Scalar fields: the secret sauce of theoretical physics | by Ethan Siegel | Starts With A Bang! | Dec, 2024

Scalars, vectors, and tensors come up all the time in physics. They’re more than mathematical structures. They help describe the Universe.

There are many goals of science, but they all fall into the broad category of how to understand and describe our reality as accurately as possible. If you give us a setup — and tell us what the initial conditions of that physical system are — then so long as our best scientific theories are powerful enough, science will be able to predict for you precisely how that system will evolve into the future. If we can measure and know the properties of whatever it is we’re dealing with, from atoms to humans to planets to stars and galaxies and more, a useful scientific theory will be able to predict what they will be like a finite time from now.

But sometimes, understanding what a scientific theory is, does, or even means requires that we learn some terms we’re unfamiliar with, including ones that have their roots in mathematics and often aren’t intuitive. You might hear words like scalars, vectors, and tensors bandied about, but rarely will you see a clear and compelling explanation for what these things actually are. These fields are of vital importance in both classical and quantum physics, both for…