What is the difference between field and disturbance?

Question

In my textbook Sears & Zemansky's University Physics, 15th ed, Page-399, it is written that,

"A useful way to describe forces that act at a distance is in terms of a field. One object sets up a disturbance or field at all points in space, and the force that acts on a second object at a particular point is its response to the first object's field at that point."

Everything is written very well, except for: "sets up a disturbance or field at all points in space." Why is the field referred to as a disturbance here? Because a disturbance typically occurs when waves are present in space, not fields, which are just hypothetical concepts to describe forces that act at a distance.

Answer 1

They’re just using more reminiscent words. A ‘field’, to a lay-person means the place where you plant crops/fruits/vegetables… this is obviously not what we mean in Physics. So, they’re trying to give first of all introduce you to Physics jargon, and second, give you a rough intuitive explanation of what a field is. The most common types are vector fields which are to be thought of as a vector at every point, and the physical things which these model are certain types of disturbances in some medium (e.g fluids, and their velocity vector fields). Of course, we don’t need a medium for these fields to make sense (e.g light, which is an electromagnetic wave, arising from the electric and magnetic fields, doesn’t need any medium), but that’s besides the point here.

Compare with the following purely abstract mathematical definition which makes zero sense to an introductory student:

A vector field on a manifold is a (smooth) section of its tangent bundle.

Or more generally:

A field refers to a section of some fiber bundle over a base manifold $M$ which is used to model spacetime.