Question

What is a scalar field?

Answer 1

A scalar field associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In a physical context, scalar fields are required to be independent of the choice of coordinate system, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, etc.