In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime). Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory
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“The poet will write for his peers alone. He will remember only that he saw truth and beauty from his position, and expect the time when a vision as broad shall overlook the same field as freely.”
—Henry David Thoreau (1817–1862)