Point particle

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Examples of point particles: Point mass for Newton's law of universal gravitation; Point particles to measure distance between two charged particles; Ideal gas particles do not interact (no collisions, no gravity force between them, no Coulomb's force); Simple pendulum (point mass attached to the end of the string with no mass). Collage of point particles.png
Examples of point particles: Point mass for Newton's law of universal gravitation; Point particles to measure distance between two charged particles; Ideal gas particles do not interact (no collisions, no gravity force between them, no Coulomb's force); Simple pendulum (point mass attached to the end of the string with no mass).

A point particle, ideal particle [1] or point-like particle (often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space. [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 a Dirac delta function.

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In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume. For example, the atomic orbit of an electron in the hydrogen atom occupies a volume of ~10−30 m3. There is nevertheless a distinction between elementary particles such as electrons or quarks, which have no known internal structure, versus composite particles such as protons, which do have internal structure: A proton is made of three quarks. Elementary particles are sometimes called "point particles" in reference to their lack of internal structure, but this is in a different sense than discussed above.

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 linear dimensions. 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 Newtonian gravitation behave in such a way as if all their matter were concentrated in their centers of mass. [3] In fact, this is true for all fields described by an inverse square law. [4] [5]

Point charge

Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right. Scalar potential of a point charge.jpg
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 point charge, a point particle with a nonzero electric charge. [6] 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 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

A proton is a combination of two up quarks and one down quark, held together by gluons. Quark structure proton.svg
A proton is a combination of two up quarks and one down quark, held together by gluons.

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 (see figure). However, neither elementary nor composite particles are spatially localized, because of the 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 states 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 10−18 m. [7] 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

Notes and references

Notes

  1. 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.
  2. Udwadia, F. E.; Kalaba, R. E. (2007). Analytical Dynamics: A New Approach. Cambridge University Press. p. 1. ISBN   978-0-521-04833-0.
  3. Fowles, Grant R; Cassiday, George L. Analytical Mechanics. §6.2 Gravitational Force between a Uniform Sphere and a Particle.
  4. 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.
  5. 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.
  6. Snieder, R. (2001). A Guided Tour of Mathematical Methods for the Physical Sciences. Cambridge University Press. pp. 196–198. ISBN   0-521-78751-3.
  7. "Precision pins down the electron's magnetism". 4 October 2006.

Bibliography

Further reading

Related Research Articles

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<span class="mw-page-title-main">Elementary particle</span> Subatomic particle having no known substructure

In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

<span class="mw-page-title-main">Nucleon</span> Particle that makes up the atomic nucleus (proton or neutron)

In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number.

<span class="mw-page-title-main">Particle physics</span> Study of subatomic particles and forces

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<span class="mw-page-title-main">Quark</span> Elementary particle

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<span class="mw-page-title-main">Weak interaction</span> Interaction between subatomic particles and one of the four known fundamental interactions

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<span class="mw-page-title-main">Standard Model</span> Theory of forces and subatomic particles

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<span class="mw-page-title-main">Subatomic particle</span> Particle smaller than an atom

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<span class="mw-page-title-main">Annihilation</span> Collision of a particle and its antiparticle

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In particle physics, preons are hypothetical point particles, conceived of as sub-components of quarks and leptons. The word was coined by Jogesh Pati and Abdus Salam, in 1974. Interest in preon models peaked in the 1980s but has slowed, as the Standard Model of particle physics continues to describe physics mostly successfully, and no direct experimental evidence for lepton and quark compositeness has been found. Preons come in four varieties: plus, anti-plus, zero, and anti-zero. W bosons have six preons, and quarks and leptons have only three.

In particle physics, flavour or flavor refers to the species of an elementary particle. The Standard Model counts six flavours of quarks and six flavours of leptons. They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles. They can also be described by some of the family symmetries proposed for the quark-lepton generations.

In physics, mainly quantum mechanics and particle physics, a spin magnetic moment is the magnetic moment caused by the spin of elementary particles. For example, the electron is an elementary spin-1/2 fermion. Quantum electrodynamics gives the most accurate prediction of the anomalous magnetic moment of the electron.

<span class="mw-page-title-main">Matter</span> Something that has mass and volume

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<span class="mw-page-title-main">Particle</span> Small localized object considered in physical sciences

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<span class="mw-page-title-main">History of subatomic physics</span>

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The nucleon magnetic moments are the intrinsic magnetic dipole moments of the proton and neutron, symbols μp and μn. The nucleus of an atom comprises protons and neutrons, both nucleons that behave as small magnets. Their magnetic strengths are measured by their magnetic moments. The nucleons interact with normal matter through either the nuclear force or their magnetic moments, with the charged proton also interacting by the Coulomb force.