Where does scalar collide?

A quantity fully specified by a single number, carrying magnitude but no direction, and in linear algebra an element of the underlying field of numbers by which the vectors of a space are multiplied. Halmos's 1974 Finite-Dimensional Vector Spaces defined a vector space over a field whose members are the scalars, so that scaling a vector means multiplying it by one such number, and a scalar itself has no direction to speak of. The referent here is a plain number used to measure or rescale, contrasted with the directed vector it acts on, and it is neither a physical field filling space nor a single stored value in a program.[1]

Unit

One number from the underlying field, with magnitude but no direction

Recovery means

Not applicable

Measured by

Written as a real or complex number and combined with vectors by the scalar multiplication of the space

In field theory a scalar field assigns a single number to every point of space and stays unchanged under rotations of the coordinates, so its value at a point does not turn when the axes turn, as with a temperature map; the particle that is the quantum of such a field carries no spin and is called a scalar boson. Higgs's 1964 Broken Symmetries and the Masses of Gauge Bosons introduced the scalar field whose excitation is now the Higgs boson, the spin-0 particle confirmed in 2012. The referent is a physical quantity spread through space and its associated particle, not a bare number used to rescale a vector, and not a single value held in a variable.[2]

Unit

A number attached to each point of space, unchanged by rotation, with a spin-0 quantum

Recovery means

Not applicable

Measured by

Mapped as a value across space and probed as its quantum in particle collisions, as with the mass and decays of the Higgs boson