Concept
Field (physics)
Overview
In science, a field or field quantity is a physical quantity – represented by a scalar, vector, spinor, or tensor – that has a value for each point in space and time. An example of a scalar field is a weather map of surface temperatures, described by assigning a number to each point on the map. A map of surface winds, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field. Strain tensor, representing the deformation of matter caused by stress, is an example of a tensor field.
Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another vector field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single rank-2 tensor field.
In the modern framework of the quantum field theory, even without referring to a test particle, a field occupies space, contains energy, and its presence precludes a classical "true vacuum". This has led physicists to consider electromagnetic fields to be a physical entity, making the field concept a supporting paradigm of the edifice of modern physics. Richard Feynman said, "The fact that the electromagnetic field can possess momentum and energy makes it very real, and [...] a particle makes a field, and a field acts on another particle, and the field has such familiar properties as energy content and momentum, just as particles can have." In practice, the strength of most fields diminishes with distance, eventually becoming undetectable. For instance the strength of many relevant classical fields, such as the gravitational field in Newton's theory of gravity or the electrostatic field in classical electromagnetism, is inversely proportional to the square of the distance from the source (i.e. they follow Gauss's law).
A field has a consistent tensor rank character wherever it is defined, i.e., a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. In this theory an equivalent representation of field is a field particle, for instance a boson.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Field (physics) is discussed.
A good rice field is a bog at all seasons, and at one season a bog covered with water. It is unfit either for corn, or pasture, or vineyard, or, indeed, for any other vegetable produce that is very useful to men; and the lands which are fit for those purposes are not fit for rice.
Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations
names the idea; states what it is; opens on it
As to their Agriculture, all their Fields (where any thing is planted) whether high or low, are made into such Plots as may retain the Water on them when they please. They Plow up their Ground with one Buffalo or one Cow. Where they are to Sow Rice, they prepare the Fields very well, by clearing it of all manner of Weeds, moistening to a Pulp, and smoothing it with a Frame drawn across; on which they Sow the Rice…
Royal Society, Miscellanea Curiosa, Vol. 3
names the idea; states what it is; opens on it
Also this dependence can be conceived as a transmission. But viewing the cause which effects changes on the electron within that region, it is solely that field within the region, which field is coincident with that electron both in time and in space. This process of conceiving the actuality underlying a possibility is the uniform process by which regularity and permanence is introduced into scientific thought…
Alfred North Whitehead, The organisation of thought, educational and scientific
names the idea; states what it is; opens on it
There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space. On the other hand a part of space may very well be imagined without an electromagnetic field; thus in contrast with the gravitational field, the…
Albert Einstein, Sidelights on Relativity
names the idea; states what it is; opens on it
If γ_{μν}^{τ}’s vanish, the point moves uniformly and in a straight line; these magnitudes therefore determine the deviation from uniformity. They are the components of the gravitational field. §14. The Field-equation of Gravitation in the absence of matter. In the following, we differentiate gravitation-field from matter in the sense that everything besides the gravitation-field will be signified as matter…
Albert Einstein, The Principle of Relativity
names the idea; a chapter is titled for it
Related ideas
- Eugene Wigner
- Force
- General relativity
- Isaac Newton
- Gravitational field
- Paradigm
- Latin
- Luminiferous aether
- Function (mathematics)
- Mass
- Mathematical object
- Classical mechanics
- Maxwell's equations
- Infinity
- Velocity
- Real number
- Particle physics
- Photon
- Newton's law of universal gravitation
- Quark
- Quantum mechanics
- Quantum field theory
- Science
- Solar System
Place in the tradition
Part of Philosophy of physics.