As best as I can understand this largely inpenetrable book, Hesse explains the basis for action (movement) between objects in the non-organic world. Most interactions between objects are understood mechanically, between one object contacting another in a cause-effect relationship. Gravity challenges this mechanical explanation as there is evident movement between two objects without contact. Beginning with Faraday, the development of field theory provides an explanation for this "action at a distance" by stating that "'matter' is everywhere continuous and that "'atoms' are highly elastic and deformable, mutually penetrable, and," quoting Faraday, "'that matter fills all space, or, at least, all space to which gravitation extends.'" In this way, Hesse appears to be saying that atoms are seamed together, creating the fabric of space, and that it is this field that creates a linkage between two bodies.
While this explanation applies to substantive (such as they are) atoms, it is less clear if Hesse includes photons as part of the field as she writes that "photons can be called 'particles' only in the sense that they are bearers of this energy...but that they have none of the other usual mechanical properties of particles." This, in turn, prompts a question about whether a field in this sense is the same thing as dark energy and dark matter that is said to be space (fill space or space itself?).
Hesse exclusively focuses on inorganic matter, but there are questions about how the field concept might apply to life. She says that fields also operate at the micro level (electricity, magnetism; radiation) and, therefore, within our bodies. Are our bodies held together and moved not just by mechanical linkage (muscles, tendons) but also by fields of interconnected atoms? Is this how we pick up "vibes" from others?
Justly considered a classic in the history and philosophy of physics. Detailed, comprehensive, and richly insightful. At the centre stands conceptualisations of action at a distance, its rivals, and what it/they entail for our understanding of what it takes to be physical. Although old, it has lost none of its relevance. If you’re interested in the history of gravitation - as I am - and its relation to what historically has been *the* “hard problem” of human intellectual inquiry - the problem of motion - then you must read this indispensable work. My recommendation would be to read this alongside Max Jammer’s, “Concepts of Force: A Study in the Foundations of Dynamics.”