Field (physics)

In physics, a field describes the spatial distribution of a physical quantity. This may be a scalar, such as the gravitational potential, or the electrostatic potential, or a vector field such as a gravitational field or the electric field. The value of the field at a particular location is in some cases referred to as the field strength.

Further areas of physical objects themselves:

• They fulfill the equations of motion, here called field equations. The dynamics of fields is treated in the field theory. Maxwell's equations, the equations of motion for the electric and magnetic field.
• As bodies have energy fields ( the field energy ), momentum and also angular momentum. The force between two bodies in empty space is explained that a field takes these sizes of a body and transfers it to the other body.

In quantum field theory, the field is the fundamental concept from which all the properties of matter and forces are developed. A field can here be excited only in defined steps, which are described as generating a corresponding number of quanta. All known matter particles consist of such field quanta of certain fields, while the forces are caused by exchange particles between them, ie field quanta of certain other fields. The individual field quanta are the fundamental elementary particles.

General

Different conceptions of the field concept

Boxes indicate on the one hand to the spatial distribution of certain physical properties: For example, the spatial distribution of the temperature of a hot plate can be described by a temperature field, or the spatial distribution of the density in one body by a mass density field. In this sense, a field is a mathematical tool that summarizes the actually pointwise defined physical properties of an extended or composed of subsystems in a system size, the field.

A field can also be a separate physical entity which may not be considered as a composite system or auxiliary mathematical quantity. The field can then just as a particle is a rigid body or other physical system carry a momentum and angular momentum, contain energy and are in excited states. For example, a beam of light energy is transported by the vacuum, as described by the Poynting vector, a ( time-dependent ) field, and is in the physical hierarchy of the entities on the same level as particles or other matter.

In this sense, for example, the electric field on the one hand simply be regarded as a spatial distribution of the electric field strength, or as an independent non- reducible system.

Dynamics of fields

In general, fields are time-dependent, ie, functions of space and time. The dynamics of a particle is described by equations of motion, is in accordance with the dynamics of fields, ie, the spatial-temporal change of the field size, described by field equations. The main difference between field equations and equations of motion of particles is that a field equation, the dynamics of infinitely many degrees of freedom describes as a field has infinitely many degrees of freedom ( the field size at each point in space is a degree of freedom and a field is generally at an infinite number of points in space defined ). The equations of motion of a particle, however, only describe the dynamics of a finite number of degrees of freedom (usually the temporal evolution of the three spatial coordinates of the particle ).

History of the field concept

The origin of the concept of the field is located in the 18th century, when the spatial distribution of certain variables was discussed in continuum mechanics and fluid mechanics. It was not considered a separate entity and the dynamics of the fields derived using the Newtonian particle mechanics from the properties of the underlying field molecules or solids. A whole new meaning given the term by the emerging field electrodynamics at the end of the 19th century, since the electromagnetic field could be explained not designed as a macroscopic state of microscopic subsystems. The electromagnetic field became a new irreducible entity. Michael Faraday and James Clerk Maxwell were still of the opinion that the electromagnetic field is just an excited state of the ether and thus led the field to movement or mechanical stresses in a form of matter, the ether, back. But the Michelson - Morley experiment contradicted the ether theory. The existence of the ether, which fill out the empty space, was henceforth discarded in physics. The observation that the electromagnetic field in a vacuum, without a carrier material, without an invisible carrier substance exists as the ether, led to regard the electric field as a separate physical system. Today, the concept of the field is against the concept of matter (at least) equally. The empty space can contain both matter fields. In quantum field theory, finally, the matter particles as field quanta, ie quantized excitations of fields are considered.

The field as a carrier of interactions

The Newtonian theory of gravitation is a long-range effect theory, since this theory does not explain how a distant body A body B feels the presence of A, so how the gravitational interaction is transported through the empty room. Furthermore, the propagation speed of the interaction of this field -free theory is unlimited. According to the theory of relativity, but there is a limit to the velocity of propagation of all the interactions and that the speed of light. Interaction theories must, in order not to violate the causality of events, be local. Using the concept of field interactions can be described locally. The body A is surrounded by the gravitational field and responsive to the changes of the field in its environment and not directly to the rescheduling of another body that produce the field. So the field is the recipient of the interaction. Field equations describe how and with what speed disturbances spread to such an interaction field, including the speed at which the displacement of A from B experiences. The field equations of gravitation, the Einstein field equations, the field equations of electromagnetism Maxwell's equations.

Classification of fields

The field concept is used in all branches of physics apply, and specific characterization of many special field terms are enforced. Here, the same field may fall under more than one of the following special field terms.

A criterion for the characterization of fields is the physical nature of the field: density field, temperature field, velocity field, gravitational field, electric field, magnetic field, ( conservative ) force field and sound field.

Another criterion is the mathematical nature of the field: scalar fields have scalars as a function of values ​​, such as the mass density or the temperature. An important scalar field is the physical potential. Vector fields have vectors as function values ​​, such as the force or the electric field strength; Tensor tensors as a function of values ​​, such as the elastic stress; Spinor fields have spinors as function values ​​, such as the current density in relativistic field description ( Dirac ) field, or fields with spinors of higher order. The name field strength is common for the field size of some vector fields.

Fields can also according to their temporal ( Un) be characterized variability: Static fields have function values ​​that are independent of time, and are thus, for example, the subject of statics, electrostatics, magnetostatics, hydrostatic or aerostatic. Stationary fields have function values ​​that are generally not independent of time though, but does not change the currently considered case time. Examples include the magnetic field around a stationary, a constant direct current -carrying conductor or a stationary flow of a liquid. Quasi- stationary fields is called, the function values ​​are indeed change with time, but so little that this change is negligible.

Fields can be classified according to their variability also local ( Un). The field size is in a homogeneous field at any location is equal, so regardless of location. This is not the case, ie inhomogeneous field.

Vector fields can be characterized according to the course of their field lines. Field lines posed by certain points in space and on other points disappear ( source and sink ) - Fields of this type are called in general source fields. Example is the electrostatic field of a positive and negative electric charge, or a gravitational field. Field lines can but as always closed loops occur in itself - Fields of this type are called in general vortex fields. The most famous example is the magnetic field. The vector field that is obtained from the gradient at each location of a potential field, called gradient field.

Pictorial representation of fields

Two-dimensional scalar fields or two-dimensional sections of higher-dimensional scalar fields can be represented by means of contour lines or the height appropriately colored points in a plane ( see top picture on the left ).

Two-dimensional vector fields can be vividly illustrated by means of field lines (see lower picture on the left ). The tangent to a field line gives the direction of the field size (vector) at the appropriate place; the spacing of the lines from one another is inversely proportional to the magnitude of the field size.