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In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position ''x'' and momentum ''p'', can be known simultaneously. Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.〔. Annotated pre-publication proof sheet of (Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik ), March 23, 1927.〕 The formal inequality relating the standard deviation of position ''σx'' and the standard deviation of momentum ''σp'' was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928: ( is the reduced Planck constant, / ). Historically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.〔Werner Heisenberg, ''The Physical Principles of the Quantum Theory'', p. 20〕 It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, ''the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology''. It must be emphasized that ''measurement'' does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.〔 Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number–phase uncertainty relations in superconducting or quantum optics systems. Applications dependent on the uncertainty principle for their operation include extremely low noise technology such as that required in gravitational-wave interferometers. ==Introduction== (詳細はsupervene on quantum mechanical descriptions which includes Heisenberg's uncertainty relationship. However, humans do not form an intuitive understanding of this uncertainty principle in everyday life. This is because the constraint is not readily apparent on the macroscopic scales of everyday experience. So it may be helpful to demonstrate how it is integral to more easily understood physical situations. Two alternative conceptualizations of quantum physics can be examined with the goal of demonstrating the key role the uncertainty principle plays. A wave mechanics picture of the uncertainty principle provides for a more visually intuitive demonstration, and the somewhat more abstract matrix mechanics picture provides for a demonstration of the uncertainty principle that is more easily generalized to cover a multitude of physical contexts. Mathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding orthonormal bases in Hilbert space are Fourier transforms of one another (i.e., position and momentum are conjugate variables). A nonzero function and its Fourier transform cannot both be sharply localized. A similar tradeoff between the variances of Fourier conjugates arises in all systems underlain by Fourier analysis, for example in sound waves: A pure tone is a sharp spike at a single frequency, while its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave. In quantum mechanics, the two key points are that the position of the particle takes the form of a matter wave, and momentum is its Fourier conjugate, assured by the de Broglie relation , where is the wavenumber. In matrix mechanics, the mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits. An eigenstate of an observable represents the state of the wavefunction for a certain measurement value (the eigenvalue). For example, if a measurement of an observable is performed, then the system is in a particular eigenstate of that observable. However, the particular eigenstate of the observable need not be an eigenstate of another observable : If so, then it does not have a unique associated measurement for it, as the system is not in an eigenstate of that observable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Uncertainty principle」の詳細全文を読む スポンサード リンク
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