MentalModel

A mental model is a simplified, analogical, "toy" description of some Phenomena, that predicts those phenomena more or less accurately, at least in certain Contexts.

The old physics joke "assume a spherical cow on a frictionless plane" points out just how simplified mental models can be and still be useful.

A Theory is a mental model that has been shared, subjected to critique and peer review, thoroughly tested, etc.

In Structure and Interpretation of Computer Programs

SICP talks a lot about models. Here's a good example:

[. . .] the substitution model for procedure application [. . .] can be taken as a model that determines the “meaning” of procedure application, insofar as the procedures in this chapter are concerned. However, there are two points that should be stressed:

• The purpose of the substitution is to help us think about procedure application, not to provide a description of how the interpreter really works. Typical interpreters do not evaluate procedure applications by manipulating the text of a procedure to substitute values for the formal parameters. [. . .]
• Over the course of this book, we will present a sequence of increasingly elaborate models of how interpreters work, culminating with a complete implementation of an interpreter and compiler [. . .]. The substitution model is only the first of these models—a way to get started thinking formally about the evaluation process. In general, when modeling phenomena in science and engineering, we begin with simplified, incomplete models. As we examine things in greater detail, these simple models become inadequate and must be replaced by more refined models. —pp. 19–20

Models Aren't Noumenal

From ZenAndTheArtOfMotorcycleMaintenance:

"The law of gravity and gravity itself did not exist before Isaac Newton. No other conclusion makes sense." "And what that means," I say before he can interrupt, "and what that means is that the law of gravity exists nowhere except in people's heads! It's a ghost!" [. . .] "Laws of nature are human inventions, like ghosts. Laws of logic, of mathematics are also human inventions, like ghosts. The whole blessed thing is a human invention, including the idea that it isn't a human invention." —pp. 41–42

I spotted this question on StackExchange: "How does an electric field apply force to charged particles". The author expresses their confusion better than I can:

Im curious as how exactly a “field” (in this case the electric field) physically applies a force to positive and negative charges within its field. What interact action takes place? Does a charge simply “touch” the field and experiences a force at the point of contact? I understand this may not be the correct terminolgy but any clarification that can help me visualize this would be greatly appreciated!

The author seems to believe that "electric fields" and "charges" are noumenal objects, which scientific investigation has discovered by sensing them directly, and that the nature of their interaction is similarly noumenal and directly observable.

All of the answers to the question approach, with varying degrees of clarity, the idea that fields and charges are not noumenal objects, but human-invented mental models. They're just mental models that help us map reality to something mathematically tractable, in order to predict certain phenomena.