Home > Scalar

The concept of a scalar is used in mathematics and physics. The concept used in physics is a more concrete version of the same idea that goes by that name in mathematics.

In mathematics, the meaning of scalar depends on the context; it can refer to real numbers or complex numbers or rational numbers, or to members of some other specified field. Generally, when a vector space over the field F is studied, then F is called the field of scalars.

In physics a scalar is a quantity that can be described by a single number (either dimensionless, or in terms of some physical quantity). Scalar quantities have magnitude, but not a direction and should thus be distinguished from vectors. More formally, a scalar is a quantity that is invariant under coordinate rotations (or Lorentz transformations, for relativity). A scalar is formally a tensorFor more technical Wiki articles on tensors, see the section later in this article. In mathematics, a tensor is a certain kind of geometrical entity which generalizes the concepts of scalar, vector (spatial) and linear operator in a way that is independen of rank zero.

Examples of (non-relativistic) scalar quantities include:

• electric chargeElectric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. It is one of the quantum numbers. Matter that possesses a charge is influenced by, and produces, electromagnetic fields. The intera
• distanceFor distance between people, see proxemics. Distance between two points The distance between two points is the length of a straight line between them. In the case of two locations on Earth, usually the distance along the surface is meant: either " as the
• massMass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. It is a central concept of classical mechanics and related subjects. Strictly speaking, there are two different quantities called mass Inertial mass
• speedFor alternate uses, see Speed (disambiguation). Speed (symbol: v is the rate of motion, or equivalently the rate of change of position, expressed as distance d moved per unit of time t''. Speed is a scalar quantity with dimensions Length/ Time; the equiva
• temperatureTemperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter. General description The formal properties of temperature are studied in thermodynamics.
• timeFor alternate uses of "time", see Time (disambiguation). Time quantifies or measures the interval between events, or the duration of events. Time has long been perceived as a dimension in which each event has a definite (but not necessarily unique) positi
• energyThis article is about the scientific concept. Energy use by humans is discussed in other articles''. Energy generally and qualitatively speaking, is the property (or the quantity of the property) of doing things or supplying power. The expressions energy (and thus power, work, etcetera).

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 volume. (Another example, if it existed, would be magnetic charge.)

The word scalar derives from the English word "scale" for a range of numbers, which in turn is derived from scala ( Latin for "ladder"). According to a citation in the Oxford English Dictionary the first usage of the term (by W. R. Hamilton in 1846) described it as:

"The algebraically real part may receive, according to the question in which it occurs, all values contained on the one scale of progression of numbers from negative to positive infinity; we shall call it therefore the scalar part."

Hamilton's usage actually describes his quaternion-based notation, which (in modern terms) represented scalars by the real part of the quaternion and vectors by the other three parts. (This notation eventually proved unpopular.)