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uncertainty principle

uncertainty principle, physical principle, enunciated by Werner Heisenberg in 1927, that places an absolute, theoretical limit on the combined accuracy of certain pairs of simultaneous, related measurements. The accuracy of a measurement is given by the uncertainty in the result; if the measurement is exact, the uncertainty is zero. According to the uncertainty principle, the mathematical product of the combined uncertainties of simultaneous measurements of position and momentum in a given direction cannot be less than Planck's constanth divided by 4π. The principle also limits the accuracies of simultaneous measurements of energy and of the time required to make the energy measurement. The value of Planck's constant is extremely small, so that the effect of the limitations imposed by the uncertainty principle are not noticeable on the large scale of ordinary measurements; however, on the scale of atoms and elementary particles the effect of the uncertainty principle is very important. Because of the uncertainties existing at this level, a picture of the submicroscopic world emerges as one of statistical probabilities rather than measurable certainties. On the large scale it is still possible to speak of causality in a framework described in terms of space and time; on the atomic scale this is not possible. Such a description would require exact measurements of such quantities as position, speed, energy, and time, and these quantities cannot be measured exactly because of the uncertainty principle. It does not limit the accuracy of single measurements, of nonsimultaneous measurements, or of simultaneous measurements of pairs of quantities other than those specifically restricted by the principle. Even so, its restrictions are sufficient to prevent scientists from being able to make absolute predictions about future states of the system being studied. The uncertainty principle has been elevated by some thinkers to the status of a philosophical principle, called the principle of indeterminacy, which has been taken by some to limit causality in general. See quantum theory.

See W. Heisenberg, The Physical Principles of the Quantum Theory (tr. 1949); D. Lindley, Uncertainty (2007).

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uncertainty principle

uncertainty principle In particle physics, principle stating that it is not possible to know both the position and the momentum of a particle at the same time, because the act of measuring would disturb the system. German physicist Werner Heisenberg established the principle.

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Uncertainty Principle

UNCERTAINTY PRINCIPLE

The uncertainty principle in quantum mechanics states that the velocity and the position of a particle cannot be measured simultaneously with complete accuracy.

After the original ideas were laid down in 1927 by W. Heisenberg, a period followed in which the concepts of quantum mechanics were critically debated. The Gedanken experiments provided the primary intellectual ammunition in these discussions between physicists who believed that quantum mechanics was a closed structure free of internal contradictions and those who did not. (See, e.g., the discussions at the Solvay Congresses of 1927 and 1930.) The final word was the famous Niels Bohr paper that included details and examples of what became known as the "Copenhagen Interpretation of Quantum Mechanics." Most physicists accept this interpretation, and modern textbooks treat it in an almost dogmatic fashion. The two important opponents of Bohr are Einstein and D. Bohm.

Philosophical Interpretations. Not all philosophers of science are agreed on the interpretation to be given to the uncertainty principle. The multiplicity of teachings can be separated into broad classes. (1) The first maintains that Heisenberg's uncertainty relations express subjective indeterminacies; i.e., they refer to man's imperfect knowledge of things, not to things themselves. (2) The second holds that they express objective indeterminacies; i.e., they refer to something that characterizes matter or reality.

Epistemological Indeterminacy. The first type of interpretation, which is epistemological in character, subdivides into a variety of teachings. Some hold that the uncertainties arise from the inability of the human mind to comprehend the microcosm, an inability that necessitates the application of the concepts of particle dynamics to the description of wave phenomena (or vice versa), with a consequent loss of clarity. Others teach that the uncertainty arises from the coarseness of the measuring apparatus, which is very large compared to the thing being measured and thus leaves the result of the measurement indeterminate. Still others hold that the Heisenberg relations are exclusively a consequence of statistical methods of measurement and are independent of the perturbations caused by any measuring instrument. Yet others argue that the uncertainties refer to "observables," but not to "hidden variables," which have precise values at any given instant.

Particularly suited to this type of interpretation is the solution proposed by H. Reichenbach, who has developed a three-valued formal logic that permits questions about the microcosm to be answered with statements that are either true, false, or undecided. Also in accord with it are the solutions adopted by many logical positivists and linguistic philosophers, who hold generally that the complimentary and uncertainty principles refer not to objects but to ways in which words and concepts are used by contemporary physicists.

Ontological Indeterminacy. Among those who hold that Heisenberg's uncertainty relations express indeterminacies that are objective, or ontological in character, some propose these as ultimately reducible, others as irreducible. Those who claim that such indeterminacies are objective but reducible maintain that they arise from some lower level motion or sub-quantum state that is yet to be identified but nonetheless exists. Those who regard the indeterminacies as irreducible ascribe them either to the operation of absolute chance at the subatomic level or to a basic indeterminacy that resides in some protomatter or substrate of which elementary particles are composed. Related to both views is that of those who see such indeterminacies as irreducible because of something "in the very nature of things" that prevents one ever from drawing a clear line of demarcation between subject and object at the subatomic level.

Philosophers in the Catholic or scholastic tradition recognize elements of truth in both the ontological and the epistemological interpretations of the uncertainty principle. In general they reject solutions that are anti-metaphysical or antirealist in character; at the same time, they are wary of attempts to extrapolate interpretations relating to the substructure of matter to the domain of ethical or religious inquiry, e.g., proposing such theories as arguments for the existence of free will or God's influence in the world. Because of traditional teachings in the philosophy of nature, they are sympathetic to ontological interpretations that root quantum indeterminacy not in absolute chance, which they hold does not exist, but in the potency of primary matter (see matter and form). Such interpretations have gained support from Heisenberg himself, who, in discussing the meaning of probability in quantum theory, states:

The probability function combines objective and subjective elements. It contains statements about possibilities or better tendencies (potentia in Aristotelian philosophy), and these statements are completely objective, they do not depend on any observer; and it contains statements about our knowledge of the system, which of course are subjective in so far as they may be different for different observers. In ideal cases the subjective element in the probability function may be practically negligible as compared with the objective one [53].

If this is true, ontological and epistemological uncertainties do not bespeak incompatible interpretations but rather alternative ways of describing objective properties of matter and man's subjective limitations in comprehending them.

See Also: indeterminism; science, philosophy of.

Bibliography: h. reichenbach, Philosophic Foundations of Quantum Mechanics (Berkeley 1944). w. heisenberg, Physics and Philosophy (New York 1958). m. a. bunge, Metascientific Queries (Springfield, Ill. 1959). e. cassirer, Determinism and Indeterminism in Modern Physics, tr. o. t. benfey (New Haven, Conn. 1956). m. born, Natural Philosophy of Cause and Chance (Oxford 1949).

[w. a. wallace/

[p. h. e. meijer]

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