field theory a theory that proceeds by assigning values of physical quantities to the points of space, or of space-time, and then lays down laws relating these values. For example, a field theory might suppose a value for matter density, or a temperature for each space-time point, and then relate these values, usually in terms of differential equations. In these examples there is at least the tacit assumption of a physical substance that fills the relevant region of space-time. But no such assumption need be made. For instance, in Maxwell’s theory of the electromagnetic field, each point of space-time carries a value for an electric and a magnetic field, and these values are then governed by Maxwell’s equations. In general relativity, the geometry (e.g., the curvature) of space-time is itself treated as a field, with lawlike connections with the distribution of energy and matter.
Formulation in terms of a field theory resolves the problem of action at a distance that so exercised Newton and his contemporaries. We often take causal connection to require spatial contiguity. That is, for one entity to act causally on another, the two entities need to be contiguous. But in Newton’s description gravitational attraction acts across spatial distances. Similarly, in electrostatics the mutual repulsion of electric charges is described as acting across spatial distances. In the times of both Newton and Maxwell numerous efforts to understand such action at a distance in terms of some space-filling mediating substance produced no viable theory. Field theories resolve the perplexity. By attributing values of physical quantities directly to the space-time points one can describe gravitation, electrical and magnetic forces, and other interactions without action at a distance or any intervening physical medium. One describes the values of physical quantities, attributed directly to the space-time points, as influencing only the values at immediately neighboring points. In this way the influences propagate through space-time, rather than act instantaneously across distances or through a medium.
Of course there is a metaphysical price: on such a description the space-time points themselves take on the role of a kind of dematerialized ether. Indeed, some have argued that the pervasive role of field theory in contemporary physics and the need for space-time points for a field-theoretic description constitute a strong argument for the existence of the space-time points. This conclusion contradicts ‘relationalism,’ which claims that there are only spatiotemporal relations, but no space-time points or regions thought of as particulars.
Quantum field theory appears to take on a particularly abstract form of field theory, since it associates a quantum mechanical operator with each space-time point. However, since operators correspond to physical magnitudes rather than to values of such magnitudes, it is better to think of the field-theoretic aspect of quantum field theory in terms of the quantum mechanical amplitudes that it also associates with the space-time points. See also EINSTEIN , NEWTON , PHILOSOPHY OF SCIENCE , QUANTUM MECHANICS , SPACE – TIM. P.Te.