Scalar (physics)

A scalar in physics is a physical quantity that can be described by a single element of a number field such as a real number, often accompanied by units of measurement. A scalar is usually said to be a physical quantity that only has magnitude and no other characteristics. This is in contrast to vectors, tensors, etc. which are described by several numbers that characterize their magnitude, direction, and so on. A vector is usually said to be a physical quantity that has magnitude and direction. Formally, a scalar is unchanged by coordinate system rotations or reflections (in Newtonian mechanics), or by Lorentz transformations or space-time translations (in relativity). A related concept is a pseudoscalar, which is invariant under proper rotations but (like a pseudovector) flips sign under improper rotations. The concept of a scalar in physics is essentially the same as in mathematics. A physical scalar field is one type of more general fields, like vector fields, spinor fields, and tensor fields.

An example of a scalar quantity is temperature: the temperature at a given point is a single number. Velocity, on the other hand, is a vector quantity: velocity in three-dimensional space is specified by three values; in a Cartesian coordinate system the values are the speeds relative to each coordinate axis. The associated fields describe the temperature and velocity in each point of some space. Considering the norms of the velocity vectors results in a scalar field of the speeds in each point of the space.

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