Point particle

A point particle (ideal particle 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 zero-dimensional, it does not take up space. 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. A point particle can also be referred in the case of a moving body in terms of physics In the theory of gravity, physicists often discuss a point mass, meaning a point particle with a nonzero mass and no other properties or structure. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge. Sometimes, due to specific combinations of properties, extended objects behave as point-like even in their immediate vicinity. For example, spherical objects interacting in 3-dimensional space whose interactions are described by the inverse square law behave in such a way as if all their matter were concentrated in their centers of mass. In Newtonian gravitation and classical electromagnetism, for example, the respective fields outside a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere. 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', but this is in a different sense than discussed above. When a point particle has an additive property, such as mass or charge, concentrated at a single point in space, this can be represented by a Dirac delta function. 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. A common use for point mass lies in the analysis of the gravitational fields. When analyzing the gravitational forces in a system, it becomes impossible to account for every unit of mass individually. However, a spherically symmetric body affects external objects gravitationally as if all of its mass were concentrated at its center. A point mass in probability and statistics does not refer to mass in the sense of physics, but rather refers to a finite nonzero probability that is concentrated at a point in the probability mass distribution, where there is a discontinuous segment in a probability density function. To calculate such a point mass, an integration is carried out over the entire range of the random variable, on the probability density of the continuous part. After equating this integral to 1, the point mass can be found by further calculation.