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96:. 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
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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
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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.
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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
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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.
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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.
39:
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Jefimenko, Oleg D. (1994). "Direct calculation of the electric and magnetic fields of an electric point charge moving with constant velocity".
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315:, has an internal structure (see figure). However, neither elementary nor composite particles are spatially localized, because of the
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behave, as long as they do not touch each other, in such a way as if all their matter were concentrated in their
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100:. In classical mechanics there is usually no concept of rotation of point particles about their "center".
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For example, for the electron, experimental evidence shows that the size of an electron is less than
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350:. This is consistent with the expected value of exactly zero. (This should not be confused with the
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327:: The electron is an elementary particle, but its quantum states form three-dimensional patterns.
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Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right.
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131:. There is nevertheless a distinction between elementary particles such as
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Cornish, F. H. J. (1965). "Classical radiation theory and point charges".
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Fundamental
University Physics Volume III: Quantum and Statistical Physics
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configuration solely by the electrostatic interaction of the charges. The
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particles devoid of interactions (no collisions, gravitational force, or
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A Guided Tour of
Mathematical Methods for the Physical Sciences
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Principia: Mathematical Principles of Natural Philosophy
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wherein the particle is exactly localized. Moreover, the
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195:. In fact, this is true for all fields described by an
46:(point mass attached to the end of a massless string),
323:always occupies a nonzero volume. For example, see
519:I. Newton, A. Motte, J. Machin (1729), p. 270–271.
524:The Mathematical Principles of Natural Philosophy
88:. Its defining feature is that it lacks spatial
576:"Precision pins down the electron's magnetism"
139:, which have no known internal structure, and
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92:; being dimensionless, it does not take up
495:. Translated by Cohen, I. B.; Whitman, A.
187:whose interactions are described by the
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27:Idealised model of a particle in physics
499:. p. 956 (Proposition 75, Theorem 35).
418:Ohanian, H. C.; Markert, J. T. (2007).
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527:. Translated by Motte, A.; Machin, J.
447:Udwadia, F. E.; Kalaba, R. E. (2007).
476:Fowles, Grant R; Cassiday, George L.
295:. An elementary particle, such as an
291:(also called "point particle") and a
40:Newton's law of universal gravitation
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420:Physics for Engineers and Scientists
287:, there is a distinction between an
175:(infinitely small) in its volume or
688:Proceedings of the Physical Society
449:Analytical Dynamics: A New Approach
227:, a point particle with a nonzero
167:, of a physical object (typically
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378:(general concept, not limited to
267:A proton is a combination of two
163:) is the concept, for example in
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317:Heisenberg uncertainty principle
109:Heisenberg uncertainty principle
36:(counterclockwise from top left)
654:M. Alonso; E. J. Finn (1968).
497:University of California Press
422:. Vol. 1 (3rd ed.).
1:
34:Examples of point particles:
215:Similar to point masses, in
719:American Journal of Physics
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709:10.1088/0370-1328/86/3/301
552:Cambridge University Press
453:Cambridge University Press
352:classical electron radius
631:Encyclopedia Americana
624:S. L. Glashow (2009).
601:Encyclopedia Americana
596:"Particle, Elementary"
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127:occupies a volume of ~
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394:Wave–particle duality
332:quantum superposition
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219:physicists discuss a
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189:Newtonian gravitation
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762:at Wikimedia Commons
554:. pp. 196–198.
546:Snieder, R. (2001).
478:Analytical Mechanics
400:Notes and references
259:In quantum mechanics
98:Dirac delta function
781:Classical mechanics
776:Concepts in physics
732:1994AmJPh..62...79J
701:1965PPS....86..427C
521:Newton, I. (1729).
491:Newton, I. (1999).
390:of particle physics
289:elementary particle
275:, held together by
185:3-dimensional space
179:. In the theory of
141:composite particles
113:elementary particle
70:point-like particle
293:composite particle
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245:Earnshaw's theorem
231:. The fundamental
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197:inverse square law
111:, because even an
74:pointlike particle
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54:between particles)
758:Media related to
594:C. Quigg (2009).
578:. 4 October 2006.
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285:quantum mechanics
177:linear dimensions
165:classical physics
105:quantum mechanics
16:(Redirected from
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249:equilibrium
770:Categories
646:2009-07-04
616:2009-07-04
321:wavepacket
273:down quark
157:Point mass
152:Point mass
348:10 m
269:up quarks
133:electrons
129:10 m
90:extension
82:particles
48:ideal gas
358:See also
297:electron
271:and one
233:equation
143:such as
121:electron
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626:"Quark"
313:neutron
181:gravity
145:protons
123:in the
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309:proton
305:photon
277:gluons
169:matter
137:quarks
119:of an
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405:Notes
371:Brane
303:, or
301:quark
94:space
664:ISBN
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