In a gravitational field, massive objects such as planets and stars move in directions and with speeds pre-scribed by Newton’s law. In an electromagnetic field, electric charges move similarly according to Maxwell’s laws. In the various gauge laws of quantum theory, particles move in accordance with symmetry laws. However, we don’t know in what form these forces exist in the fields in the absence of the masses, charges, or particles to be moved.

For example, to study a magnetic field, we can use iron filings to indicate the strengths and directions (vectors) of the magnetic forces. But without the presence of the filings, we know nothing. And what exactly do we mean by the “density” of the magnetic lines of forces, or “squeezing” or “bending” them, or “excluding” them from some substances? The lines of force are purely imaginary, the image of iron filings abstractly generalized from a physical observation. How many we draw per cubic centimeter is purely arbitrary, and they are not precisely located where we arbitrarily draw them. So how can these immaterial lines be squeezed, bent, or excluded?

Forces and fields were introduced into mechanistic materialist physics in order to explain observed phenomena in mechanics and electromagnetism, and the usage then expanded to other observations (quantum theory). These concepts were needed for theoretical explanations of observed phenomena, but their introduction profoundly undermined the materialistic basis of the sciences in which they were used.

Newton had especial philosophical problems with “action at a distance” in gravitational attraction, and this also affected Maxwell’s theory, even though the distances involved there were smaller. Originally, in mechanics, a force was defined as a pull or a push, but that required that the bodies in question had to be in direct contact. How can a push or a pull be transmitted through empty space?

At first it was proposed that space is not empty, but is filled with “ether” which facilitates the transmission of forces. However, the Michelson-Morley experiment (which gave rise to the special theory of relativity) proved that there is no ether. After that, no new proposal for explaining action at a distance was made; people just accepted the notion that it exists, and went on from there.

All that can be said is the following: A field is a configuration of forces, such that the forces would move particles or charges if the latter were present. That is, forces and fields represent the tendency or ability to move matter. This is usually identified with energy, also defined as the ability to move matter. So a field stores energy; but in what form? We can say it is potential (not kinetic) energy, that becomes manifest (translated into kinetic energy) when the object it can act upon is present. That is like the potential energy of a pendulum at the extreme end of its swing, just before it starts back, transforming its potential energy to kinetic energy.

That comparison helps somewhat; it is still a metaphor in terms of something material (the pendulum). However, in the case of a force field, what exactly corresponds to the pendulum at the end of its swing? Nothing material seems to be there; only the tendency to move mass or charge.

If force fields are not material in the usual sense, could they be mental? That is pushing it too far; there may be such things as mental or psychic fields, but gravitational and electromagnetic fields are purely physical, though not material. Could they be phenomena where matter and mind meet – a kind of a bridge between two essences? Or in terms of the three spheres of Roger Penrose,* could fields (with their mathematical description) represent the Platonic sphere abutting both the material and the mental sphere? But perhaps there is a simpler explanation.

Einstein showed, in his theory of general relativity, that gravitational forces are equivalent to distortion (curvature) of space. It certainly could be the case that electromagnetic forces (as well as nuclear weak and strong forces) could also distort space, the latter on a much more local tiny scale. Then we can picture the particles and charges as simply sliding down the geodesic lines. The “particles” can be as large as planets or stars, or as small as electrons. The “charges” can be electric charges or “colour” charges in quantum chromodynamics.

However, probably such a general explanation will have to await the unification of all the four forces, the much desired and hotly pursued “theory of everything”.

• See my essay Abstract Structures