science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...

, an empirical relationship or phenomenological relationship is a relationship or correlation that is supported by experiment and observation but not necessarily supported by

theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be ...

Analytical solutions without a theory

An empirical relationship is supported by confirmatory data irrespective of theoretical basis such as

first principles In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from First Cause attitudes and taught by Aristotelians, and nua ...

. Sometimes theoretical explanations for what were initially empirical relationships are found, in which case the relationships are no longer considered empirical. An example was the

Rydberg formula In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It wa ...

to predict the

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...

s of hydrogen

spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...

s. Proposed in 1876, it perfectly predicted the wavelengths of the

Lyman series In physics and chemistry, the Lyman series is a hydrogen spectral series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from ''n'' ≥ 2 to ''n'' = 1 (where ''n'' is the princip ...

, but lacked a theoretical basis until

Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922 ...

produced his

Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Syst ...

of the atom in 1925.McMullin, Ernan (1968), “What Do Physical Models Tell Us?”, in B. van Rootselaar and J. F. Staal (eds.), Logic, Methodology and Science III. Amsterdam: North Holland, 385–396. On occasion, what was thought to be an empirical factor is later deemed to be a fundamental physical constant.

Approximations

Some empirical relationships are merely approximations, often equivalent to the first few terms of the

Taylor series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...

of an analytical solution describing a phenomenon. Other relationships only hold under certain specific conditions, reducing them to special cases of more general relationship. Some approximations, in particular

phenomenological model A phenomenological model is a scientific model that describes the empirical relationship of phenomena to each other, in a way which is consistent with fundamental theory, but is not directly derived from theory. In other words, a phenomenological ...

s, may even contradict theory; they are employed because they are more mathematically tractable than some theories, and are able to yield results.

References

{{Reflist Empiricism Concepts in epistemology Epistemology of science

Analytical solutions without a theory

Approximations

See also

References