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49:, and theoretical and experimental developments have suggested that Heisenberg's intuitive explanation of his mathematical result might be misleading. While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument when measured at the level of an individual
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Some interpretations of quantum mechanics question whether an electron actually has a determinate position before it is disturbed by the measurement used to establish said determinate position. Under the
Copenhagen interpretation, an electron has some probability of showing up at any point in the
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universe, though the probability that it will be far from where one expects becomes very low at great distances from the neighborhood in which it is originally found. In other words, the "position" of an electron can only be stated in terms of a
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53:. The formal mathematical result remains valid, however, and the original intuitive argument has also been vindicated mathematically when the notion of disturbance is expanded to be independent of any specific state.
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under which it was constructed, thereby contributing to the development of an area of physics—namely, quantum mechanics—that redefined the terms under which the original thought experiment was conceived.
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An observer perceives an image of the particle because the light rays strike the particle and bounce back through the microscope to the observer's eye. We know from experimental evidence that when a
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520:{\displaystyle \Delta x\Delta p_{x}\approx \left({\frac {\lambda }{\sin \varepsilon }}\right)\left({\frac {h}{\lambda }}\sin \varepsilon \right)=h}
316:
175:
629:
Lee A. Rozema; et al. (6 Sep 2012). "Violation of
Heisenberg's Measurement-Disturbance Relationship by Weak Measurements".
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Entanglement : the unlikely story of how scientists, mathematicians, and philosophers proved
Einstein's spookiest theory
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photon is undetermined within the bundle of rays entering the microscope." In particular, the electron's momentum in the
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shown as blue lines. Photons that enter the microscope deviate from the vertical by an angle less than
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237:
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711:; Pekka Lahti; Richard Werner (Oct 2013). "Proof of Heisenberg's error-disturbance relation".
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of the light rays. Then, according to the laws of classical optics, the microscope can only
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of light rays leaving the microscope lens and focusing on the electron make an angle
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off it. The depiction of the wavefronts inside the microscope is unphysical due to
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Although the thought experiment was formulated as an introduction to
Heisenberg's
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361:{\displaystyle \Delta p_{x}\approx {\frac {h}{\lambda }}\sin \varepsilon .}
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879:"The Quantum Postulate and the Recent Development of Atomic Theory"
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The electron is illuminated from below by light depicted as both
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that has served as the nucleus of some commonly held ideas about
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Physics & philosophy : the revolution in modern science
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212:{\displaystyle \Delta x={\frac {\lambda }{\sin \varepsilon }}.}
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989:. Vol. II. City: Dover Publications. p. 1051-1055.
691:"Scientists cast doubt on Heisenberg's uncertainty principle"
889:(3050). Springer Science and Business Media LLC: 580–590.
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direction along a line below the microscope. Let the
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169:the position of the electron up to an accuracy of
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45:The concept was criticized by Heisenberg's mentor
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774:"Scientists prove Heisenberg's intuition correct"
590:Philosophical interpretation of classical physics
34:. In particular, it provides an argument for the
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962:. Vol. I. Dover Publications. p. 143.
93:Heisenberg supposes that an electron is like a
85:effects that produce a blurred image and hence
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791:The Physical Principles of the Quantum Theory
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16:Thought experiment establishing quantum ideas
77:and impart momentum to the electron as they
38:on the basis of the principles of classical
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560:, as can predictions of where it may move.
547:, one of the pillars of modern physics, it
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935:. New York: HarperPerennial. p. 46.
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1046:Thought experiments in quantum mechanics
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226:strikes an electron, the latter has a
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1031:Lectures on Heisenberg's Microscope
585:Interpretation of quantum mechanics
310:direction is only determined up to
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1019:History of Heisenberg's Microscope
851:. New York: Plume. p. 77-79.
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795:. Courier Dover Publications.
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743:10.1103/PhysRevLett.111.160405
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1:
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987:The World of Mathematics Set
417:{\displaystyle \Delta p_{x}}
371:Combining the relations for
134:{\displaystyle \varepsilon }
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772:Lett, Caron (17 Oct 2013).
580:Basics of quantum mechanics
563:
10:
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840:
787:Werner Heisenberg (1949).
255:{\displaystyle h/\lambda }
823:"Heisenberg's Microscope"
610:Electromagnetic radiation
549:attacks the very premises
958:Messiah, Albert (2014).
558:probability distribution
387:{\displaystyle \Delta x}
154:{\displaystyle \lambda }
713:Physical Review Letters
141:with the electron. Let
20:Heisenberg's microscope
985:Newman, James (2003).
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895:1928Natur.121..580B
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960:Quantum Mechanics
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802:978-0-486-60113-7
595:Schrödinger's cat
575:Quantum mechanics
570:Atom localization
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303:{\displaystyle x}
284:Planck's constant
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110:{\displaystyle x}
67:photons and waves
32:quantum mechanics
28:Werner Heisenberg
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89:in position.
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26:proposed by
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87:uncertainty
83:diffraction
1040:Categories
709:Paul Busch
616:References
163:wavelength
71:wavefronts
47:Niels Bohr
1005:691512261
978:874097814
951:135128032
913:0028-0836
726:1306.1565
644:1208.0034
504:ε
501:
493:λ
473:ε
470:
463:λ
454:≈
441:Δ
435:Δ
402:Δ
379:Δ
353:ε
350:
342:λ
334:≈
321:Δ
288:scattered
250:λ
201:ε
198:
191:λ
180:Δ
149:λ
129:ε
1022:Archived
931:(2007).
877:(1928).
875:Bohr, N.
867:53378914
759:24507489
751:24182239
677:37576344
669:23005268
564:See also
262:, where
232:momentum
75:ε/2
921:4097746
891:Bibcode
841:Sources
731:Bibcode
649:Bibcode
167:resolve
161:be the
79:scatter
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224:photon
40:optics
917:S2CID
828:1 Sep
755:S2CID
721:arXiv
673:S2CID
639:arXiv
230:with
51:state
22:is a
1001:OCLC
991:ISBN
974:OCLC
964:ISBN
947:OCLC
937:ISBN
909:ISSN
863:OCLC
853:ISBN
830:2016
797:ISBN
747:PMID
665:PMID
394:and
119:cone
899:doi
887:121
739:doi
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467:sin
347:sin
282:is
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