Effective theory

In science, an effective theory is a deliberately limited scientific theory applicable under specific circumstances. In practice, all theories are effective theories, with the name "effective theory" being used to signal that the limitations are built in by design.

An early example is Galileo Galilei's theory of falling bodies. Using observed values, Galileo deduced a relationship between a falling body as constant acceleration, written here in modern notation: $${\frac {d^{2}z}{dt^{2}}}=-g$$ Within the scope of objects falling on Earth, this theory works well. However, as Isaac Newton discovered in his Newton's law of universal gravitation, a more elaborate but still effective theory, has more scope at the expense of additional complications. The next layer was Albert Einstein's general relativity, with more scope but even more complications.

For example, effective field theory is a method used to describe physical theories when there is a hierarchy of scales. Effective field theories in physics can include quantum field theories in which the fields are treated as fundamental, and effective theories describing phenomena in solid-state physics. For instance, the BCS theory of superconduction treats vibrations of the solid-state lattice as a "field" (i.e. without claiming that there is really a field), with its own field quanta, known as phonons. Such "effective particles" derived from effective fields are also known as quasiparticles.

In a certain sense, quantum field theory, and any other currently known physical theory, could be described as "effective", as in being the "low energy limit" of an as-yet unknown theory of everything.

See also

• Effective mass (solid-state physics)
• Emergence
• Empirism
• Epistemology
• Heuristics
• Hypotheses non fingo
• Phenomenological model
• Phenomenology (physics)
• Scientific method
• Turing test