Effective theory
In science , usually in physics , an effective theory is a theory that simplifies or summarizes a deeper, underlying theory. An effective theory allows for simpler calculations as long as the microscopic properties can be averaged.
Effective theories are often the only viable method of scientifically investigating a phenomenon. It is necessary to carry out the considerations within the limits of the effective theory; otherwise the results will be incorrect.
Examples
Newtonian mechanics
The Newtonian mechanics describes the motion of bodies and gases at speeds well below the speed of light are. Ultimately, however, it is an approximation of the special theory of relativity for small speeds.
optics
In optics , the so-called " effective medium theory " is used to calculate the optical properties of non-interacting particle systems in a matrix. For this purpose, the dielectric constants of the matrix and particle system, as well as the fill factor of the particle system, are combined into an effective dielectric function. Different special cases and demands on the particle shape , particle shape distribution etc. are taken into account by different theories such as those of DAG Bruggeman or H. Looyenga .
In the case of very small, round particles, the Mie theory provides a more precise description. It describes, among other things, the Mie scatter .
thermodynamics
The thermodynamics is an effective theory because it the movement of individual atoms and molecules neglected and considered only moderate quantities such as pressure and temperature. However, she is very successful in her description of gases.
Statistical thermodynamics is the corresponding extension of thermodynamics. With this it is possible to calculate the thermodynamic quantities like temperature and pressure, but also internal energy , entropy etc. from the system properties.
Fluid mechanics
The fluid dynamics is believed that the matter from any small particles, and therefore neglects the atomic structure of matter. Nevertheless, it is very successful, for example in the construction of aircraft .
Nuclear physics
In nuclear physics , the properties of atomic nuclei are investigated and described in nuclear models. These models work on the level of the core building blocks ( protons and neutrons ), but neglect the fact that they are made up of quarks .
Quantum field theory
In quantum field theory , divergences are avoided by introducing a cutoff . The cutoff is the maximum energy scale up to which the theory can be viewed; Particles whose mass is beyond this scale are neglected. While only the coupling constants change for the theory when a high cutoff is selected, i.e. it can be renormalized , the effective theories that are limited by the choice of a low cutoff can usually no longer be renormalized in terms of perturbation theory . So z. B. the renormalizable Glashow-Weinberg-Salam theory of the electroweak interaction for low energy into the non-renormalizable, effective Fermi theory , in which a hadron and a lepton current describe the beta decay through a vector-vector coupling .
The decays of heavy hadrons are described by the effective theory of heavy quarks (HQET for Heavy Quark Effective Theory ).
Questions of principle
The previous development of science in search of a basic theory has repeatedly replaced existing theories with new theories in which the previous phenomena can be understood by considering smaller components.
Hence, the question arises whether such a search is endless in the sense that inside every theory there is another one - or whether there is an innermost theory from which ultimately all theories can be understood (at least theoretically).
The superstring theory is currently considered a candidate for such an innermost theory.