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A central concept of physical theory. A field is defined by the distribution of a physical quantity, such as temperature, mass density, or potential energy, at different points in space. In the particularly important example of force fields, such as gravitational, electrical, and magnetic fields, the field value at a point is the force which a test particle would experience if it were located at that point. The philosophical problem is whether a force field is to be thought of as purely potential, so the presence of a field merely describes the propensity of masses to move relative to each other, or whether it should be thought of in terms of the physically real modifications of a medium whose properties result in such powers. That is, are force fields purely potential, fully characterized by dispositional statements or conditionals, or are they categorical or actual? The former option seems to require faith in ungrounded dispositions, or regions of space that differ only in what happens if an object is placed there. The lawlike shape of these dispositions, apparent for example in the curved lines of force of the magnetic field, may then seem quite inexplicable. To atomists such as Newton it would represent a return to Aristotelian entelechies, or quasi-psychological affinities between things, which are responsible for their motions (see mover, unmoved). The latter option requires understanding how forces of attraction and repulsion can be ‘grounded’ in the properties of the medium.

The basic idea of a field is arguably present in Leibniz, who was certainly hostile to Newtonian atomism, although his equal hostility to action at a distance muddies the waters. It is usually credited to Boscovich and Kant, both of whom influenced the scientist Faraday, with whose work the physical notion became established. In his paper ‘On the Physical Character of the Lines of Magnetic Force’ (1852), Faraday suggests several criteria for assessing the physical reality of lines of force, such as whether they are affected by an intervening material medium, whether they take time to propagate, and how the motion depends on the nature of what is placed at the receiving end. As far as electromagnetic fields go, Faraday himself inclined to the view that the mathematical similarity between heat flow, currents, and electro-magnetic lines of force was evidence for the physical reality of the intervening medium.

Subjects: Science and Mathematics — Philosophy.

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