Apoint particle,ideal particle[1] orpoint-like particle (often spelledpointlike particle) is anidealization ofparticles heavily used inphysics. Its defining feature is that it lacks spatialextension; being dimensionless, it does not take upspace.[2] 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 aDirac delta function. In classical mechanics there is usually no concept of rotation of point particles about their "center".
Inquantum mechanics, the concept of a point particle is complicated by theHeisenberg uncertainty principle, because even anelementary particle, with no known internal structure, occupies a nonzero volume. There is nevertheless a distinction between elementary particles such aselectrons orquarks, which have no known internal structure, andcomposite particles such asprotons and neutrons, whose internal structures are made up of quarks.Elementary particles are sometimes called "point particles" in reference to their lack of known internal structure, but this is in a different sense than that discussed herein.
Point mass (pointlike mass) is the concept, for example inclassical physics, of a physical object (typicallymatter) that has nonzero mass, and yet explicitly and specifically is (or is being thought of or modeled as)infinitesimal (infinitely small) in its volume orlinear dimensions.In the theory ofgravity, extended objects can behave as point-like even in their immediate vicinity. For example, spherical objects interacting in3-dimensional space whose interactions are described by theNewtonian gravitation behave, as long as they do not touch each other, in such a way as if all their matter were concentrated in theircenters of mass.[3] In fact, this is true for all fields described by aninverse square law.[4][5]
Inelectromagnetism, apoint charge is a point particle with a nonzeroelectric charge.[6] It can also be defined as a charged body orcharge carrier whose effective diameter is much smaller than the distance to another charged object.[7] The fundamentalequation ofelectrostatics isCoulomb'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 staticequilibrium configuration solely by the electrostatic interaction of the charges. Theelectric field associated with a classical point charge increases to infinity as the distance from the point charge decreases towards zero, which indicates that the model is no longer accurate in this limit.
Inquantum mechanics, there is a distinction between anelementary particle (also called "point particle") and acomposite particle. An elementary particle, such as anelectron,quark, orphoton, is a particle with no known internal structure. Whereas a composite particle, such as aproton orneutron, has an internal structure.However, neither elementary nor composite particles are spatially localized, because of theHeisenberg uncertainty principle. The particlewavepacket always occupies a nonzero volume. For example, seeatomic 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 aquantum superposition ofquantum states wherein the particle is exactly localized. Moreover, theinteractions 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.
For example, for the electron, experimental evidence shows that the size of an electron is less than10−18 m.[8] (This should not be confused with theclassical electron radius, which, despite the name, is unrelated to the actual size of an electron.)
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