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dc.contributor.authorGarretson, Joshen_US
dc.contributor.authorWiseman, Howarden_US
dc.contributor.authorPope, Damianen_US
dc.contributor.authorPegg, Daviden_US
dc.date.accessioned2017-04-24T08:47:39Z
dc.date.available2017-04-24T08:47:39Z
dc.date.issued2004en_US
dc.date.modified2009-10-08T06:27:38Z
dc.identifier.issn14644266en_US
dc.identifier.doi10.1088/1464-4266/6/6/008en_AU
dc.identifier.urihttp://hdl.handle.net/10072/5729
dc.description.abstractA which-way measurement destroys the twin-slit interference pattern. Bohr argued that this can be attributed to the Heisenberg uncertainty relation: distinguishing between two slits a distance s apart gives the particle a random momentum transfer P of order h/s. This was accepted for more than 60 years, until Scully, Englert and Walther (SEW) proposed a which-way scheme that, they claimed, entailed no momentum transfer. Storey, Tan, Collett and Walls (STCW), on the other hand, proved a theorem that, they claimed, showed that Bohr was right. This work reviews and extends a recent proposal (Wiseman 2003 Phys. Lett. A 311 285) to resolve the issue using a weak-valued probability distribution for momentum transfer, Pwv(P). We show that Pwv(P) must be nonzero for some P : |P| > h/6s. However, its moments can be identically zero, such as in the experiment proposed by SEW. This is possible because Pwv(P) is not necessarily positive definite. Nevertheless, it is measurable experimentally in a way understandable to a classical physicist. The new results in this paper include the following. We introduce a new measure of spread for Pwv(P): half the length of the unit-confidence interval. We conjecture that it is never less than h/4s, and find numerically that it is approximately h/1.59s for an idealized version of the SEW scheme with infinitely narrow slits. For this example, the moments of Pwv(P), and of the momentum distributions, are undefined unless a process of apodization is used. However, we show that by considering successively smoother initial wavefunctions, successively more moments of both Pwv(P) and the momentum distributions become defined. For this example the moments of Pwv(P) are zero, and these moments are equal to the changes in the moments of the momentum distribution. We prove that this relation also holds for schemes in which the moments of Pwv(P) are nonzero, but it holds only for the first two moments. We also compare these moments to the moments of two other momentum-transfer distributions that have previously been considered, and with the moments of 谦 - 谩 (which is defined in the Heisenberg picture). We find agreement between all of these, but again only for the first two moments. Our results reconcile the seemingly opposing views of SEW and STCW.en_US
dc.description.peerreviewedYesen_US
dc.description.publicationstatusYesen_AU
dc.format.extent196750 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglishen_US
dc.language.isoen_AU
dc.publisherInstitute of Physics Publishingen_US
dc.publisher.placeUKen_US
dc.publisher.urihttp://www.iop.org/EJ/journal/JOptBen_AU
dc.relation.ispartofpagefromS506en_US
dc.relation.ispartofpagetoS517en_US
dc.relation.ispartofjournalJournal of Optics B: Quantum and Semiclassical Opticsen_US
dc.relation.ispartofvolume6en_US
dc.subject.fieldofresearchcode240402en_US
dc.titleThe uncertainty relation in "which-way" experiments: how to observe directly the momentum transfer using weak valuesen_US
dc.typeJournal articleen_US
dc.type.descriptionC1 - Peer Reviewed (HERDC)en_US
dc.type.codeC - Journal Articlesen_US
gro.facultyGriffith Sciences, School of Natural Sciencesen_US
gro.rights.copyrightCopyright 2004 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version.en_AU
gro.date.issued2004
gro.hasfulltextFull Text


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