In the sciences, an experimentum crucis (English: crucial experiment or critical experiment) is an experiment capable of decisively determining whether or not a particular hypothesis or theory is superior to all other hypotheses or theories whose acceptance is currently widespread in the scientific community. In particular, such an experiment must typically be able to produce a result that rules out all other hypotheses or theories if true, thereby demonstrating that under the conditions of the experiment (i.e., under the same external circumstances and for the same "input variables" within the experiment), those hypotheses and theories are proven false but the experimenter's hypothesis is not ruled out.
For an opposite view putting into question the decisive value of the experimentum crucis in choosing one hypothesis or theory over its rival see Pierre Duhem.
Francis Bacon in his Novum Organum first described the concept of a situation in which one theory but not others would hold true, using the name instantia crucis; the phrase experimentum crucis, denoting the deliberate creation of such a situation for the purpose of testing the rival theories, was later coined by Robert Hooke and then famously used by Isaac Newton.
The production of such an experiment is considered necessary for a particular hypothesis or theory to be considered an established part of the body of scientific knowledge. It is not unusual in the history of science for theories to be developed fully before producing a critical experiment. A given theory which is in accordance with known experiment but which has not yet produced a critical experiment is typically considered worthy of exploration in order to discover such an experimental test.
In his Philosophiæ Naturalis Principia Mathematica, Isaac Newton (1687) presents a disproof of Descartes' vortex theory of the motion of the planets. In his Opticks, Newton describes an optical experimentum crucis in the First Book, Part I, Proposition II, Theorem II, Experiment 6, to prove that sunlight consists of rays that differ in their index of refraction.
A 19th-century example was the prediction by Poisson, based on Fresnel's mathematical analysis, that the wave theory of light predicted a bright spot in the center of the shadow of a perfectly circular object, a result that could not be explained by the (then current) particle theory of light. An experiment by François Arago showed the existence of this effect, now called the Arago spot, or "Poisson's bright spot", which led to the acceptance of the wave theory.
A famous example in the 20th century of an experimentum crucis was the expedition led by Arthur Eddington to Principe Island in Africa in 1919 to record the positions of stars around the Sun during a solar eclipse. The observation of star positions confirmed predictions of gravitational lensing made by Albert Einstein in the general theory of relativity published in 1915. Eddington's observations were considered to be the first solid evidence in favor of Einstein's theory.
In some cases, a proposed theory can account for existing anomalous experimental results for which no other existing theory can furnish an explanation. An example would be the ability of the quantum hypothesis, proposed by Max Planck in 1900, to account for the observed black-body spectrum, an experimental result that the existing classical Rayleigh-Jeans law could not predict. Such cases are not considered strong enough to fully establish a new theory, however, and in the case of quantum mechanics, it took the confirmation of the theory through new predictions for the theory to gain full acceptance.