Scalar (physics)

Scalar (physics)

In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations (in Newtonian mechanics), or by Lorentz transformations or space-time translations (in relativity). (Contrast to vector.)


For example, the distance between two points in space is a scalar, as are the mass, charge, and kinetic energy of an object, or the temperature and electric potential at a point inside a medium. On the other hand, the electric field at a point is not a scalar in this sense, since to specify it one must give three real numbers that depend on the coordinate system chosen. The speed of an object is a scalar (e.g. 180 km/h), while its velocity is not (i.e. 180 km/h "north"). The gravitational force acting on a particle is not a scalar, but its magnitude is.

Examples of scalar quantities in Newtonian mechanics:
* electric charge and charge density
* mass and mass density
* speed, but not velocity or momentum
* temperature
* energy and energy density
* time
* pressure
* entropy
* negentropy

A physical quantity is expressed as the product of a numerical value and a physical unit, not just a number. It does not depend on the unit distance (1 km is the same as 1000 m), although the number depends on the unit. Thus distance does not depend on the length of the base vectors of the coordinate system. Also, other changes of the coordinate system may affect the formula for computing the scalar (for example, the Euclidean formula for distance in terms of coordinates relies on the basis being orthonormal), but not the scalar itself. In this sense, physical distance deviates from the definition of metric in not being just a real number; however it satisfies all other properties. The same applies for other physical quantities which are not dimensionless.

calars in relativity theory

In the theory of relativity, one considers changes of coordinate systems that trade space for time. As a consequence, several physical quantities that are scalars in "classical" (non-relativistic) physics need to be combined with other quantities and treated as four-dimensional vectors or tensors. For example, the charge density at a point in a medium, which is a scalar in classical physics, must be combined with the local current density (a 3-vector) to comprise a relativistic 4-vector. Similarly, energy density must be combined with momentum density and pressure into the stress-energy tensor.

Examples of scalar quantities in relativity:
* electric charge
* spacetime interval (e.g., proper time and proper length)
* invariant mass

A related concept is a pseudoscalar, which is invariant under proper rotations but (like a pseudovector) flips sign under improper rotations. One example is the scalar triple product (see vector), and thus the signed volume. Another example is magnetic charge (as it is mathematically defined, regardless of whether it actually exists physically).

See also

*Scalar field
*Scalar field theory
*Pseudoscalar (physics)
*Scalar (mathematics)
*Lorentz scalar

Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Scalar (mathematics) — In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.More generally, the scalars… …   Wikipedia

  • Scalar — A scalar is a variable that only has magnitude, e.g. a speed of 40 km/h. Compare it with vector, a quantity comprising both magnitude and direction, e.g. a velocity of 40km/h north .* Scalar (mathematics), a quantity which is independent of… …   Wikipedia

  • Scalar-tensor theory — Scalar tensor theories are theories that include a scalar field as well as a tensor field to represent an interaction, especially the gravitational one. Tensor fields and field theory Modern physics tries to derive all physical theories from as… …   Wikipedia

  • Scalar-tensor-vector gravity — (STVG) is a theory of gravity which, like other theories including Modified Newtonian dynamics (otherwise known as MOND ), attempts to explain the rotation of galaxies by doing away with dark matter. Unlike MOND, STVG explains galactic clustering …   Wikipedia

  • scalar Mathematics & Physics — [ skeɪlə] adjective (of a quantity) having only magnitude, not direction. noun a scalar quantity. Origin C17: from L. scalaris, from scala (see scale3) …   English new terms dictionary

  • scalar — Mathematics & Physics ► ADJECTIVE ▪ having only magnitude, not direction. ► NOUN ▪ a scalar quantity (especially as opposed to a vector). ORIGIN Latin scalaris, from scala ladder …   English terms dictionary

  • Scalar field theory (pseudoscience) — For the quantum mechanical scalar field theory which is a field theory of spinless particles, see Scalar field theory Scalar field theory (SFT) is a set of theories in a model which posits that there is a basic mechanism that produces the… …   Wikipedia

  • Scalar field — In mathematics and physics, a scalar field associates a scalar value, which can be either mathematical in definition, or physical, to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature… …   Wikipedia

  • Scalar field theory — In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a scalar , in contrast to a vector or tensor field. The quanta of the… …   Wikipedia

  • Scalar meson — In high energy physics, a scalar meson is a meson with total spin 0 and even parity (usually noted as JP =0+). Compare to pseudoscalar meson.These mesons are most often observed in proton antiproton annihilation, radiative decays of vector mesons …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”