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Point particle
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<h2 id="point-mass">Point mass</h2> <p>Point mass (pointlike mass) is the concept, for example in <a href="/facts/Classical_physics/gGnINVPE">classical physics</a>, of a physical object (typically <a href="/facts/Matter/osyc04UN">matter</a>) that has nonzero mass, and yet explicitly and specifically is (or is being thought of or modeled as) <a href="/facts/Infinitesimal/JKcTMIgD">infinitesimal</a> (infinitely small) in its volume or <a href="/facts/Length/EwFyAqGH">linear dimensions</a>. In the theory of <a href="/facts/Gravity/bqAN7DdQ">gravity</a>, extended objects can behave as point-like even in their immediate vicinity. For example, spherical objects interacting in <a href="/facts/3-dimensional_space/KAqKWUbS">3-dimensional space</a> whose interactions are described by the <a href="/facts/Law_of_universal_gravitation/F6qH2XC3">Newtonian gravitation</a> behave, as long as they do not touch each other, in such a way as if all their matter were concentrated in their <a href="/facts/Center_of_mass/n4Lr9GAz">centers of mass</a>.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> In fact, this is true for all fields described by an <a href="/facts/Inverse_square_law/DxG4T15l">inverse square law</a>.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p> <h2 id="point-charge">Point charge</h2> <p>Similar to point masses, in <a href="/facts/Electromagnetism/oAkmALHT">electromagnetism</a> physicists discuss a point charge, a point particle with a nonzero <a href="/facts/Electric_charge/xxsBfmlB">electric charge</a>.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> The fundamental <a href="/facts/Equation/pxFzLAVR">equation</a> of <a href="/facts/Electrostatics/bxkuW6s4">electrostatics</a> is <a href="/facts/Coulomb%2527s_law/V0lR5NKv">Coulomb's law</a>, which describes the electric force between two point charges. Another result, <a href="/facts/Earnshaw%2527s_theorem/DAcAS4Pk">Earnshaw's theorem</a>, states that a collection of point charges cannot be maintained in a static <a href="/facts/Mechanical_equilibrium/N2XKaK6s">equilibrium</a> configuration solely by the electrostatic interaction of the charges. The <a href="/facts/Electric_field/tt4MooBs">electric field</a> 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. </p> <h2 id="in-quantum-mechanics">In quantum mechanics</h2> <p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, there is a distinction between an <a href="/facts/Elementary_particle/CTFDM97U">elementary particle</a> (also called "point particle") and a <a href="/facts/Composite_particle/FwR0Ab6u">composite particle</a>. An elementary particle, such as an <a href="/facts/Electron/L0KBo5cW">electron</a>, <a href="/facts/Quark/hwuuVkV5">quark</a>, or <a href="/facts/Photon/mFNhAEzA">photon</a>, is a particle with no known internal structure. Whereas a composite particle, such as a <a href="/facts/Proton/clCjepXP">proton</a> or <a href="/facts/Neutron/oRCM1geb">neutron</a>, has an internal structure. However, neither elementary nor composite particles are spatially localized, because of the <a href="/facts/Uncertainty_principle/UUSoSp4T">Heisenberg uncertainty principle</a>. The particle <a href="/facts/Wavepacket/4HLR2joo">wavepacket</a> always occupies a nonzero volume. For example, see <a href="/facts/Atomic_orbital/tKhgl6mL">atomic orbital</a>: The electron is an elementary particle, but its quantum states form three-dimensional patterns. </p><p>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 <a href="/facts/Quantum_superposition/4z1UJg9o">quantum superposition</a> of <a href="/facts/Quantum_state/7jbxd7Dx">quantum states</a> wherein the particle is exactly localized. Moreover, the <i>interactions</i> 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. </p><p>For example, for the electron, experimental evidence shows that the size of an electron is less than 10−18 m.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> This is consistent with the expected value of exactly zero. (This should not be confused with the <a href="/facts/Classical_electron_radius/dU9jFS10">classical electron radius</a>, which, despite the name, is unrelated to the actual size of an electron.) </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Test_particle/EJfWtPRX">Test particle</a></li> <li></li> <li><a href="/facts/Brane/fPHTVchc">Brane</a></li> <li><a href="/facts/Charge_(physics)/jnQEDBI3">Charge (physics)</a> (general concept, not limited to <i><a href="/facts/Electric_charge/xxsBfmlB">electric charge</a></i>)</li> <li><a href="/facts/Standard_Model/LhVGf9ow">Standard Model</a> of particle physics</li> <li><a href="/facts/Wave%25E2%2580%2593particle_duality/Au3UlcwQ">Wave–particle duality</a></li></ul> <h2 id="notes-and-references">Notes and references</h2> <h3>Notes</h3> <h3>Bibliography</h3> <ul><li>C. Quigg (2009). <a href="https://wayback.archive-it.org/all/20130401135900/http://auth.grolier.com/login/go_login.html?bffs=N">"Particle, Elementary"</a>. <i><a href="/facts/Encyclopedia_Americana/rsmEnQT5">Encyclopedia Americana</a></i>. <a href="/facts/Grolier/pdhCBG0c">Grolier Online</a>. Archived from <a href="http://ea.grolier.com/article?id=0303750-00">the original</a> on 2013-04-01. Retrieved 2009-07-04.</li> <li>S. L. Glashow (2009). <a href="https://wayback.archive-it.org/all/20130401135900/http://auth.grolier.com/login/go_login.html?bffs=N">"Quark"</a>. <i><a href="/facts/Encyclopedia_Americana/rsmEnQT5">Encyclopedia Americana</a></i>. <a href="/facts/Grolier/pdhCBG0c">Grolier Online</a>. Archived from <a href="http://ea.grolier.com/article?id=0325780-00">the original</a> on 2013-04-01. Retrieved 2009-07-04.</li> <li>M. Alonso; E. J. Finn (1968). <i>Fundamental University Physics Volume III: Quantum and Statistical Physics</i>. <a href="/facts/Addison-Wesley/A7UFATEG">Addison-Wesley</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-00262-0.</li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Cornish, F. H. J. (1965). "Classical radiation theory and point charges". <i><a href="/facts/Proceedings_of_the_Physical_Society/W8eCzVa6">Proceedings of the Physical Society</a></i>. 86 (3): 427–442. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1965PPS....86..427C">1965PPS....86..427C</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1088%2F0370-1328%2F86%2F3%2F301">10.1088/0370-1328/86/3/301</a>.</li> <li>Jefimenko, Oleg D. (1994). "Direct calculation of the electric and magnetic fields of an electric point charge moving with constant velocity". <i><a href="/facts/American_Journal_of_Physics/GYzhvGaC">American Journal of Physics</a></i>. 62 (1): 79–85. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1994AmJPh..62...79J">1994AmJPh..62...79J</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1119%2F1.17716">10.1119/1.17716</a>.</li></ul> <h2 id="external-links">External links</h2> <ul><li> Media related to Point particle at Wikimedia Commons</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Ohanian, H. C.; Markert, J. T. (2007). Physics for Engineers and Scientists. Vol. 1 (3rd ed.). Norton. p. 3. ISBN 978-0-393-93003-0. <a href="978-0-393-93003-0" target="_blank">978-0-393-93003-0</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Udwadia, F. E.; Kalaba, R. E. (2007). Analytical Dynamics: A New Approach. Cambridge University Press. p. 1. ISBN 978-0-521-04833-0. <a href="978-0-521-04833-0" target="_blank">978-0-521-04833-0</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Fowles, Grant R; Cassiday, George L. Analytical Mechanics. §6.2 Gravitational Force between a Uniform Sphere and a Particle. <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Newton, I. (1999). The Principia: Mathematical Principles of Natural Philosophy. Translated by Cohen, I. B.; Whitman, A. University of California Press. p. 956 (Proposition 75, Theorem 35). ISBN 0-520-08817-4. <a href="0-520-08817-4" target="_blank">0-520-08817-4</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>I. Newton, A. Motte, J. Machin (1729), p. 270–271.Newton, I. (1729). The Mathematical Principles of Natural Philosophy. Translated by Motte, A.; Machin, J. Benjamin Motte. pp. 270–271. <a href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ" target="_blank">https://archive.org/details/bub_gb_Tm0FAAAAQAAJ</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Snieder, R. (2001). A Guided Tour of Mathematical Methods for the Physical Sciences. Cambridge University Press. pp. 196–198. ISBN 0-521-78751-3. <a href="0-521-78751-3" target="_blank">0-521-78751-3</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>"Precision pins down the electron's magnetism". 4 October 2006. <a href="https://cerncourier.com/a/precision-pins-down-the-electrons-magnetism" target="_blank">https://cerncourier.com/a/precision-pins-down-the-electrons-magnetism</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> </ol>