magnetism | title=Precision pins down the electron's magnetism | date=4 October 2006 }}</ref> This is consistent with the expected value of exactly zero. (This should not be confused with the [[classical electron radius]], which, despite the name, is unrelated to the actual size of an electron.)

==See also==
* [[Test particle]]
*
* [[Brane]]
* [[Charge (physics)]] (general concept, not limited to ''[[electric charge]]'')
* [[Standard Model]] of particle physics
*[[Wave–particle duality]]

==Notes and references==

===Notes===
{{Reflist}}

===Bibliography===
{{refbegin}}
*{{cite encyclopedia
 | author = C. Quigg
 | year = 2009
 | title = Particle, Elementary
 | url = http://ea.grolier.com/article?id=0303750-00
 | archive-url = https://wayback.archive-it.org/all/20130401135900/http://auth.grolier.com/login/go_login.html?bffs=N
 | url-status = dead
 | archive-date = 2013-04-01
 | encyclopedia = [[Encyclopedia Americana]]
 | publisher = [[Grolier|Grolier Online]]
 | access-date = 2009-07-04
 }}
*{{cite encyclopedia
 | author = S. L. Glashow
 | year = 2009
 | title = Quark
 | url = http://ea.grolier.com/article?id=0325780-00
 | archive-url = https://wayback.archive-it.org/all/20130401135900/http://auth.grolier.com/login/go_login.html?bffs=N
 | url-status = dead
 | archive-date = 2013-04-01
 | encyclopedia = [[Encyclopedia Americana]]
 | publisher = [[Grolier|Grolier Online]]
 | access-date = 2009-07-04
 }}
*{{cite book
 | author1 = M. Alonso | author2 = E. J. Finn
 | year = 1968
 | title = Fundamental University Physics Volume III: Quantum and Statistical Physics
 | publisher = [[Addison-Wesley]]
 | isbn = 0-201-00262-0
}}
{{refend}}

==Further reading==
*{{cite journal |last1=Cornish |first1=F. H. J. |title=Classical radiation theory and point charges |journal=[[Proceedings of the Physical Society]] |year=1965 |volume=86 |issue=3 |pages=427–442 |doi=10.1088/0370-1328/86/3/301|bibcode=1965PPS....86..427C }}
*{{cite journal |last1=Jefimenko |first1=Oleg D. |title=Direct calculation of the electric and magnetic fields of an electric point charge moving with constant velocity |journal=[[American Journal of Physics]] |year=1994 |volume=62 |issue=1 |pages=79–85 |doi=10.1119/1.17716|bibcode=1994AmJPh..62...79J }}

==External links==
*{{Commonscatinline|Point particle}}

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{{DEFAULTSORT:Point Particle}}
[[Category:Concepts in physics]]
[[Category:Classical mechanics]]