Uncertainty principle information

The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known.

More formally, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position, x, and momentum, p.^[1] Such paired-variables are known as complementary variables or canonically conjugate variables.

First introduced in 1927 by German physicist Werner Heisenberg,^[2]^[3]^[4]^[5] the formal inequality relating the standard deviation of position σ_x and the standard deviation of momentum σ_p was derived by Earle Hesse Kennard^[6] later that year and by Hermann Weyl^[7] in 1928:

$\sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}$

where $\hbar ={\frac {h}{2\pi }}$ is the reduced Planck constant.

The quintessentially quantum mechanical uncertainty principle comes in many forms other than position–momentum. The energy–time relationship is widely used to relate quantum state lifetime to measured energy widths but its formal derivation is fraught with confusing issues about the nature of time. The basic principle has been extended in numerous directions; it must be considered in many kinds of fundamental physical measurements.

^ Sen, D. (2014). "The Uncertainty relations in quantum mechanics" (PDF). Current Science. 107 (2): 203–218. Archived (PDF) from the original on 2019-09-24. Retrieved 2016-02-14.
^ Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
^ Werner Heisenberg (1989), Encounters with Einstein and Other Essays on People, Places and Particles, Princeton University Press, p. 53. ^{[ISBN missing]}
^ Dolling, Lisa M.; Gianelli, Arthur F.; Statile, Glenn N., eds. (2003). The Tests of Time. doi:10.1515/9781400889167. ISBN 978-1400889167.
^ Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality. 1st American ed., 2008. Chap. 10, Note 37. ^{[ISBN missing]}
^ Kennard, E. H. (1927), "Zur Quantenmechanik einfacher Bewegungstypen", Zeitschrift für Physik (in German), 44 (4–5): 326–352, Bibcode:1927ZPhy...44..326K, doi:10.1007/BF01391200, S2CID 121626384.
^ Weyl, H. (1928). Gruppentheorie und Quantenmechanik (in German). Leipzig: Hirzel.^{[page needed]}

[Sen2014-1] Sen, D. (2014). "The Uncertainty relations in quantum mechanics" (PDF). Current Science. 107 (2): 203–218. Archived (PDF) from the original on 2019-09-24. Retrieved 2016-02-14.

[:0-2] Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik

[3] Werner Heisenberg (1989), Encounters with Einstein and Other Essays on People, Places and Particles, Princeton University Press, p. 53. ^{[ISBN missing]}

[4] Dolling, Lisa M.; Gianelli, Arthur F.; Statile, Glenn N., eds. (2003). The Tests of Time. doi:10.1515/9781400889167. ISBN 978-1400889167.

[5] Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality. 1st American ed., 2008. Chap. 10, Note 37. ^{[ISBN missing]}

[Kennard-6] Kennard, E. H. (1927), "Zur Quantenmechanik einfacher Bewegungstypen", Zeitschrift für Physik (in German), 44 (4–5): 326–352, Bibcode:1927ZPhy...44..326K, doi:10.1007/BF01391200, S2CID 121626384.

[Weyl1928-7] Weyl, H. (1928). Gruppentheorie und Quantenmechanik (in German). Leipzig: Hirzel.^{[page needed]}

Uncertainty principle information

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