- Scalar (physics)
In

physics , a**scalar**is a simplephysical quantity that is not changed bycoordinate system rotations or translations (in Newtonian mechanics), or byLorentz transformations or space-time translations (in relativity). (Contrast to vector.)**Examples**For example, the

distance between two points in space is a scalar, as are themass , charge, andkinetic energy of an object, or thetemperature andelectric potential at a point inside a medium. On the other hand, theelectric 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. Thespeed of an object is a scalar (e.g. 180 km/h), while itsvelocity is not (i.e. 180 km/h "north"). Thegravitation alforce acting on a particle is not a scalar, but its magnitude is.Examples of scalar quantities in Newtonian mechanics:

*electric charge andcharge density

*mass andmass density

*speed , but notvelocity ormomentum

*temperature

*energy andenergy density

*time

*pressure

*entropy

*negentropy A physical

quantity is expressed as the product of a numerical value and aphysical 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 beingorthonormal ), 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, thecharge density at a point in a medium, which is a scalar in classical physics, must be combined with the localcurrent density (a 3-vector) to comprise a relativistic 4-vector. Similarly,energy density must be combined with momentum density andpressure into thestress-energy tensor .Examples of scalar quantities in relativity:

*electric charge

* spacetime interval (e.g.,proper time andproper length )

*invariant mass A related concept is a

**pseudoscalar**, which is invariant underproper rotation s but (like apseudovector ) flips sign underimproper rotation s. One example is the scalartriple product (see vector), and thus the signed volume. Another example ismagnetic 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.*